Numerical Simulation of Aerodynamic Noise Radiated form Vertical Axis Wind Turbines Akiyoshi Iida, Akisato Mizuno and Keiko Fukudome Department of Mechanical Engineering Kogakuin University
[email protected],
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Abstract Vertical Axis Wind Turbines (hereafter VAWT) are one of the useful renewable energy systems. They have several advantages in comparison with the conventional, propeller-typed, horizontal axis wind turbines. VAWTs operate independently of the wind direction. Moreover, maximum power coefficient can be obtained at lower tip-speed ratio compared to the conventional wind turbines. Flow induced noise is therefore smaller than that of the conventional ones. In this paper, we attempt to simulate an unsteady flow filed and aerodynamic noise radiated from VAWT by using the discrete vortex method and Ffowcs Williams-Hawkings equation. The result shows that the power coefficient is almost the same as the conventional typed wind turbines. Moreover, the predicted noise level of the developed VAWT is about 70dB, which is 10 dB lower than that of the horizontal axis wind turbine. We also attempted to estimate noise spectrum by using three dimensional vortex methods. However, the applied vortex methods can not simulate turbulent eddy motions such as the combination process and vortex break down process. Aerodynamic noise simulation by using discrete vortex methods is therefore limited to overall noise level estimation. However, vortex methods are useful to estimate aerodynamic noise from VAWT with smallscale computers.
In this paper, we attempt to simulate an unsteady flow filed and aerodynamic noise radiated from VAWT by using the discrete vortex method. Aerodynamic noise from moving surface, such as fan blades or turbines, can be solved by using the Ffowcs Williams-Hawkings equation [1]. According to this equation, aerodynamic sound source of fan blades can be divided into the dipole source (surface pressure fluctuation) and the moving source (moving boundary). In order to predict aerodynamic noise from fan blades, simulation of the instantaneous surface pressure fluctuation and relative Mach number are necessary. LES with overset mesh is one of the most effective methods to solve the above simulation. However, LES requires much computational resources and long computational time. In order to estimate the performance and aerodynamic noise of wind turbines with small-scale computers, we should consider to develop an unsteady flow simulation with mesh less and simple algorithm. Therefore, we attempted to predict aerodynamic noise by using discrete vortex methods. The numerical results show the aerodynamic performance of VAWT is almost same as the HAWT ones, and noise is smaller than that of the HAWT. It reveals that the VAWT is useful candidates of low-noise wind turbines.
1. Introduction Darrieus turbine is well known vertical axis wind turbines with beautiful and unique curved blades, which removed centrifugal force on the blades. Fig.1 shows straight winged VAWT, which is also known as Giromill. These types of VAWT have several advantages in comparison with the conventional propeller-typed wind turbines. For example, the conventional wind turbines have to be set into the wind direction to operate at maximum efficiency point; however, VAWTs operate independently of the wind direction. Moreover, maximum power coefficient can be obtained at lower tip-speed ratio compared to the conventional wind turbines. Flow induced noise is therefore smaller than that of the conventional ones.
Figure 1: Vertical axis wind turbine with straight airfoils
2. Numerical Methods 2.1. Vortex Methods An aerodynamic difference between VAWT and horizontal axis wind turbine (HAWT) is the appearance of unsteady flow phenomena. During a revolution of the rotor of VAWTs in a steady wind stream, the flow direction and velocity relative to the rotor blade vary in a cyclic way. In the case of VAWT, the angle of attack is over 20 degree even at effective operation point. The angle of attack becomes about 180 degrees at off design point. The strong interaction between the separated boundary layer and moving airfoils observed during the rotor rotation. In order to solve this complicated turbulent flow field around VAWT, the large eddy simulation (LES) with overset mesh [2] is one of the most suitable methods for the flow around the moving boundaries. However, LES require much computational resources and long computational time [3]. In order to develop the renewable energy systems, such as the wind turbines, development cost and time is one of the most important factors. Therefore, LES are used only to understand the flow structures and validate for other simulations. In order to estimate the performance and aerodynamic noise of wind turbines with small-scale computers, we should consider to develop an unsteady flow simulation with mesh less and simple algorithm. Vortex methods are based on the discretization of the vorticity field and Lagrangian description of the governing equations. It has advantages such as the use of computational elements only in cases in which the velocity field is nonzero. Therefore, vortex method is initially conceived as a tool to simulate unsteady flow fields and it is also useful for the simulation of moving airfoil such as the wind turbines, because of it has meshless algorithm. We therefore attempted to predict flow field around the VAWT by using the vortex method. The instantaneous flow around an airfoil with large separated regions is not two dimensional. However, three dimensional vortex methods require much computational resources. The time averaged flow field of VAWT with straight airfoils is closer to twodimensional than that of the conventional HAWT. Then, we attempt to simulate flow around a VAWT with two dimensional vortex methods. The governing equations of viscous and incompressible flows have been solved by the vorticity transport equation.
∂ω + (u ⋅ grad )ω = (ω ⋅ grad )u − (u ⋅ grad )u + ν∇ 2ω (1) ∂t where u and ω=rotu denote velocity and vorticity vector, respectively. The vorticity field ω is modeled by using a large number of discrete vorticity elements. Flow fields can be written by using the Biot-Savart law as follows;
∫ 1 − α∫
u( r ) =
1 α
V
ω×ζ dV ζβ
(2)
( u ⋅ n ) ζ ( n × u) × ζ , + dS ζβ ζβ S 1+ S 2
where α=2π，β=2 for two-dimensional flow. no denotes the normal unit vector at a point on a boundary surface S. ζ denotes distance between the vorticity elements. In equation (2), the first term of right hand side denotes induced velocity of vorticities interactions, and the second term of the right hand side denotes normal and tangential velocity component on the boundary surface. To simulate the viscous diffusion, we utilize the core spreading method [4]. Vorticity element is modeled by small blob that carries constant circulation. The core radius of vorticity blob is expanded by the diffusion process. After time step ∆t, the core radius can be written as,
ε(t + ∆t ) = εo 2 + c 2ν∆t .
(3)
where c=2.242. Fig. 2 shows shed vortex system of rotating blades of VAWT. During the rotor blades rotation, new vorticity blobs shed from the rotor blades in order to keep the total circulation [5].
Γnew = Γi '−Γi
(4)
Where Γi is the circulation of the previous time step, Γi’ is the circulation of the current time step. Γnew is resulting circulation to keep total circulation. Therefore, the instantaneous circulation and its core radius are estimated from eq.(3) and (4). (−dΓ/dθ･∆θ)2 Γ2
Γ1 θ Ω
(−dΓ/dθ･∆θ)1
Vortex sheet shed from rotating blade Figure 2: Shed vortex system of rotating blade of VAWT in a steady stream Finally, the intensity of the i-th vorticity blob can be written as follows;
ω( R ) =
R 2 Γi exp − πεi εi
(5)
According to Eq.(5) , the intensity of the vorticity depends on the circulation of the vortex blobs and its core radius. On the other hand, the circulations are
2.2. Aerodynamic Noise Simulation
Aerodynamic noise radiated from the rotor blades can be solved by using the Ffowcs Williams-Hawkings equation [1]: pa =
1 4πa
∂
nip( y, t ) ∂Mr dy ∂t r
∫ r (1 − M ) ∂t n p( y, t)dy + 1 − M ri
2
i
r 2
S
(6) where a denotes the speed of sound, Mr the relative Mach number of the moving surface, p the surface pressure, Pa the far field sound pressure, r the distance between the measurement point and sound source. The tip-speed ratio of VAWT is not so high, and then the relative Mach number is small. Moreover, the chord length of the rotor blades is smaller than that of the wavelength of the resulting aerodynamic sound. Therefore, the second term and relative Mach number effect are negligibly small at low speed wind turbines.
3.1. Aerodynamic Performance
According to the Betz limit, the maximum power coefficient of the VAWT can be obtained at induced factor α = u/U=1/3. The relative velocity vectors (ux-Uref, uy) of the VAWT at tip speed ratio 3.5 is shown in Fig 3. The reference velocity of Uref equals 1/3U which correspond to the velocity of effective power coefficient of the wind turbines. When the velocity vectors are almost zero in Fig.3, it means that the velocity is almost the same as the effective velocity.
6
λ=3.5
Y [m]
2 0 -2 -4 -6
-4
0
4
8
12
0.6
Momentum Theory
0.5
Calculated by Aerodynamic Force
0.4 0.3 0.2 0.1
λ=3.5, U=12 m/s Number of Blades: 3
0 0
1
2
3
4
5
6
Tip-speed ratio
Figure 4: Power coefficient of VAWT by aerodynamic forces by the momentum theory
●Calculated ■Calculated
3.2. Aerodynamic Noise form a VAWT
3. Numerical Results
4
Fig 4 shows the power coefficient of VAWT with three airfoils. The maximum power coefficient was obtained at λ = 3.5. The power coefficient was almost 0 at λ = 0.5 and up to about 0.4 at effective tip-speed ratio. After that, the power coefficient rapidly decreased and almost 0 at λ = 5.5. At the low tip-speed ratio, angle of attack was over 20 degree at every rotating position. The flow separation was occurred. As a result, the aerodynamic lift was small but aerodynamic drag was large.
Power Coefficient
related with aerodynamic lifting force. Then, the intensity of the vorticity can be calculated by using the aerodynamic lifting force of the airfoil. Wind tunnel experiments were therefore carried out with a single airfoil (NACA0012) at angle of attack from 0 to 180 degrees as a database for vorticity generation model.
16
20
X [m]
Figure 3: Velocity field as an observer moving downstream at effective velocity of Uref =1/3U.
The aerodynamic noise is estimated at 5 m distance from the rotor axis. Using the compact body and low-Mach number assumptions, sound refraction and reflection are not considered. Retard time is also negligibly small in this simulation. Since the relative Mach number of Mr equal to 0.12, the dipole sound dominates the aerodynamic noise radiated from low-speed vertical axis wind turbines. When the moving source term dominates the whole aerodynamic noise, the power law may indicate fifth power of the velocity. Therefore, in this case, moving source term is negligibly small. Aerodynamic noise is therefore increases to the sixth power of the tip-speed as shown in Fig. 5. Simulation is conducted under the constant inlet velocity of U. Predicted noise pressure levels are proportional to the sixth power of the tip-speed velocity. An unsteady vorticity motion generates large aerodynamic noise, and then the separated flow at low tip-speed ratio generates large aerodynamic noise. At high tip-speed ratio (λ
