- Email: [email protected]
Numerical investigations on control strategies of wake deviation for large wind turbines in an offshore wind farm
Ocean Engineering 173 (2019) 794–801
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Numerical investigations on control strategies of wake deviation for large wind turbines in an offshore wind farm
T
Yuanbo Wanga, Weipao Miaoa,b, Qinwei Dinga,c, Chun Lia,∗, Bin Xianga a
School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai, 20093, China Department of Engineering Industrial, University of Padua, Padua, 35131, Italy c School of Engineering, University of Plymouth, Plymouth, PL4 8AA, UK b
A R T I C LE I N FO
A B S T R A C T
Keywords: Wind turbine Wake deviation Yaw Tilt Total output power Offshore wind farm
The OpenFOAM package incorporated with actuator line method (ALM) is employed to calculate the aerodynamic characteristics of large wind turbines in an offshore wind farm. In order to mitigate the wake effect of upstream wind turbines and conduct the overall optimization of output power for the offshore wind farm, wake deviation simulations of nine yaw angles and fifteen tilt angles are carried out. Taking total output power of the offshore wind farm as the reference point and combining fluid field profiles of cross-sections in all simulations, we investigate the flow mechanism of wake's influence on the downstream turbines with different control strategies. The results show that, although the output power of the upstream wind turbine may decreases mildly, changing the wake direction with different control methods can significantly increase the total output power of the whole wind farm due to the substantial enhancement of the downstream wind turbine. Both control strategies of wake deviation can globally optimize the offshore wind farm and each has an optimal angle, while the yaw control strategy has better results and with regard to the tilt control strategy, the plus tilt angle is comparatively better than the minus angle.
1. Introduction For centuries, increasing demand for energy has chiefly depended on fossil fuels, which leads to unintended global consequences, especially in air pollution and climate change (Elginoz and Bas, 2017). Accordingly, various technologies of renewable energy have been developed to replace fossil fuels. Among them, wind power appears to be a prominent and promising alternative. Up to now, wind energy technology has been exploited on a wide commercial scale, establishing itself as a mature approach of renewable energy generation (Karimi et al., 2017). With the decrease of available onshore wind farm resources, strong consistent and weak turbulent offshore winds have become a hot research topic among scientific staff around the word in recent years (Kang et al., 2017). Furthermore, compared with onshore wind farms, offshore wind farms have some notable advantages, such as higher energy production, less wind shear, and lower environmental impact (noise, visual pollution and so on) (Hou et al., 2017). Consequently, the fact that offshore wind power will be the main field of future utilization of wind energy has been widely acknowledged in both academic and the industrial circles (Chen et al., 2018; Yang et al., 2018). In fact, the offshore wind power capacity has been rising rapidly
∗
year by year, as illustrated by the annual cumulative capacity (2011–2017) of the offshore wind turbine in Fig. 1 (GWEC, 2018). Customarily, tens or even hundreds of wind turbines would be arranged in one offshore wind farm, for the purpose of maximal use of wind energy as well as reduction of construction costs (Shakoor et al., 2016; Puneet et al., 2017). However, this pattern of the offshore wind farm (as well as the onshore wind farm) has an inherent phenomenon that the velocity of the wake from the upstream wind turbine will experience a deficit and its turbulence turns intense, as shown in Fig. 2 (NREL, 2016; Tian et al., 2018). In turn, the wind turbine in the downstream wind farm, located within and suffered from such wakes, reduce its inflow quality. As a result, the output power of downstream wind turbine turns to be less. Overall, wind energy and offshore water area resources are actually wasted. Therefore, it is of vital importance to study the offshore wind farm, especially the valid wake control strategies, and then to apply the optimal strategy to achieve the aim of increasing total output power of the offshore wind farm. At present, there are two main methods can that are used to conduct the wake control. The first is to alter the axial induction factor of wind turbine rotor by changing the pitch angle to alleviate the wake velocity deficit. The second way is to adopt the wake
Corresponding author. E-mail address: [email protected] (C. Li).
https://doi.org/10.1016/j.oceaneng.2019.01.042 Received 16 August 2018; Received in revised form 29 December 2018; Accepted 16 January 2019 0029-8018/ © 2019 Elsevier Ltd. All rights reserved.
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
Fig. 1. The annual global cumulative offshore wind power capacity.
Fig. 4. Schematic representation of the NREL 5 MW wind turbine.
of wind farm output power. Nevertheless, the study of Miao et al. (2017) indicated that the total output power of two tandem wind turbines in a wind farm shown a gratifying discrepancy between different yaw directions of the upstream wind turbine, as illustrated in Fig. 3. For the aforementioned reasons, we propose employing the control strategy of wake deviation to redirect the wake of upstream wind turbine in an offshore wind farm. Subsequently, a mainstream wind turbine type and an appropriate research approach need to be determined to conduct wake deviation realistically in an offshore wind farm. We based our study on a 5 MW horizontal axis wind turbine designed by the National Renewable Energy Laboratory (NREL) (See the schematic of the turbine in Fig. 4). Although the NREL 5 MW wind turbine doesn't reach the largest scale level among existing wind turbines, at least it is unrealistic to conduct aerodynamic experiments in a wind tunnel. Moreover, due to the requirement of precision, time restriction and computational cost, there are few aerodynamically numerical studies on the whole wind turbine for the 5 MW and higher at present. As fat as numerical studies are concerned, there are mainly three conventional approaches, each having its own merits and demerits, as seen in Table 1. Bangga et al. (2018) combined the pure blade element momentum (BEM) with a stall delay model for a wind turbine operating under pitch fault circumstance, and the accuracy of the result was assessed by comparing the results of computational fluid dynamics (CFD) simulations data. However, Bangga et al. (2018) couldn't calculate the flow field and wind turbine wake, although their approach could predict the aerodynamic characteristics of a single wind turbine quickly. Meghlaoui et al. (2017) took into account both the tangential and longitudinal vorticity of the vortex system formed behind the rotor based on vortex wake method (VWM). They found that the development of the near wake of a horizontal axis wind turbine under different inflow speeds showed a good agreement between the calculation and experience. However, the rotor diameter they used is only 0.54 m. In contrast, the rotor diameter of the 5 MW wind turbine is 126 m and the flow field spans five size scales from macroscopic to microcosmic. VWM performs with a low precision when it is used to predict the small vortex in a large scale domain. Miao et al. (2017) used commercial CFD software STAR-CCM + to simulate the wind farm arranged with two intandem wind turbines. Their results showed that, when the upstream wind turbine applied a positive yaw angle, the wind farm's total power increased. However, according to Miao's work, in order to capture the boundary layer flows around three long wind turbine blades, massive complex mesh need to be imposed. This would cost too much time and it is computationally too expensive to conduct numerical simulation. We find that the ALM approach proposed by Sorensen and Shen (2002) can redress the above problems. It
Fig. 2. Sketch of the wake in a wind farm.
Fig. 3. Total output power of two turbines varies with yaw angle.
redirection control strategy to make the wake after upstream wind farm deviate from rotor center of the downstream wind turbine. In this way, part of or the entire downstream wind turbine rotor could avoid interacting with the wake, thus eventually improving energy capturing of the overall offshore wind farm. In general, the second method mainly consists of yaw and tilt control strategy. As for the first method, Fleming et al. (2015) used individual pitch control (IPC) to change the rotor power efficiency of the upstream wind turbine, with an aim to weaken the wake velocity defect, and the results showed that total output power of the whole wind farm increased slightly, but the blade root moment increased exponentially. Gebraad et al. (2015) used the SOWFA, a high-fidelity computational simulation software for wind farm, to carry out a numerical calculation of adjusting the pitch and torque, but the results were not satisfactory for the global optimization 795
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
Table 1 Three main traditional numerical approaches. Approaches Features
BEM
VWM
CFD
Advantages Disadvantages
timesaving incompetent in wake and flow fields
timesaving and competent in wake incompetent in small vortex in some cases
precise cost much time and computing resources
(a)
(b)
Fig. 5. Sketch of the distribution of body forces: (a) plane of the wind turbine rotor; (b) section plane of the ALM.
extra model combined with tabulated two-dimensional airfoil characteristics. ALM accesses the information of flow fields at each CFD time step and meanwhile calculates the aerodynamic characteristics of blades by the following equations.
is a fully three-dimensional and unsteady aerodynamic model for studying the flow field around the wind turbine. However, it has received little attention and application in the study of total output power of a large offshore wind farm. In our study, based on the ALM involved in the OpenFOAM package, we simulated 24 operation conditions of wake redirection, including 9 yaw angles and 15 tilt angles. Then, we analyzed the impact of wake control strategies on aerodynamic characteristics of wind turbines, and in turn on the total output power of offshore wind farm. The characteristics of wind turbine wakes at different control strategies are studied in detail by researching the variables of the flow field; meanwhile the influence of wake on the downstream turbine is also discussed. The finding of this work will provide significant instructions for operating offshore wind farms.
Fτ =
1 ρW 2⋅c⋅Cτ⋅τ 2
(3)
Fn =
1 ρW 2⋅c⋅Cn⋅n 2
(4)
Fs
(5)
= Fτ + Fn
Where.
W = relative velocity of the local airfoil c = local chord of the airfoil Cτ = coefficient of the tangential force τ = tangential unit vector Cn = coefficient of the normal force n = normal unit vector Fτ , Fn and F s = tangential, normal and resultant forces of the unit length blade
2. Methodology of ALM In terms of time and computational cost, compared with the conventional CFD method, ALM has a great advantage. ALM can produce preferable results at equivalent precision as the traditional CFD method does, but with less computing resources and time. Therefore, ALM is especially suitable for the simulation of three-dimensional flow fields for offshore wind farms. The basis of the ALM is the incompressible Navier-Stokes (NS) equations.
Automatically, the body force of fluid flow given by blades can be represented as the following: (6)
F f = −F s
DV 1 = − ∇P + ν∇2 V + f Dt ρ
(1)
∇⋅V = 0
(2)
In the end, body force is distributed radially along lines representing the blades via numerically smearing, as shown in Fig. 5. The body force needs to be distributed within a certain scope around the lines (blades) in order to avoid singular behavior. Otherwise, the CFD simulation may not converge if the area of body force distribution is smaller; whereas if bigger, vortexes on tip and root of blades would be weakened excessively (Wimshurst and Willden, 2016). To ensure the body force smear smoothly, a three-dimensional Gaussian manner like equation (7) is adopted.
Where t and ρ are the time and density respectively, and V is the velocity vector. P represents the stresses tensor. ν is the kinematic viscosity. And the source term f denotes the body force, which represents the load on the flow field imposed by rotating blades. Based on the Newton's third law, the body force can be attained using the force applied on blades by flow field. Since there are no solid walls of blades in the ALM, the force acted on blades needs to be calculated via an extra model, which can achieve the equivalent effect of real blades with solid walls. In this paper, we adopt the BEM as the
f (r ) =
796
1 3 ε 3π 2
r 2
e−( ε )
(7)
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
Table 2 Main specifications of NREL 5 MW wind turbine. Parameters
Values
Unit
Rated power Rated wind speed Rated rotor speed Rotor diameter Blade number Shaft tilt Rotor cone Hub diameter Hub height
5.0 11.4 12.1 126.0 3 5.0 2.5 3 90.0
MW m·s-1 rpm m m ° ° m m
3. Computational implementation 3.1. Wind turbine
Where r represents the distance between the body force center on blade and the distributed point in fluid domain, and ε is the smearing factor that controls the gradient of body force distributing. Troldborg (2008) points out that the distribution of body force has a significant influence on the results of the simulations. And in three-dimensional distribution of Gauss for ALM, the equation ε = 2Δs should be met if the effect of ALM wants to be extremely close to the real wind turbine situation, while Δs is the distance of points on the actuator line. Compared with what would be needed for simulating the actual geometry of the blades, the advantage of representing the blades by airfoil data, as it is done in the actuator line model, is that much fewer grid points are needed to capture the influence of the blades. Therefore, the ALM provides a detailed study of the dynamics of different wake structures using a reasonably number of grid nodes. Furthermore, the model benefits from being applicable with simple structured grids and consequently issues connected to grid generation do not occur. On the other hand, a drawback of the method is its reliance on tabulated airfoil characteristics. However, as the main purpose of the present paper is to study fundamental wake effects, it is of minor importance to capture the dynamic stall or other flow regimes on the blades exactly. The ALM technic described above is implemented in the OpenFOAM package, which is an open source CFD software developed with objectoriented C++. It has the benefit of being free and, therefore, essentially provides unlimited licenses. This means its source codes are available, which helps users know exactly how codes function and allows modification and expansion that are necessary for new code development and research on this fundamental level. And it should be pointed that the version of OpenFOAM 3.0.1 is employed in this paper. We construct a new solver NewTurbinepisoFoam based on the built-in solver pisoFoam in OpenFOAM 3.0.1. It is based on the Pressure Implicit Split Operator (PISO) method that is more efficient and accurate compared to the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) method. The New solver NewTurbinepisoFoam is intended for the numerical simulation of horizontal axis wind turbine based on the ALM. Compared with the pisoFoam, NewTurbinepisoFoam constructs a C++ class turbines, which can function a series of operations, such as defining the array of the body force, solving the body force, distributing the body force and so on. Accordingly, a wind turbine can be added expediently in offshore wind farm just through setting the locations of coordinate values of the wind turbine. The piece of code below this paragraph is a part of source codes of the ALM solver implementation, and properly speaking, it is the moment predictor step equation from the include file UEq.H in NewTurbinepisoFoam. Finally, the equation is evaluated using built-in class fvVectorMatrix that discretizes and distributes the operators specified within first-order curled brackets.
The computational object employed in the present work is a 5 MW rating wind turbine designed by the NREL affiliated to the U.S. Department of Energy. NERL 5 MW wind turbine generally refers to the publicly available information of the Multibrid M5000 and REpower 5M prototype wind turbines. As detailed information on those two machines is not available, NERL 5 MW wind turbine also refers to the publicly available properties from the conceptual models used in the WindPACT, RECOFF and DOWEC projects (NREL, 2009). The main specifications of NERL 5 MW wind turbine are illustrated in Table 2. 3.2. Offshore wind farm configuration In order to avoid tunnel blockage effect in computational simulation, we created a larger numerical offshore wind farm with a flow domain of 20D in length, 6D in width and 6D in height (D represents the wind turbine rotor diameter). Two tandem wind turbines substituted by WT1 and WT2 respectively, were located in the offshore wind farm, and the two wind turbines was set at a distance of 7D. With regard to the reasons for the choice of 7D, first of all, turbine performance at separation distances from 3D to 7D was examined and it was observed that the performance of downstream wind turbine decreased notably when the distance was less than 6D (Miao et al., 2016). In addition, the inter-turbine distance in a wind farm needs to be estimated carefully to balance the power output efficiency and construction costs. For example, due to some constraints such as the cost of electrical connections or the availability of land surface, an oversized separation is inappropriate (Son et al., 2014). Besides, there is 3D from WT1 to the inlet of the wind farm, and WT2 has been placed sufficiently far away from the outlet, 10D, to eliminate the effect on the flow of wake. The flow domain and wind turbines are illustrated in Fig. 6. 3.3. Control strategies of wake deviation We implemented control strategies by executing changes of yaw and
Fig. 6. The flow domain and its configure. 797
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
(a)
(b) Fig. 7. Control strategies of wake deviation: (a) yaw; (b) tilt.
tilt angles for the upstream WT1, and in this way the wake of WT1 would deviate from the rotor center of the downstream WT2. For the purpose of better comparison, we investigated 24 operation conditions associated with control strategies that consisted of 9 yaw angles and 15 tilt angles, while the range of yaw angles were from 230° to 310°with the step length of 10°and tile angles were from −35°to 35°with the step length of 5°. Fig. 7 is the sketch of the control strategies of wake deviation, and the Ye direction is along the offshore wind farm's width that is perpendicular to the plane determined by X and Z axis. Moreover, in order to avoid the accident of blade-tower collision, it should be noted that the tilt angles between 0° and 35°are intended for the type of downwind wind turbine.
standard atmospheric pressure. Two lateral sides were set to periodic boundary conditions, which meant when a flow variable appears on the unit cell of one side, it would simultaneously re-appear on the opposite side with the same value. The reason why the lateral sides used the periodic boundary was mainly that, in practice, there were flow domains at both sides of the offshore wind farm and they were the same. Besides, the upper and the lower faces consisted of two slip boundaries. And if we would like to apply the numerical method presented in this paper to onshore wind farms, we should change the boundary conditions according to the land-based characteristics.
3.4. Mesh generation
4.1. Output power of wind turbines
In consideration of the application of ALM and FAST, there was no need to model solid wind turbine rotors or to resolve the boundary layer behavior around the blade, which would need huge cell numbers and computational resources (Nedjari et al., 2017). Therefore, the flow domain was meshed into structure elements with hexahedral cuboid grids through the built-in mesh solver blockMesh in the OpenFOAM. It began with a coarse resolution of mesh in the flow domain. Then, in order to confirm that the mesh was sufficient to capture the wake structure like blade-tip vortices, which was considered to be the most important flow characteristics and required the finer grids, we locally refined the mesh in accordance to areas covered by wake. Corresponding to the rotation motion of the rotors in reality, we chose the cylinder-shaped zone associated with the refined region. Besides, we added two transition zones between coarse mesh and the refined mesh to avoid fluctuations of the numerical simulation. Therefore, the final mesh was composed of three sub-domains: coarse mesh, transition zones (two layers) and refined mesh. The most refined resolution of the mesh for the wake was 3.94 m, which was enough for the simulation of large scale wind turbines in the offshore wind farm according to the previous investigation (Fleming et al., 2014). The meshes on the section plane that is orthotropic with the X-direction and the meshes which cover the entire computational domain are shown in Fig. 8a and b respectively.
In this paper, the computational simulation was unsteady. We employed the parallel block technic with thirty cores to compute all cases. With regard to the convergence criteria, the residuals for the pressure and velocity were set to 1 × 10−5 and 1 × 10−6 respectively, which were sufficient to produce converged solutions within every numerical interval and guarantee the reliability of the simulation. For every computational time step, the ALM calculated and output the power of wind turbines. When the wind blows from the inlet of computational domain to the outlet, which took approximate 220s, we continued to calculate until the total time reached the 300s. We use the average of the last 80s's data as the final power of wind turbines. Fig. 10 presents the output power of wind turbines under the circumstances of wake deviation control strategies. For better distinction, we use different colours to represent the output power of wind turbines respectively. From the output results of yaw control in Fig. 10a, it can be easily seen that there are evident discrepancies between WT1 and WT2. The output power of WT1 changes obviously when the yaw angles varies from 230° to 310°with the step length of 10°. While at the 230°of yaw angle, the output power of WT1 is 2.8663 MW, which only makes up 57.5% of the output power when it is at the zero yaw angle. With further enlargement of the yaw angle, the output power of WT1 is increasing gradually. At the yaw angle of 270°, the power output arrives at the peak value of 4.9849 MW. In the yaw angles from 270° to 310°, the output power of WT1 declines continuously, falling to 2.8671 MW at the high angle of 310°, which is about the same value at the yaw angle of 230°. The trend of power output of WT2 is in sharp contrast to that of WT1. When the yaw angles are at 230°and 310°, the power output of WT1 are at the maximum values, 4.5765 MW and 4.5939 MW respectively; whereas, the minimum of power output of WT2 occurs at the yaw angle of 270°, with a value of only 0.8570 MW. Moreover, the distribution law in Fig. 10a indicates that our work using
4. Results and discussions
3.5. Boundary conditions The boundary conditions of the offshore wind farm are shown in Fig. 9. The inlet condition was a uniform freestream velocity boundary, whose direction was parallel to the X-direction and magnitude was equal to the nominal rated velocity of NREL 5 MW, 11.4 m/s. The outlet employed a pressure outlet, the magnitude of which was as large as a 798
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
(a)
(b)
Fig. 8. Mesh generation: (a) section plane that is orthotropic with the X-direction; (b) entire computational domain.
output reaches the maximum of 5.0205 MW at the tilt angle of 0°. While the tilt angles are −35°and 35°respectively, the power of WT1 are 3.4016 MW and 3.4002 MW accordingly. In contrast, compared with WT1, WT2 has an opposite variation tendency of power output. When the tilt angle is 0°, WT2 falls to its minimum power value, only 0.7900 MW. While the angles are −35°and 35°, the output power of WT2 are 4.1728 MW and 4.3038 MW respectively. Moreover, we also find that the power output at plus tilt angles is higher than that at the corresponding minus tilt angles. In order to clearly reveal distinctly the changes of output power of wind turbines with both of the two control strategies of wake deviation, we define the power output ratio as the power output of WT1 without the yaw or tilt divided by the power output with control strategies. Table 3 and Table 4 indicate the power output ratios of wind turbines obtained from the yaw and tilt control strategies.
4.2. Total output power of the offshore wind farm Fig. 11 illustrates the total output power of the offshore wind farm in the condition of the control strategies of yaw and tilt. From Fig. 11 we find that the total output power of the two control strategies both have two maximum values and one minimum values, which fit well to Fig. 10. It should be noted that the effects of two control strategies on total output power of the offshore wind farm are not absolutely the same. Instead, the yaw control strategy generates a bit more total output power than the tilt control strategy does. The
Fig. 9. Boundary conditions of the offshore wind farm.
ALM and OpenFOAM to optimize the offshore wind farm is correct and valid. In the output results of tilt control in Fig. 10b, we find that the power output of WT1 increases at first and then decreases as the tilt angles varies from −35°to 35°with the step length of 5°. The power
(b)
(a) Fig. 10. Output power of wind turbines: (a) yaw; (b) tilt. 799
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
Table 3 The power output ratio of WTs for the yaw control strategy. yaw angle
230°
240°
250°
260°
270°
280°
290°
300°
310°
WT1 WT2
57.5% 91.8%
76.4% 82.2%
89.9% 60.6%
97.4% 31.4%
100% 17.2%
97.4% 32.3%
89.9% 60.5%
76.4% 82.0%
57.5% 92.2%
Table 4 The power output ratio of WTs for the tilt control strategy.
Table 5 Differences between total output power of positive and negative tilt angles.
tilt angle
35°
30°
25°
20°
15°
10°
5°
WT1 WT2
67.8% 83.1%
76.8% 75.8%
84.5% 66.4%
90.0% 55.2%
94.3% 41.3%
97.4% 26.7%
99.3% 17.1%
0°
5°
10°
15°
20°
25°
30°
35°
100% 15.7%
99.3% 17.6%
97.4 27.6
94.3% 43.1%
90.0% 57.3%
84.5% 69.3%
76.8% 78.9%
67.8% 85.7%
yaw
yaw angle /°
300
ti l t
20
280
10
270
0
260
-10
250
-20
240
-30
230
-40
P2 =
+
+ 0.0034φ + 6.2509
25°
30°
35°
total output power/kW
32.9
50.2
97.4
101.6
147.1
157.1
130.0
4.3. Velocity nephogram Fig. 12 is the velocity nephogram of horizontal cross-section, namely the top view, at the height of hub for nine operating conditions of the yaw control strategy. From these nephograms, we could access intuitively the influence of wake from upstream wind turbine on the downstream and the mechanism of the yaw control strategy to weaken the effect of wake. As illustrated in Fig. 12, the yaw control strategy can remarkably change the orientation of the wake fromWT1. If the yaw angle is greater, the deviation of the wake is more obvious. When the yaw angle is 260°or 280°, the wake of WT1 begins to deviate from the rotor center of WT2. Therefore, the influence of wake from the upstream wind turbine is weakened and the average velocity of the inflow of WT2 increases. In this condition, the output power of WT2 is about two times of the output power without the wake control strategy. The enlargement of the output power of WT2 is apparent, which is in good agreement with Fig. 10a. With further increase of the yaw angle, the effect of WT1 on WT2 becomes weaker. Consequently, the proportion of inflow of WT2 that is not influenced by WT1 rises, and the average velocity of inflow of WT2 increases. Especially when the yaw angle of WT1 is 310°or 230°, wake of WT1 almost deviates from the rotor of WT2, and the influence of WT1 on WT2 is so weak that the output power of WT2 approximately approaches to its rated power. However, when the yaw angle of WT1 is too big, its operating condition is seriously away from the designed optimal condition. In consequence, the output power of WT1 may decline drastically, causing the total output power of the offshore wind farm too less than that at the 300°or 230°of the yaw angle. Therefore, when the yaw angle is too big or too small, the total output power of the offshore wind farm cannot reach the maximum. While the yaw angle is 300°or 240°, WT1 and WT2 are both at an ideal operating condition, and the total output power of the offshore wind farm arrives at the largest. The above substance fits well to the results of Fig. 11. Fig. 13 is the velocity nephogram of vertical cross-section, namely see from one side to another of the offshore wind farm, through two rotor centers in fifteen operating conditions of the tilt control strategy, which perspicuously displays the deviation of the wake.
maximum and the minimum total output power of the offshore wind farm under the yaw control strategy are 7.9071 MW and 5.8419 MW respectively, while the maximum and the minimum total output power under the tilt control strategy are 7.8146 MW and 5.8105 MW. In addition, the total output power of plus tilt angles is about one hundred thousand watts more than that of the corresponding minus tilt angles. From Fig. 11 we can also see that the maximums of total output power all appear to be at the 30°of the deviation angle. That is because at this deviation angle the output power of WT1 and WT2 are all considerable. We define the deviation angle as the absolute difference value between the yaw angle and the tilt angle with the angle of no control strategy. Based on the three order polynomial as the base function, we fit the relations of total output power of the offshore wind farm with the angles of control strategies of yaw and tilt using the least square method. Finally, we can attain equations (8) and (9).
0.0015φ2
20°
difference values here are all positive. And with the absolute value of the deviation angle increasing, the difference values are getting bigger.
Fig. 11. Total output power of the offshore wind farm.
−1.0914φ3
15°
Fig. 12. The velocity nephogram of the yaw control strategy.
6.2 6.7 7.2 7.7 total output powers of the offshore wind farm /MW
P1 = −3.0724θ3 + 0.0008θ 2 + 0.427θ + 63.9563
10°
30
290
5.7
5°
40
tilt angle / °
310
absolute value of the deviation angle
(8) (9)
Where P1 represents total output power of the offshore wind farm under yaw control strategy, θ is the yaw angle from 230° to 310°. P2 represents total output power of the offshore wind farm under tilt control strategy; φ is the tilt angle from −35°to 35°. Besides, mainly because of the restriction of computing resources and time, it is impossible to compute all angles, so we only simulate the integer angle values. Anyway, it should be noted that the general tendency of equations (8) and (9) is accurate. Table 5 shows the differences between total output power of positive and negative tilt angles in the tilt control strategy. As mentioned above, we know that the total output power of positive tilt angles is in general more than that of the corresponding negative tilt angles, so the 800
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
to produce some considerable economic performance. Acknowledgements The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China under Project Number 51176129&51676131, and the financial support from the International/Regional Cooperation and Communication Project under Project Number 51811530315. References Fig. 13. The velocity nephogram of the tilt control strategy.
Bangga, G., Hutomo, G., Syawitri, T., Kusumadewi, T., et al., 2018. Enhancing BEM simulations of a stalled wind turbine using a 3D correction model. In: Proceedings of the 3rd International Conference on Mathematics: Pure, Applied and Computation, Surabaya, Indonesia, Paper No. (974), , 012020. Chen, J., Hu, Z., Wan, D., Xiao, Q., 2018. Comparisons of the dynamical characteristics of a semi-submersible floating offshore wind turbine based on two different blade concepts. Ocean. Eng. 153, 305–318. Elginoz, N., Bas, B., 2017. Life cycle assessment of a multi-use offshore platform: combining wind and wave energy production. Ocean. Eng. 145, 430–443. Fleming, P.A., Gebraad, P.M.O., Sang, L., Wingerden, J.W.V., et al., 2014. Evaluating techniques for redirecting turbine wakes using SOWFA. Renew. Energy 70 (5), 211–218. Fleming, P., Gebraad, P.M.O., Lee, S., Wingerden, J., et al., 2015. Simulation comparison of wake mitigation control strategies for a two-turbine case. Wind Energy 18 (12), 2135–2143. Gebraad, P.M.O., Fleming, P., Van Wingerden, J.W., 2015. Comparison of actuation methods for wake control in wind plants. In: Proceedings of the 2015 American Control Conference, Chicago, USA, pp. 1695–1701. GWEC, 2018. Global Wind Statistics 2017. GWEC 2018, Brussels, Belgium. Hou, P., Hu, W., Soltani, M., Chen, C., et al., 2017. Combined optimization for offshore wind turbine micro siting. Appl. Energy 189, 271–282. Kang, J., Sun, L., Sun, H., Wu, C., 2017. Risk assessment of floating offshore wind turbine based on correlation-FMEA. Ocean. Eng. 129, 382–388. Karimi, M., Hall, M., Buckham, B., Crawford, C., 2017. A multi-objective design optimization approach for floating offshore wind turbine support structures. J. Ocean Eng. Mar. Energy 3 (1), 69–87. Meghlaoui, I., Dobrev, I., Massouh, F., Benretem, A.O., et al., 2017. Computationally inexpensive free vortex method to obtain vortex core position in the wake of a horizontal axis wind turbine. Int. J. Fluid Mech. Res. 44, 427–443. Miao, W., Li, C., Pavesi, G., Yang, J., et al., 2017. Investigation of wake characteristics of a yawed HAWT and its impacts onthe inline downstream wind turbine using unsteady CFD. J. Wind Eng. Ind. Aerod. 168, 60–71. Miao, W., Li, C., Yang, J., Yang, Y., et al., 2016. Numerical investigation of wake control strategies for maximizing the power generation of wind farm. J. Sol. Energy Eng. 138 (3), 1–7. National Renewable Energy Laboratory (NREL), 2018, (URL): < https://nwtc.nrel. gov/ > . Nedjari, H.D., Guerri, O., Saighi, M., 2017. CFD wind turbines wake assessment in complex topography. Energy Convers. Manag. 138, 224–236. NREL, 2009. Definition of a 5-MW Reference Wind Turbine for Offshore System Development. NREL 2009, Golden, Colorado. Puneet, V., Yunjun, X., Kuo, C.L., 2017. Optimal power planning of wind turbines in a wind farm. U.S. J. Elec. Power 6 (2), 7–15. Shakoor, R., Hassan, M.Y., Raheem, A., Wu, Y.K., 2016. Wake effect modeling: a review of wind farm layout optimization using Jensen׳s model. Renew. Sustain. Energy Rev. 58, 1048–1059. Son, E., Lee, S., Hwang, B., Lee, S., et al., 2014. Characteristics of turbine spacing in a wind farm using an optimal design process. Renew. Energy 65 (5), 245–249. Sorensen, J.N., Shen, W.Z., 2002. Numerical modeling of wind turbine wakes. J. Fluid Eng. 124 (2), 393–399. Tian, W., Ozbay, A., Hu, H., 2018. An experimental investigation on the wake interferences among wind turbines sited in aligned and staggered wind farms. Wind Energy 21 (2), 100–114. Troldborg, N., 2008. Actuator Line Modeling of Wind Turbine Wakes. Technical University of Denmark, Copenhagen, Denmark. Wimshurst, A., Willden, R.H.J., 2016. Extracting lift and drag polars from blade-resolved computational fluid dynamics for use in actuator line modelling of horizontal axis turbines. Wind Energy 20, 815–833. Yang, Y., Ye, K., Li, C., Michailides, C., et al., 2018. Dynamic behavior of wind turbines influenced by aerodynamic damping and earthquake intensity. Wind Energy 21 (5), 303–319.
In Fig. 13, we can find that the greater the absolute value of the tilt angle, the more obvious the wake deviation is; as a result, the effect of the upstream wind turbine on WT2 becomes feebler. Hence, the quality of inflow of WT2 turns higher, and the output power remarkably improves. This fits well to Figs. 10b and 11. Besides, in Fig. 10b, the total output power of plus tilt angles is about one hundred thousand watts more than that of the corresponding minus tilt angles. This is realistic and can be interpreted according to Fig. 13. That is to say, when the tilt angle is plus, the wake of WT1 deviates downwards, and enhanced by gravity, it will further increase the output power of WT2. While the tilt angle is minus, the wake of WT1 deviates upwards, and the deviation is weakened by gravity, so the output power of WT2 turns less. 5. Conclusions In this paper, we have modified the standard solver pisoFoam in the open source software OpenFOAM and developed a new solver NewTurbinepisoFoam. On this basis, we conducted computational simulations for the NREL 5WM wind turbines in an offshore wind farm. Two control strategies of wake deviation were adopted to simulate 24 operating conditions. The results demonstrate an instructional significance for the offshore wind farm in operating wind turbines. By numerical analysis, the following conclusions can be drawn. (1) The power of wind turbines, flow fields and wake deviation have been simulated with relatively far less computing resources and time. It indicates the present modified solver has good accuracy and extensive applicability. (2) The influence of wake from the upstream wind turbine on the downstream wind turbine cannot be negligible. By controlling the deviation of the wake from the upstream wind turbine, we could effectively weaken the impact of the wake on the performance of the downstream wind turbine. (3) Compared with the tilt control strategy, the yaw control strategy could attain more total output power of the offshore wind farm. With regard to the tilt control strategy, plus tilt angles are better than the minus. (4) There is an optimal angle, generally being the 30°of the deviation angle, for both the yaw and tilt control strategy with regard to the total output power of the offshore wind farm. Under these circumstances, the output power of the upstream and the downstream wind turbines are all considerable. (5) The present work has the potential to be extended to a simulation of an offshore wind farm with hundreds of wind turbines. Above all, it can be directly applied to the real offshore wind farms and is likely
801
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Numerical investigations on control strategies of wake deviation for large wind turbines in an offshore wind farm
T
Yuanbo Wanga, Weipao Miaoa,b, Qinwei Dinga,c, Chun Lia,∗, Bin Xianga a
School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai, 20093, China Department of Engineering Industrial, University of Padua, Padua, 35131, Italy c School of Engineering, University of Plymouth, Plymouth, PL4 8AA, UK b
A R T I C LE I N FO
A B S T R A C T
Keywords: Wind turbine Wake deviation Yaw Tilt Total output power Offshore wind farm
The OpenFOAM package incorporated with actuator line method (ALM) is employed to calculate the aerodynamic characteristics of large wind turbines in an offshore wind farm. In order to mitigate the wake effect of upstream wind turbines and conduct the overall optimization of output power for the offshore wind farm, wake deviation simulations of nine yaw angles and fifteen tilt angles are carried out. Taking total output power of the offshore wind farm as the reference point and combining fluid field profiles of cross-sections in all simulations, we investigate the flow mechanism of wake's influence on the downstream turbines with different control strategies. The results show that, although the output power of the upstream wind turbine may decreases mildly, changing the wake direction with different control methods can significantly increase the total output power of the whole wind farm due to the substantial enhancement of the downstream wind turbine. Both control strategies of wake deviation can globally optimize the offshore wind farm and each has an optimal angle, while the yaw control strategy has better results and with regard to the tilt control strategy, the plus tilt angle is comparatively better than the minus angle.
1. Introduction For centuries, increasing demand for energy has chiefly depended on fossil fuels, which leads to unintended global consequences, especially in air pollution and climate change (Elginoz and Bas, 2017). Accordingly, various technologies of renewable energy have been developed to replace fossil fuels. Among them, wind power appears to be a prominent and promising alternative. Up to now, wind energy technology has been exploited on a wide commercial scale, establishing itself as a mature approach of renewable energy generation (Karimi et al., 2017). With the decrease of available onshore wind farm resources, strong consistent and weak turbulent offshore winds have become a hot research topic among scientific staff around the word in recent years (Kang et al., 2017). Furthermore, compared with onshore wind farms, offshore wind farms have some notable advantages, such as higher energy production, less wind shear, and lower environmental impact (noise, visual pollution and so on) (Hou et al., 2017). Consequently, the fact that offshore wind power will be the main field of future utilization of wind energy has been widely acknowledged in both academic and the industrial circles (Chen et al., 2018; Yang et al., 2018). In fact, the offshore wind power capacity has been rising rapidly
∗
year by year, as illustrated by the annual cumulative capacity (2011–2017) of the offshore wind turbine in Fig. 1 (GWEC, 2018). Customarily, tens or even hundreds of wind turbines would be arranged in one offshore wind farm, for the purpose of maximal use of wind energy as well as reduction of construction costs (Shakoor et al., 2016; Puneet et al., 2017). However, this pattern of the offshore wind farm (as well as the onshore wind farm) has an inherent phenomenon that the velocity of the wake from the upstream wind turbine will experience a deficit and its turbulence turns intense, as shown in Fig. 2 (NREL, 2016; Tian et al., 2018). In turn, the wind turbine in the downstream wind farm, located within and suffered from such wakes, reduce its inflow quality. As a result, the output power of downstream wind turbine turns to be less. Overall, wind energy and offshore water area resources are actually wasted. Therefore, it is of vital importance to study the offshore wind farm, especially the valid wake control strategies, and then to apply the optimal strategy to achieve the aim of increasing total output power of the offshore wind farm. At present, there are two main methods can that are used to conduct the wake control. The first is to alter the axial induction factor of wind turbine rotor by changing the pitch angle to alleviate the wake velocity deficit. The second way is to adopt the wake
Corresponding author. E-mail address: [email protected] (C. Li).
https://doi.org/10.1016/j.oceaneng.2019.01.042 Received 16 August 2018; Received in revised form 29 December 2018; Accepted 16 January 2019 0029-8018/ © 2019 Elsevier Ltd. All rights reserved.
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
Fig. 1. The annual global cumulative offshore wind power capacity.
Fig. 4. Schematic representation of the NREL 5 MW wind turbine.
of wind farm output power. Nevertheless, the study of Miao et al. (2017) indicated that the total output power of two tandem wind turbines in a wind farm shown a gratifying discrepancy between different yaw directions of the upstream wind turbine, as illustrated in Fig. 3. For the aforementioned reasons, we propose employing the control strategy of wake deviation to redirect the wake of upstream wind turbine in an offshore wind farm. Subsequently, a mainstream wind turbine type and an appropriate research approach need to be determined to conduct wake deviation realistically in an offshore wind farm. We based our study on a 5 MW horizontal axis wind turbine designed by the National Renewable Energy Laboratory (NREL) (See the schematic of the turbine in Fig. 4). Although the NREL 5 MW wind turbine doesn't reach the largest scale level among existing wind turbines, at least it is unrealistic to conduct aerodynamic experiments in a wind tunnel. Moreover, due to the requirement of precision, time restriction and computational cost, there are few aerodynamically numerical studies on the whole wind turbine for the 5 MW and higher at present. As fat as numerical studies are concerned, there are mainly three conventional approaches, each having its own merits and demerits, as seen in Table 1. Bangga et al. (2018) combined the pure blade element momentum (BEM) with a stall delay model for a wind turbine operating under pitch fault circumstance, and the accuracy of the result was assessed by comparing the results of computational fluid dynamics (CFD) simulations data. However, Bangga et al. (2018) couldn't calculate the flow field and wind turbine wake, although their approach could predict the aerodynamic characteristics of a single wind turbine quickly. Meghlaoui et al. (2017) took into account both the tangential and longitudinal vorticity of the vortex system formed behind the rotor based on vortex wake method (VWM). They found that the development of the near wake of a horizontal axis wind turbine under different inflow speeds showed a good agreement between the calculation and experience. However, the rotor diameter they used is only 0.54 m. In contrast, the rotor diameter of the 5 MW wind turbine is 126 m and the flow field spans five size scales from macroscopic to microcosmic. VWM performs with a low precision when it is used to predict the small vortex in a large scale domain. Miao et al. (2017) used commercial CFD software STAR-CCM + to simulate the wind farm arranged with two intandem wind turbines. Their results showed that, when the upstream wind turbine applied a positive yaw angle, the wind farm's total power increased. However, according to Miao's work, in order to capture the boundary layer flows around three long wind turbine blades, massive complex mesh need to be imposed. This would cost too much time and it is computationally too expensive to conduct numerical simulation. We find that the ALM approach proposed by Sorensen and Shen (2002) can redress the above problems. It
Fig. 2. Sketch of the wake in a wind farm.
Fig. 3. Total output power of two turbines varies with yaw angle.
redirection control strategy to make the wake after upstream wind farm deviate from rotor center of the downstream wind turbine. In this way, part of or the entire downstream wind turbine rotor could avoid interacting with the wake, thus eventually improving energy capturing of the overall offshore wind farm. In general, the second method mainly consists of yaw and tilt control strategy. As for the first method, Fleming et al. (2015) used individual pitch control (IPC) to change the rotor power efficiency of the upstream wind turbine, with an aim to weaken the wake velocity defect, and the results showed that total output power of the whole wind farm increased slightly, but the blade root moment increased exponentially. Gebraad et al. (2015) used the SOWFA, a high-fidelity computational simulation software for wind farm, to carry out a numerical calculation of adjusting the pitch and torque, but the results were not satisfactory for the global optimization 795
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
Table 1 Three main traditional numerical approaches. Approaches Features
BEM
VWM
CFD
Advantages Disadvantages
timesaving incompetent in wake and flow fields
timesaving and competent in wake incompetent in small vortex in some cases
precise cost much time and computing resources
(a)
(b)
Fig. 5. Sketch of the distribution of body forces: (a) plane of the wind turbine rotor; (b) section plane of the ALM.
extra model combined with tabulated two-dimensional airfoil characteristics. ALM accesses the information of flow fields at each CFD time step and meanwhile calculates the aerodynamic characteristics of blades by the following equations.
is a fully three-dimensional and unsteady aerodynamic model for studying the flow field around the wind turbine. However, it has received little attention and application in the study of total output power of a large offshore wind farm. In our study, based on the ALM involved in the OpenFOAM package, we simulated 24 operation conditions of wake redirection, including 9 yaw angles and 15 tilt angles. Then, we analyzed the impact of wake control strategies on aerodynamic characteristics of wind turbines, and in turn on the total output power of offshore wind farm. The characteristics of wind turbine wakes at different control strategies are studied in detail by researching the variables of the flow field; meanwhile the influence of wake on the downstream turbine is also discussed. The finding of this work will provide significant instructions for operating offshore wind farms.
Fτ =
1 ρW 2⋅c⋅Cτ⋅τ 2
(3)
Fn =
1 ρW 2⋅c⋅Cn⋅n 2
(4)
Fs
(5)
= Fτ + Fn
Where.
W = relative velocity of the local airfoil c = local chord of the airfoil Cτ = coefficient of the tangential force τ = tangential unit vector Cn = coefficient of the normal force n = normal unit vector Fτ , Fn and F s = tangential, normal and resultant forces of the unit length blade
2. Methodology of ALM In terms of time and computational cost, compared with the conventional CFD method, ALM has a great advantage. ALM can produce preferable results at equivalent precision as the traditional CFD method does, but with less computing resources and time. Therefore, ALM is especially suitable for the simulation of three-dimensional flow fields for offshore wind farms. The basis of the ALM is the incompressible Navier-Stokes (NS) equations.
Automatically, the body force of fluid flow given by blades can be represented as the following: (6)
F f = −F s
DV 1 = − ∇P + ν∇2 V + f Dt ρ
(1)
∇⋅V = 0
(2)
In the end, body force is distributed radially along lines representing the blades via numerically smearing, as shown in Fig. 5. The body force needs to be distributed within a certain scope around the lines (blades) in order to avoid singular behavior. Otherwise, the CFD simulation may not converge if the area of body force distribution is smaller; whereas if bigger, vortexes on tip and root of blades would be weakened excessively (Wimshurst and Willden, 2016). To ensure the body force smear smoothly, a three-dimensional Gaussian manner like equation (7) is adopted.
Where t and ρ are the time and density respectively, and V is the velocity vector. P represents the stresses tensor. ν is the kinematic viscosity. And the source term f denotes the body force, which represents the load on the flow field imposed by rotating blades. Based on the Newton's third law, the body force can be attained using the force applied on blades by flow field. Since there are no solid walls of blades in the ALM, the force acted on blades needs to be calculated via an extra model, which can achieve the equivalent effect of real blades with solid walls. In this paper, we adopt the BEM as the
f (r ) =
796
1 3 ε 3π 2
r 2
e−( ε )
(7)
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
Table 2 Main specifications of NREL 5 MW wind turbine. Parameters
Values
Unit
Rated power Rated wind speed Rated rotor speed Rotor diameter Blade number Shaft tilt Rotor cone Hub diameter Hub height
5.0 11.4 12.1 126.0 3 5.0 2.5 3 90.0
MW m·s-1 rpm m m ° ° m m
3. Computational implementation 3.1. Wind turbine
Where r represents the distance between the body force center on blade and the distributed point in fluid domain, and ε is the smearing factor that controls the gradient of body force distributing. Troldborg (2008) points out that the distribution of body force has a significant influence on the results of the simulations. And in three-dimensional distribution of Gauss for ALM, the equation ε = 2Δs should be met if the effect of ALM wants to be extremely close to the real wind turbine situation, while Δs is the distance of points on the actuator line. Compared with what would be needed for simulating the actual geometry of the blades, the advantage of representing the blades by airfoil data, as it is done in the actuator line model, is that much fewer grid points are needed to capture the influence of the blades. Therefore, the ALM provides a detailed study of the dynamics of different wake structures using a reasonably number of grid nodes. Furthermore, the model benefits from being applicable with simple structured grids and consequently issues connected to grid generation do not occur. On the other hand, a drawback of the method is its reliance on tabulated airfoil characteristics. However, as the main purpose of the present paper is to study fundamental wake effects, it is of minor importance to capture the dynamic stall or other flow regimes on the blades exactly. The ALM technic described above is implemented in the OpenFOAM package, which is an open source CFD software developed with objectoriented C++. It has the benefit of being free and, therefore, essentially provides unlimited licenses. This means its source codes are available, which helps users know exactly how codes function and allows modification and expansion that are necessary for new code development and research on this fundamental level. And it should be pointed that the version of OpenFOAM 3.0.1 is employed in this paper. We construct a new solver NewTurbinepisoFoam based on the built-in solver pisoFoam in OpenFOAM 3.0.1. It is based on the Pressure Implicit Split Operator (PISO) method that is more efficient and accurate compared to the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) method. The New solver NewTurbinepisoFoam is intended for the numerical simulation of horizontal axis wind turbine based on the ALM. Compared with the pisoFoam, NewTurbinepisoFoam constructs a C++ class turbines, which can function a series of operations, such as defining the array of the body force, solving the body force, distributing the body force and so on. Accordingly, a wind turbine can be added expediently in offshore wind farm just through setting the locations of coordinate values of the wind turbine. The piece of code below this paragraph is a part of source codes of the ALM solver implementation, and properly speaking, it is the moment predictor step equation from the include file UEq.H in NewTurbinepisoFoam. Finally, the equation is evaluated using built-in class fvVectorMatrix that discretizes and distributes the operators specified within first-order curled brackets.
The computational object employed in the present work is a 5 MW rating wind turbine designed by the NREL affiliated to the U.S. Department of Energy. NERL 5 MW wind turbine generally refers to the publicly available information of the Multibrid M5000 and REpower 5M prototype wind turbines. As detailed information on those two machines is not available, NERL 5 MW wind turbine also refers to the publicly available properties from the conceptual models used in the WindPACT, RECOFF and DOWEC projects (NREL, 2009). The main specifications of NERL 5 MW wind turbine are illustrated in Table 2. 3.2. Offshore wind farm configuration In order to avoid tunnel blockage effect in computational simulation, we created a larger numerical offshore wind farm with a flow domain of 20D in length, 6D in width and 6D in height (D represents the wind turbine rotor diameter). Two tandem wind turbines substituted by WT1 and WT2 respectively, were located in the offshore wind farm, and the two wind turbines was set at a distance of 7D. With regard to the reasons for the choice of 7D, first of all, turbine performance at separation distances from 3D to 7D was examined and it was observed that the performance of downstream wind turbine decreased notably when the distance was less than 6D (Miao et al., 2016). In addition, the inter-turbine distance in a wind farm needs to be estimated carefully to balance the power output efficiency and construction costs. For example, due to some constraints such as the cost of electrical connections or the availability of land surface, an oversized separation is inappropriate (Son et al., 2014). Besides, there is 3D from WT1 to the inlet of the wind farm, and WT2 has been placed sufficiently far away from the outlet, 10D, to eliminate the effect on the flow of wake. The flow domain and wind turbines are illustrated in Fig. 6. 3.3. Control strategies of wake deviation We implemented control strategies by executing changes of yaw and
Fig. 6. The flow domain and its configure. 797
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
(a)
(b) Fig. 7. Control strategies of wake deviation: (a) yaw; (b) tilt.
tilt angles for the upstream WT1, and in this way the wake of WT1 would deviate from the rotor center of the downstream WT2. For the purpose of better comparison, we investigated 24 operation conditions associated with control strategies that consisted of 9 yaw angles and 15 tilt angles, while the range of yaw angles were from 230° to 310°with the step length of 10°and tile angles were from −35°to 35°with the step length of 5°. Fig. 7 is the sketch of the control strategies of wake deviation, and the Ye direction is along the offshore wind farm's width that is perpendicular to the plane determined by X and Z axis. Moreover, in order to avoid the accident of blade-tower collision, it should be noted that the tilt angles between 0° and 35°are intended for the type of downwind wind turbine.
standard atmospheric pressure. Two lateral sides were set to periodic boundary conditions, which meant when a flow variable appears on the unit cell of one side, it would simultaneously re-appear on the opposite side with the same value. The reason why the lateral sides used the periodic boundary was mainly that, in practice, there were flow domains at both sides of the offshore wind farm and they were the same. Besides, the upper and the lower faces consisted of two slip boundaries. And if we would like to apply the numerical method presented in this paper to onshore wind farms, we should change the boundary conditions according to the land-based characteristics.
3.4. Mesh generation
4.1. Output power of wind turbines
In consideration of the application of ALM and FAST, there was no need to model solid wind turbine rotors or to resolve the boundary layer behavior around the blade, which would need huge cell numbers and computational resources (Nedjari et al., 2017). Therefore, the flow domain was meshed into structure elements with hexahedral cuboid grids through the built-in mesh solver blockMesh in the OpenFOAM. It began with a coarse resolution of mesh in the flow domain. Then, in order to confirm that the mesh was sufficient to capture the wake structure like blade-tip vortices, which was considered to be the most important flow characteristics and required the finer grids, we locally refined the mesh in accordance to areas covered by wake. Corresponding to the rotation motion of the rotors in reality, we chose the cylinder-shaped zone associated with the refined region. Besides, we added two transition zones between coarse mesh and the refined mesh to avoid fluctuations of the numerical simulation. Therefore, the final mesh was composed of three sub-domains: coarse mesh, transition zones (two layers) and refined mesh. The most refined resolution of the mesh for the wake was 3.94 m, which was enough for the simulation of large scale wind turbines in the offshore wind farm according to the previous investigation (Fleming et al., 2014). The meshes on the section plane that is orthotropic with the X-direction and the meshes which cover the entire computational domain are shown in Fig. 8a and b respectively.
In this paper, the computational simulation was unsteady. We employed the parallel block technic with thirty cores to compute all cases. With regard to the convergence criteria, the residuals for the pressure and velocity were set to 1 × 10−5 and 1 × 10−6 respectively, which were sufficient to produce converged solutions within every numerical interval and guarantee the reliability of the simulation. For every computational time step, the ALM calculated and output the power of wind turbines. When the wind blows from the inlet of computational domain to the outlet, which took approximate 220s, we continued to calculate until the total time reached the 300s. We use the average of the last 80s's data as the final power of wind turbines. Fig. 10 presents the output power of wind turbines under the circumstances of wake deviation control strategies. For better distinction, we use different colours to represent the output power of wind turbines respectively. From the output results of yaw control in Fig. 10a, it can be easily seen that there are evident discrepancies between WT1 and WT2. The output power of WT1 changes obviously when the yaw angles varies from 230° to 310°with the step length of 10°. While at the 230°of yaw angle, the output power of WT1 is 2.8663 MW, which only makes up 57.5% of the output power when it is at the zero yaw angle. With further enlargement of the yaw angle, the output power of WT1 is increasing gradually. At the yaw angle of 270°, the power output arrives at the peak value of 4.9849 MW. In the yaw angles from 270° to 310°, the output power of WT1 declines continuously, falling to 2.8671 MW at the high angle of 310°, which is about the same value at the yaw angle of 230°. The trend of power output of WT2 is in sharp contrast to that of WT1. When the yaw angles are at 230°and 310°, the power output of WT1 are at the maximum values, 4.5765 MW and 4.5939 MW respectively; whereas, the minimum of power output of WT2 occurs at the yaw angle of 270°, with a value of only 0.8570 MW. Moreover, the distribution law in Fig. 10a indicates that our work using
4. Results and discussions
3.5. Boundary conditions The boundary conditions of the offshore wind farm are shown in Fig. 9. The inlet condition was a uniform freestream velocity boundary, whose direction was parallel to the X-direction and magnitude was equal to the nominal rated velocity of NREL 5 MW, 11.4 m/s. The outlet employed a pressure outlet, the magnitude of which was as large as a 798
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
(a)
(b)
Fig. 8. Mesh generation: (a) section plane that is orthotropic with the X-direction; (b) entire computational domain.
output reaches the maximum of 5.0205 MW at the tilt angle of 0°. While the tilt angles are −35°and 35°respectively, the power of WT1 are 3.4016 MW and 3.4002 MW accordingly. In contrast, compared with WT1, WT2 has an opposite variation tendency of power output. When the tilt angle is 0°, WT2 falls to its minimum power value, only 0.7900 MW. While the angles are −35°and 35°, the output power of WT2 are 4.1728 MW and 4.3038 MW respectively. Moreover, we also find that the power output at plus tilt angles is higher than that at the corresponding minus tilt angles. In order to clearly reveal distinctly the changes of output power of wind turbines with both of the two control strategies of wake deviation, we define the power output ratio as the power output of WT1 without the yaw or tilt divided by the power output with control strategies. Table 3 and Table 4 indicate the power output ratios of wind turbines obtained from the yaw and tilt control strategies.
4.2. Total output power of the offshore wind farm Fig. 11 illustrates the total output power of the offshore wind farm in the condition of the control strategies of yaw and tilt. From Fig. 11 we find that the total output power of the two control strategies both have two maximum values and one minimum values, which fit well to Fig. 10. It should be noted that the effects of two control strategies on total output power of the offshore wind farm are not absolutely the same. Instead, the yaw control strategy generates a bit more total output power than the tilt control strategy does. The
Fig. 9. Boundary conditions of the offshore wind farm.
ALM and OpenFOAM to optimize the offshore wind farm is correct and valid. In the output results of tilt control in Fig. 10b, we find that the power output of WT1 increases at first and then decreases as the tilt angles varies from −35°to 35°with the step length of 5°. The power
(b)
(a) Fig. 10. Output power of wind turbines: (a) yaw; (b) tilt. 799
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
Table 3 The power output ratio of WTs for the yaw control strategy. yaw angle
230°
240°
250°
260°
270°
280°
290°
300°
310°
WT1 WT2
57.5% 91.8%
76.4% 82.2%
89.9% 60.6%
97.4% 31.4%
100% 17.2%
97.4% 32.3%
89.9% 60.5%
76.4% 82.0%
57.5% 92.2%
Table 4 The power output ratio of WTs for the tilt control strategy.
Table 5 Differences between total output power of positive and negative tilt angles.
tilt angle
35°
30°
25°
20°
15°
10°
5°
WT1 WT2
67.8% 83.1%
76.8% 75.8%
84.5% 66.4%
90.0% 55.2%
94.3% 41.3%
97.4% 26.7%
99.3% 17.1%
0°
5°
10°
15°
20°
25°
30°
35°
100% 15.7%
99.3% 17.6%
97.4 27.6
94.3% 43.1%
90.0% 57.3%
84.5% 69.3%
76.8% 78.9%
67.8% 85.7%
yaw
yaw angle /°
300
ti l t
20
280
10
270
0
260
-10
250
-20
240
-30
230
-40
P2 =
+
+ 0.0034φ + 6.2509
25°
30°
35°
total output power/kW
32.9
50.2
97.4
101.6
147.1
157.1
130.0
4.3. Velocity nephogram Fig. 12 is the velocity nephogram of horizontal cross-section, namely the top view, at the height of hub for nine operating conditions of the yaw control strategy. From these nephograms, we could access intuitively the influence of wake from upstream wind turbine on the downstream and the mechanism of the yaw control strategy to weaken the effect of wake. As illustrated in Fig. 12, the yaw control strategy can remarkably change the orientation of the wake fromWT1. If the yaw angle is greater, the deviation of the wake is more obvious. When the yaw angle is 260°or 280°, the wake of WT1 begins to deviate from the rotor center of WT2. Therefore, the influence of wake from the upstream wind turbine is weakened and the average velocity of the inflow of WT2 increases. In this condition, the output power of WT2 is about two times of the output power without the wake control strategy. The enlargement of the output power of WT2 is apparent, which is in good agreement with Fig. 10a. With further increase of the yaw angle, the effect of WT1 on WT2 becomes weaker. Consequently, the proportion of inflow of WT2 that is not influenced by WT1 rises, and the average velocity of inflow of WT2 increases. Especially when the yaw angle of WT1 is 310°or 230°, wake of WT1 almost deviates from the rotor of WT2, and the influence of WT1 on WT2 is so weak that the output power of WT2 approximately approaches to its rated power. However, when the yaw angle of WT1 is too big, its operating condition is seriously away from the designed optimal condition. In consequence, the output power of WT1 may decline drastically, causing the total output power of the offshore wind farm too less than that at the 300°or 230°of the yaw angle. Therefore, when the yaw angle is too big or too small, the total output power of the offshore wind farm cannot reach the maximum. While the yaw angle is 300°or 240°, WT1 and WT2 are both at an ideal operating condition, and the total output power of the offshore wind farm arrives at the largest. The above substance fits well to the results of Fig. 11. Fig. 13 is the velocity nephogram of vertical cross-section, namely see from one side to another of the offshore wind farm, through two rotor centers in fifteen operating conditions of the tilt control strategy, which perspicuously displays the deviation of the wake.
maximum and the minimum total output power of the offshore wind farm under the yaw control strategy are 7.9071 MW and 5.8419 MW respectively, while the maximum and the minimum total output power under the tilt control strategy are 7.8146 MW and 5.8105 MW. In addition, the total output power of plus tilt angles is about one hundred thousand watts more than that of the corresponding minus tilt angles. From Fig. 11 we can also see that the maximums of total output power all appear to be at the 30°of the deviation angle. That is because at this deviation angle the output power of WT1 and WT2 are all considerable. We define the deviation angle as the absolute difference value between the yaw angle and the tilt angle with the angle of no control strategy. Based on the three order polynomial as the base function, we fit the relations of total output power of the offshore wind farm with the angles of control strategies of yaw and tilt using the least square method. Finally, we can attain equations (8) and (9).
0.0015φ2
20°
difference values here are all positive. And with the absolute value of the deviation angle increasing, the difference values are getting bigger.
Fig. 11. Total output power of the offshore wind farm.
−1.0914φ3
15°
Fig. 12. The velocity nephogram of the yaw control strategy.
6.2 6.7 7.2 7.7 total output powers of the offshore wind farm /MW
P1 = −3.0724θ3 + 0.0008θ 2 + 0.427θ + 63.9563
10°
30
290
5.7
5°
40
tilt angle / °
310
absolute value of the deviation angle
(8) (9)
Where P1 represents total output power of the offshore wind farm under yaw control strategy, θ is the yaw angle from 230° to 310°. P2 represents total output power of the offshore wind farm under tilt control strategy; φ is the tilt angle from −35°to 35°. Besides, mainly because of the restriction of computing resources and time, it is impossible to compute all angles, so we only simulate the integer angle values. Anyway, it should be noted that the general tendency of equations (8) and (9) is accurate. Table 5 shows the differences between total output power of positive and negative tilt angles in the tilt control strategy. As mentioned above, we know that the total output power of positive tilt angles is in general more than that of the corresponding negative tilt angles, so the 800
Ocean Engineering 173 (2019) 794–801
Y. Wang et al.
to produce some considerable economic performance. Acknowledgements The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China under Project Number 51176129&51676131, and the financial support from the International/Regional Cooperation and Communication Project under Project Number 51811530315. References Fig. 13. The velocity nephogram of the tilt control strategy.
Bangga, G., Hutomo, G., Syawitri, T., Kusumadewi, T., et al., 2018. Enhancing BEM simulations of a stalled wind turbine using a 3D correction model. In: Proceedings of the 3rd International Conference on Mathematics: Pure, Applied and Computation, Surabaya, Indonesia, Paper No. (974), , 012020. Chen, J., Hu, Z., Wan, D., Xiao, Q., 2018. Comparisons of the dynamical characteristics of a semi-submersible floating offshore wind turbine based on two different blade concepts. Ocean. Eng. 153, 305–318. Elginoz, N., Bas, B., 2017. Life cycle assessment of a multi-use offshore platform: combining wind and wave energy production. Ocean. Eng. 145, 430–443. Fleming, P.A., Gebraad, P.M.O., Sang, L., Wingerden, J.W.V., et al., 2014. Evaluating techniques for redirecting turbine wakes using SOWFA. Renew. Energy 70 (5), 211–218. Fleming, P., Gebraad, P.M.O., Lee, S., Wingerden, J., et al., 2015. Simulation comparison of wake mitigation control strategies for a two-turbine case. Wind Energy 18 (12), 2135–2143. Gebraad, P.M.O., Fleming, P., Van Wingerden, J.W., 2015. Comparison of actuation methods for wake control in wind plants. In: Proceedings of the 2015 American Control Conference, Chicago, USA, pp. 1695–1701. GWEC, 2018. Global Wind Statistics 2017. GWEC 2018, Brussels, Belgium. Hou, P., Hu, W., Soltani, M., Chen, C., et al., 2017. Combined optimization for offshore wind turbine micro siting. Appl. Energy 189, 271–282. Kang, J., Sun, L., Sun, H., Wu, C., 2017. Risk assessment of floating offshore wind turbine based on correlation-FMEA. Ocean. Eng. 129, 382–388. Karimi, M., Hall, M., Buckham, B., Crawford, C., 2017. A multi-objective design optimization approach for floating offshore wind turbine support structures. J. Ocean Eng. Mar. Energy 3 (1), 69–87. Meghlaoui, I., Dobrev, I., Massouh, F., Benretem, A.O., et al., 2017. Computationally inexpensive free vortex method to obtain vortex core position in the wake of a horizontal axis wind turbine. Int. J. Fluid Mech. Res. 44, 427–443. Miao, W., Li, C., Pavesi, G., Yang, J., et al., 2017. Investigation of wake characteristics of a yawed HAWT and its impacts onthe inline downstream wind turbine using unsteady CFD. J. Wind Eng. Ind. Aerod. 168, 60–71. Miao, W., Li, C., Yang, J., Yang, Y., et al., 2016. Numerical investigation of wake control strategies for maximizing the power generation of wind farm. J. Sol. Energy Eng. 138 (3), 1–7. National Renewable Energy Laboratory (NREL), 2018, (URL): < https://nwtc.nrel. gov/ > . Nedjari, H.D., Guerri, O., Saighi, M., 2017. CFD wind turbines wake assessment in complex topography. Energy Convers. Manag. 138, 224–236. NREL, 2009. Definition of a 5-MW Reference Wind Turbine for Offshore System Development. NREL 2009, Golden, Colorado. Puneet, V., Yunjun, X., Kuo, C.L., 2017. Optimal power planning of wind turbines in a wind farm. U.S. J. Elec. Power 6 (2), 7–15. Shakoor, R., Hassan, M.Y., Raheem, A., Wu, Y.K., 2016. Wake effect modeling: a review of wind farm layout optimization using Jensen׳s model. Renew. Sustain. Energy Rev. 58, 1048–1059. Son, E., Lee, S., Hwang, B., Lee, S., et al., 2014. Characteristics of turbine spacing in a wind farm using an optimal design process. Renew. Energy 65 (5), 245–249. Sorensen, J.N., Shen, W.Z., 2002. Numerical modeling of wind turbine wakes. J. Fluid Eng. 124 (2), 393–399. Tian, W., Ozbay, A., Hu, H., 2018. An experimental investigation on the wake interferences among wind turbines sited in aligned and staggered wind farms. Wind Energy 21 (2), 100–114. Troldborg, N., 2008. Actuator Line Modeling of Wind Turbine Wakes. Technical University of Denmark, Copenhagen, Denmark. Wimshurst, A., Willden, R.H.J., 2016. Extracting lift and drag polars from blade-resolved computational fluid dynamics for use in actuator line modelling of horizontal axis turbines. Wind Energy 20, 815–833. Yang, Y., Ye, K., Li, C., Michailides, C., et al., 2018. Dynamic behavior of wind turbines influenced by aerodynamic damping and earthquake intensity. Wind Energy 21 (5), 303–319.
In Fig. 13, we can find that the greater the absolute value of the tilt angle, the more obvious the wake deviation is; as a result, the effect of the upstream wind turbine on WT2 becomes feebler. Hence, the quality of inflow of WT2 turns higher, and the output power remarkably improves. This fits well to Figs. 10b and 11. Besides, in Fig. 10b, the total output power of plus tilt angles is about one hundred thousand watts more than that of the corresponding minus tilt angles. This is realistic and can be interpreted according to Fig. 13. That is to say, when the tilt angle is plus, the wake of WT1 deviates downwards, and enhanced by gravity, it will further increase the output power of WT2. While the tilt angle is minus, the wake of WT1 deviates upwards, and the deviation is weakened by gravity, so the output power of WT2 turns less. 5. Conclusions In this paper, we have modified the standard solver pisoFoam in the open source software OpenFOAM and developed a new solver NewTurbinepisoFoam. On this basis, we conducted computational simulations for the NREL 5WM wind turbines in an offshore wind farm. Two control strategies of wake deviation were adopted to simulate 24 operating conditions. The results demonstrate an instructional significance for the offshore wind farm in operating wind turbines. By numerical analysis, the following conclusions can be drawn. (1) The power of wind turbines, flow fields and wake deviation have been simulated with relatively far less computing resources and time. It indicates the present modified solver has good accuracy and extensive applicability. (2) The influence of wake from the upstream wind turbine on the downstream wind turbine cannot be negligible. By controlling the deviation of the wake from the upstream wind turbine, we could effectively weaken the impact of the wake on the performance of the downstream wind turbine. (3) Compared with the tilt control strategy, the yaw control strategy could attain more total output power of the offshore wind farm. With regard to the tilt control strategy, plus tilt angles are better than the minus. (4) There is an optimal angle, generally being the 30°of the deviation angle, for both the yaw and tilt control strategy with regard to the total output power of the offshore wind farm. Under these circumstances, the output power of the upstream and the downstream wind turbines are all considerable. (5) The present work has the potential to be extended to a simulation of an offshore wind farm with hundreds of wind turbines. Above all, it can be directly applied to the real offshore wind farms and is likely
801