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General introduction to wind turbines
Chapter 1
General introduction to wind turbines Chapter outline 1.1 Wind: a renewable energy sources 1.2 Wind turbine basic concepts and classifications 1.3 Aerodynamics and turbulence
1.1
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1.4 Betz limit 1.5 Concluding remarks References Further reading
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Wind: A renewable energy sources
Energy is an essential part of human life, and affecting many sectors including residence, transportation, agriculture, commercial and industrial activities, etc. Due to rapidly increasing demand for power generation, heat production and transport fuels manufacture, the world primary energy demand is increased by 55% between 1990 and 2013. It is projected to grow by 45% under the current policies scenario. This continues the implementation of existing energy measures and policies; 32% under the new policies scenario, which assumes more cautious policies implementation are proposed. And approximately 12% is expected under the 450 scenario, which has achieved 50% probability of limiting global temperature increase within 2 °C [1]. The strong growth in energy demand has triggered increased concern for energy security and environment sustainability. Together with constantly growing demand, it has shaped a new craving for alternative energy sources that are able to supply for escalating energy demand with minimal impact on the environment. As the global energy demand keeps increasing, the supply of fossil fuels is diminishing. The price of energy continues to rise. To keep up with the global energy demand, most of alternative energy sources being considered are renewable ones, including solar, wind, wave, biomass, geothermal and hydro energies [2]. Renewable energy supplied around 19.1% of energy consumption globally in 2013, as shown in Fig. 1.1, and contributed 22.8% of global electricity generation by the end of 2014 (see Fig. 1.2). Renewable energies’ contributions in terms of global energy consumption and electricity generation both maintain a strong growth for many decades [3]. Considering the total primary energy Wind Turbines and Aerodynamics Energy Harvesters. https://doi.org/10.1016/B978-0-12-817135-6.00001-6 © 2019 Elsevier Inc. All rights reserved.
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FIG. 1.1 Estimated renewable energy share of global final energy consumption, 2013. (Adapted from P. Ren, Renewables 2015 global status report, REN21 Secretariat, Paris, France, 2015.)
FIG. 1.2 Estimated renewable energy share of global electricity production, end-2014. (Adapted from P. Ren, Renewables 2015 global status report, REN21 Secretariat, Paris, France, 2015.)
demand, the share of renewable energies holds at about 15% throughout the period to 2040 under the current policies scenario; increases to 19% in 2040 under the New Policies Scenario; and has to reach nearly 30% to achieve goals set under the 450 Scenario [1]. The importance of renewable energy is clearly demonstrated. Among various renewable energy sources, wind energy and hydropower are the most dominant energy sources in terms of energy generation. Wind energy becomes the most widely implemented non-hydro electricity-generating renewable energy source globally (see Fig. 1.3) [4]. Examining wind energy industry by regions, it reveals that OECD (Organization for Economic Co-operation and Development) Europe is the leading player in offshore wind generation industry, while OECD Americas, OECD Europe and China are all very active in onshore wind power industry [5]. Due to the fact that these different countries are driven by the major motivations such as preserving environmental sustainability and reducing greenhouse
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FIG. 1.3 Estimated renewable energy share of global electricity production, end-2014. (Adapted from N.M. Han, Experimental and Numerical Evaluation of the Performance of Electromagnetic Miniature Energy Harvesters Driven by Air Flow (Ph.D. thesis), Nanyang Technological University, Singapore, 2017.)
200000
500000
400000
Global Cumulative Installed Wind Capacity(MW) Global Annual Installed Wind Capacity(MW) 150000
300000 100000 200000 50000 100000
0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Global Annual Installed Wind Capacity(MW)
Global Cumulative Installed Wind Capacity(MW)
gases emission, global wind power generation shows a rapid growth during the past two decades, as shown in Fig. 1.4 [6]. Under such high growth rate, the global cumulative wind capacity is expected to reach 1,684,074 MW under new policy scenario by the year 2050. And the corresponding capacity under moderate scenario and advanced scenario are 2,672,231 MW and 4,042,475 MW, respectively (see Fig. 1.5) [7]. In this book, we concentrate on wind turbines (miniature, bladeless, off-shore, or on-shore) and the spin-off application of aerodynamic energy harvesters used to generate electricity. Although the wind is ‘free’ and renewable, modern wind turbines are more expensive and suffer from one obvious drawback in comparison with other power generation devices: they produce electrical power only when the wind is blowing. Thus the power output of
0
Year
FIG. 1.4 (A) Global annual installed wind capacity 2000–2015. (B) Global cumulative installed wind capacity 2000–2015. (Adapted from Global Wind Report 2015—Annual market update, Global Wind Energy Council, 2015.)
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Wind turbines and aerodynamics energy harvesters
FIG. 1.5 Global cumulative wind power capacity projection (GW). (Adapted from Global Wind Energy Outlook 2014, Global Wind Energy Council, 2014.)
a wind turbine is inherently unsteady. Furthermore, the wind turbines need to be located where the wind blows, which is often far from traditional power grids, requiring construction of new high-voltage power lines. This is especially true for off-shore wind turbines. Nevertheless, wind turbines are expected to play an ever-increasing role in the global supply of energy for the future. In the following sections, the basic concepts and classifications of wind turbines are introduced first. The aerodynamics characteristics including turbulence model and Betz limit of wind turbines are then discussed.
1.2 Wind turbine basic concepts and classifications Wind power has been used in the past in a few different ways, such as sailing, windmills and wind turbine, etc. In modern days, a large-scale wind turbine is an energy-converting device that transforms the wind energy into mechanical energy and in turn into electrical energy [8]. Wind energy is kinetic energy of flowing air. The amount of available wind kinetic energy depends on two factors, air mass and air flow speed V. Instead of measuring air mass, it is more convenient to measure air density, thus it is more practical to find wind power (Eq. 1.1) [9]. If we define the disk area (swept area) A of a wind turbine as the area normal to the wind flow direction swept out by the blades as they are rotat˙ available in the blade swept area is detering, then the available wind power w mined as the rate of change of the wind kinetic energy: w_ available ¼
dðmV 2 =2Þ ρAV 3 ðAir densityÞðDisk=swept areaÞðWind speedÞ3 ¼ ¼ 2 2 dt (1.1)
It is apparent that the available wind power is proportional to the swept/disk area and also proportional to the cube of the wind speed. Doubling the wind
General introduction to wind turbines Chapter
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speed (for example choosing a region where the turbine can be exposed to higher-speed wind) or the turbine blade diameter will lead to 8 or 4 times as much available wind power. Additionally, wind power density is another comprehensive index to evaluate various wind turbines at different locations for comparison. It is the available wind power in moving air through a unit area of perpendicular cross-sectional plane within a period [8] as defined in Eq. (1.2) with a unit of W/m2. It can be used to evaluate the effectiveness of wind energy harvester in utilisation of space. Wind power density ¼ ẇavailable =A ¼
ðAir densityÞðWind speedÞ3 2
(1.2)
Eq. (1.2) reveals that (1) The wind power density is linearly proportional to the air density. Colder air has a larger wind power density than warmer air blowing at the same speed. However, this density effect is typically insignificant. (2) The wind power density is proportional to the cube of the wind speed. Doubling the wind speed increases the wind power density by a factor of 800%. This is the main reason why wind farms are located where wind speed is high! Eq. (1.2) provides an instantaneous value on wind power density. It is known that the wind speed various dramatically throughout the day and through the year! For this, it is a general practice to define the average wind power density as 1 Average wind powerdensity ¼ w_ available =A ¼ ρavg V 3 αe 2
(1.3)
where αe is the energy patter factor. It is a correction factor, which is related to the annual average wind speed V (basing on hourly average) and the total number N ¼ 8760 of hours in a year. αe is defined as 1 XN 3 V (1.4) αe ¼ n¼1 n NV From an engineering point of view, if the average wind power density is <100 W/m2, then the location is considered poor for construction of wind turbine. A good location is associated with 400 W/m2 and best location is above 700 W/m2. There are other factors affecting the choice of a wind turbine site selection. These include (1) atmospheric turbulence intensity, terrain, obstacles (trees, building et al.), environmental impact et al. Further details can be found in Ref. [20]. For comparison and analysis purposes, we define the aerodynamic efficiency of a wind turbine as Cp ¼
w_ rotor shaft output w_ rotor shaft output ¼ w_ available ρAV 3 =2
(1.5)
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It describes the fraction of available wind power that is extracted by the turbine blades. Cp is commonly known as the power coefficient. It is not complicated to calculate the maximum possible power coefficient for a wind turbine. This will be introduced in the following chapter. Typically, wind turbines can be classified by its axis of rotation, such as horizontal axis wind turbines (HAWT) and vertical axis one (VAWT). HAWTs are those whose axes of rotation are horizontal or nearly horizontal to the ground and almost parallel to the wind direction [9]. Most of the commercial wind turbines are HAWTs [10, 11]. Those include the most commonly seen propeller turbines, which are lift-type that work based on the lift force on the blades [9]. Unlike vertical axis wind turbines (VAWTs), HAWTs are preferred in electricity generation due to relatively higher energy conversion efficiencies [11]. There are a number of advantages involved in HAWTs [10]: l
l
l l
l
HAWT is one of the most stable and commercially applied wind turbine designs. HAWT produces electrical power resulted from relatively lower cut-in wind speed and involves with a higher energy conversion efficiency. It is possible to utilise them at higher elevation using taller towers. HAWT performs better under fluctuating wind speed due to better angle of attack control. There is easier furling by turning the HAWT’s rotor away from wind stream.
Unfortunately, there are some inherent drawbacks as well [10]: l l l l
HAWTs require yaw drives to turn the turbine toward oncoming wind. Stronger structural support is needed for a heavy generator and a gearbox. Installation and maintenance costs are higher due to a greater tower height. Taller towers are detrimental to wind farms’ visual acceptability.
In contrast, when a wind turbine’s axis of rotation is vertical to the ground and nearly perpendicular to the wind direction, the turbine is classified as an example of VAWT [9, 10]. Compared with HAWTs, VAWTs are involved with the following distinct features [10]: l l
l l
VAWT is insensitive to the wind direction, thus no yaw control is necessary. Structural requirement is less stringent as heavy components like gearbox and generators can be placed as close as to the ground level. Maintenance is easier at ground level. Pitch control is not required for VAWTs.
However, VAWTs are not so popular commercially due to some major disadvantages [10] as following: l
l
Generally, VAWTs are not able to be self-starting. Hence additional motor may be required. VAWTs are closer to the ground, where wind speed is lower than higher elevations.
General introduction to wind turbines Chapter
l
l
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Efficiency is limited as the blades have to pass through aerodynamically dead zones in a complete cycle. Guy wires may be required to support the structure, and may cause inconveniences for installation and maintenance.
Most of wind energy industry share is contributed by large-scale wind turbines, which are generally HAWTs. VAWTs also attract increasing attention for their utilisation as small- to medium-scale wind energy harvesting units [11]. An alternative way to classify wind turbines is by the mechanism that provides torque to the rotating shaft: lift or drag. By now, none of the VAWT designs or drag-type designs have achieved the efficiency or success of the lift-type HAWT. This is the main reason why the majority of wind turbines being built around the world are of this type. Every wind turbine has a characteristic power performance curve. A typical one is illustrated in Fig. 1.6, in which electrical power output is plotted as a function of wind speed V at the height of the turbine axis. We can identify 3 key locations on the wind-speed scale: l
l
l
Cut-in speed is the minimum wind speed at which useful power can be produced. Rated speed is the wind speed that delivers the rated power, typically the maximum power Cut-out speed is the maximum wind speed at which the wind turbine is designed to produce power. At wind speeds greater than the cut-out speed, the turbine blades are sopped by some type of braking mechanism to avoid damage and for safety issues. The short section of the dashed red line indicates the power that would be produced if the cut-out were not implemented.
FIG. 1.6 Typical wind turbine power performance curve with the definitions of cut-in, rated and cut-out speeds.
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The wind turbine classification can also be done basing on (1) the relative position of wind turbine, (2) the wind turbine capacity, (3) the type of generator used, (4) the power supply mode, and (5) the turbine location [8] for example, onshore and off-shore. Further details can be found in Ref. [20].
1.3 Aerodynamics and turbulence In order to convert wind kinetic energy into mechanical energy more efficiently, modern wind turbine rotors [12–14] are generally made into airfoils’ shape as shown schematically in Fig. 1.7. Due to the airfoil curvature, air flowing along upper curvature will be at a higher velocity due to a longer path travelled by air particles compared with lower streamlines. Based on Bernoulli’s theorem, the higher velocity is compensated by a reduction in pressure. The pressure difference between the two surfaces of the airfoil will generate a lift force, L (see Fig. 1.7). Meanwhile, there will be a drag force D acting on the airfoil exerted by air flow. The net force F on the airfoil will be the resultant force of drag and lift forces [9, 10]. The lift is the force perpendicular to direction of oncoming airflow. And it is formed due to pressure difference between the upper and lower airfoil surfaces [11]. In contrast, drag force is the force being parallel to the direction of oncoming air flow [11]. It is formed partially due to the unequal pressure on the airfoil surfaces, and partially due to the viscous friction forces on the surfaces. To describe these forces, lift (CL) and drag coefficient (CD) and momentum (CM) coefficients are widely used in the literature. They are defined as: CL ¼
FL FD FM , CD ¼ ,CM ¼ 1=2ρv2 c 1=2ρc2 c 1=2ρv2 c2
FIG. 1.7 Cross-sectional view of airfoil.
(1.6)
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where ρ is the air density, v is the air flow velocity and c is the chord length. FL, FD, and FM are the lift, drag force, and momentum, respectively. The tip speed ratio (λ) is another important parameter of wind turbine, and it is defined as the ratio of the blade tip tangential speed ωR to the speed of fluid flow V. Its definition can be expressed as: λ¼
ωR V
(1.7)
where ω is the angular velocity of the wind turbine rotor, R is the radius of the turbine rotor and v is the wind speed. Eq. (1.7) expressed with Reynolds number will give: λ¼
ωR ðμRe=ρDh Þ
(1.8)
where DH is the hydraulic diameter of the wind turbine in meter. μ is fluid dynamic viscosity. Generally a higher tip speed ratio indicates the wind turbine is associated with a higher efficiency, but a higher level of noise will be produced as well. Re is Reynolds number, which is typically applied to determine the flow conditions: laminar or turbulent. Since most of wind turbines are operated under turbulent flow conditions [15, 16]. It is necessary to introduce some fundamental concepts related to turbulence. Turbulence is a condition in fluid flow where the velocity, pressure and other flow properties at given points in the turbulent region change stochastically with time. The Reynolds number (Re) of a fluid flow is defined as: Re ¼
ρVL μ
(1.9)
where: ρ: the density of the fluid, V: characteristic velocity of the flow, L: characteristic length of the flow, μ: the dynamic viscosity of the fluid. Re determines whether it is turbulent, with the onset of turbulent flow marked by a value of Re higher than a critical value. Due to the randomness of turbulent flow, it is not easily represented by simple formulae. The common practice in CFD is to decompose the flow properties, represented generally by φ (t), into a steady mean value Φ with a fluctuating component φ’(t) superimposed on it, a technique known as Reynolds decomposition is given as: φðtÞ ¼ Φ + φ0 ðtÞ
(1.10)
Consider the instantaneous continuity and Navier–Stokes momentum equations [15] with a velocity vector u, comprising the Cartesian components u, v and w: div u ¼ 0
(1.11)
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∂u 1 ∂P + div ðuuÞ ¼ + ν div ð grad uÞ ∂t ρ ∂x
(1.12)
∂v 1 ∂P + div ðvuÞ ¼ + ν div ð grad vÞ ∂t ρ ∂y
(1.13)
∂w 1 ∂P + div ðwuÞ ¼ + ν div ð grad wÞ ∂t ρ ∂z
(1.14)
Applying Reynolds decomposition (Eq. 1.11) to the velocity vector u and its components and pressure P: u ¼ U + u0 ,u ¼ U + u0 , v ¼ V + v0 ,w ¼ W + w0 and p ¼ P + p0 From Eqs. (1.12)–(1.14), for the case of an incompressible flow, div U ¼ 0
(1.15)
Applying Reynolds decomposition to the momentum equations and re-arranging so that the Reynolds stress terms are grouped together: 2 3 02 ∂ ρu0 v0 ∂ ρu0 w0 5 ∂U 1 ∂P 1 4∂ ρu + + + div ðUUÞ ¼ + ν div ð grad U Þ + ∂y ∂z ∂x ∂t ρ ∂x ρ
(1.16) 2 3 ∂ ρv0 2 ∂ ρv0 w0 5 ∂V 1 ∂P 1 4∂ ρu0 v0 + + + div ðVUÞ ¼ + ν div ð grad V Þ + ∂x ∂z ∂y ∂t ρ ∂y ρ (1.17) 3 2 ∂ ρw0 2 ∂ ρv0 w0 ∂W 1 ∂P 1 4∂ ρu0 w0 5 + + + div ðWUÞ ¼ + ν div ð grad W Þ + ∂z ∂x ∂y ∂t ρ ∂z ρ (1.18)
The above four equations are known as the Reynolds-averaged NavierStokes (RANS) equations. Equations for time-averaged scalar properties with similar extra turbulent terms can be derived in the same manner. These additional terms are then modelled with turbulence models. Equations for compressible flow are slightly different due to the need to consider non-constant density. However, since the wind turbine aerodynamics research involves incompressible flow in most cases, compressible flow is not elaborated here. To handle the Reynolds stresses, Boussinesq proposed the use of turbulent viscosity or eddy viscosity μt in the usual Newtonian viscosity equation using the mean flow velocities: ∂Ui ∂Uj (1.19) + τij ¼ ρu0i u0j ¼ μt ∂xj ∂xi
General introduction to wind turbines Chapter
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where i and j represent two perpendicular Cartesian directions. In the literature, there are many turbulence models available, such as 1-equation Spalart-Allmaras (SA) [40] model, 2-equation k-ε, k-ω, SST k-ω and 7-equation Reynolds stress model (RSM). In RSM, the Reynolds stresses ρu00i u00j are directly computed. The transport of the Reynolds stress equation can be illustrated as: Rate change of Transport by Rate of Transport by Rate of + ¼ + the Reynolds stress convection production diffusion dissipation +
Transport due to turbulent Transport due + pressure strain interaction to rotation
On the right hand side, the diffusion, the dissipation, and the pressure-strain interaction terms are needed to be modeled. For the pressure-strain term, the linear pressure-strain model, quadratic pressure-strain model, and the stress omega model are widely used. As this model considers the anisotropic nature of turbulence, it has six additional partial differential equations and one additional transport equation for the six independent Reynolds stresses, which turns it into a seven-equation model. However, the additional equations and the highly coupled equations also mean a significant increase in the computational cost, which may be comparable with LES. The 1-equation SA model was developed for airfoil predictions [35]. It has been applied to the well-known NREL phase VI HAWT rotor [36, 37]. It has been shown [36, 37] that the SA closure model cannot re-matches the surface distribution and reproduce the flow separation accurately. SA model has also been attempted to simulation aerodynamic loads on VAWTs [38, 39]. However, the numerical and experimental results on predicting near wake velocity profiles are found to be dramatically different for a 3-bladed H-rotor. These findings confirm that the SA turbulence model is not applicable to simulate VAWT. Although all length scales of turbulence in steady or unsteady mode may be simulated in RANS (Reynolds-averaged Navier-Stokes) methods, the 2equation models, especially, k-ε model are widely used and validated [15]. In this model, the turbulent kinetic energy k and the rate of dissipation of turbulent kinetic energy ε are used to obtain the eddy viscosity μt as follows: μt ¼ ρCμ
k2 ε
The two equations for solving k and ε are: ∂ðρkÞ μ + div ðρkUÞ ¼ div t grad k + 2μt Sij Sij ρε σk ∂t ∂ðρεÞ μ ε ε2 + div ðρεUÞ ¼ div t grad ε + C1ε 2μt Sij Sij C2ε ρ σε k ∂t k
(1.20)
(1.21) (1.22)
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where Sij Sij is the dot product of the rate of deformation tensor of the mean flow. The five constants in Eq. (1.20) to Eq. (1.22) are obtained by fitting data from a wide range of turbulent flows as follows: Cμ ¼ 0:09; σ k ¼ 1:00; σ e ¼ 1:30; C1ε ¼ 1:44; C2ε ¼ 1:92 Summing the normal Reynolds stress terms in Eqs. (1.16)–(1.18), it is found that it is exactly equal to twice the negative of turbulent kinetic energy per unit 2 2 2 0 0 0 volume: ρ u + v + w ¼ 2ρk. Hence assuming isotropic behaviour of the normal Reynolds stresses, each of them is given a value of (2ρk)/3. However, it is to be noted that this assumption is not always accurate. This method is expressed in the modified Boussinesq expression: ∂Ui ∂Uj 2 ρkδij + (1.23) τij ¼ ρu0 i u0 j ¼ μt ∂xj ∂xi 3 where σij, the Kronecker delta, is 1 if i ¼ j and zero if i 6¼ j. Although the k-ε model is widely used, it does not perform well in unconfined flows, flows with large strains (such as those over curved surfaces), rotating flows and flows in non-circular ducts. As reported by Murakami [16] et al., its key shortcoming arises from the inability of the term for turbulence kinetic energy production to take on negative values, thus over-predicting the turbulence level in front of a forward facing step bluff body. Due to this overprediction, the observed re-circulating flow above the bluff body is also not reproduced by the model. Hence, the k-ε model is not recommended for flows with separation. For the present research involving a cross flow turbine, the blades undergo full circles of angle of attack variation during normal operation, hence flow separation is inevitable. A technique for reducing the problem of excessive turbulence prediction according to Durbin and Reif [17] is to impose bounds on the turbulent viscosity, for example, by limiting it to: Cμ k2 αk , (1.24) μt ¼ min ε j Sj pffiffiffi with α 1= 6. For the flows encountered in the present research, the Shear Stress Transport (SST) k-ε model of Menter [15, 18] is more appropriate. This model arose from the original k-ε model of Wilcox [15, 19]. In this model, the turbulence frequency ω (originally named the specific dissipation rate by Wilcox) is defined as: ω ¼ ε=k
(1.25)
μt ¼ ρk=ω
(1.26)
Thus the eddy viscosity is:
General introduction to wind turbines Chapter
The transport equations for solving k and ω are:
∂ðρkÞ μt grad k + Pk β∗ ρkω + div ðρkU Þ ¼ div μ + σk ∂t
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(1.27)
2 ∂Ui δij is the rate of production of turbulent kinetic where Pk ¼ 2μt Sij Sij ρk 3 ∂xj energy, and Sij Sij is the dot product of the rate of deformation tensor of the mean flow.
∂ðρωÞ μ 2 ∂Ui δij + div ðρωU Þ ¼ div μ + t grad ω + γ 1 2ρSij Sij ρω σω ∂xj ∂t 3 β1 ρω2 (1.28) However, the model is very dependent on the proper setting of ω at the free stream boundary condition. Thus Menter developed the SST model. The model uses the standard k-ε model (which is less sensitive to assumed values in the free stream) in the fully turbulent region far from the wall and transformation into a k-ω model in the near wall region. The k-equation is unchanged from Wilcox’s model but the transformed ω-equation is as follows:
∂ðρωÞ μ 2 ∂Ui δij + div ðρωU Þ ¼ div μ + t grad ω + γ 2 2ρSij Sij ρω σ ω,1 ∂xj ∂t 3 ρ ∂k ∂ω 2 β2 ρω + 2 σ ω, 2 ω ∂xk ∂xk (1.29) To limit over prediction of shear stress in adverse pressure gradient boundary layers, limiters on the eddy viscosity μt and rate of production of turbulent kinetic energy Pk are employed. Blending functions give a smooth transition between the far field and near wall. More recently, Menter improved the SST model with revised model constants as follows: σ k ¼ 1:0; σ ω,1 ¼ 2:0; σ ω,2 ¼ 1:17; γ 2 ¼ 0:44; β2 ¼ 0:083; β∗ ¼ 0:09; Additionally, CFX also incorporates the curvature correction technique of Spalart and Shur [15], thus making the solver more suitable for the aerodynamics research on a rotating wind turbine turbine. RANS turbulence models use a single model to describe the whole range of turbulence. In many aerodynamics engineering problems, the numerical predictions are acceptable. However, the results of RANS have also revealed that perfect predictions with a single model for various applications seem to be formidable. One reason contributing to that is the different characteristic of turbulence with different scales. For example, the behaviour of large eddies whose energy comes from the main flow is highly dependent on macroscopic features, i.e. the flow domain geometries and boundary conditions. In other words, they
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are anisotropic. In contrast, the small-scale eddies have a universal behaviour and hence are almost isotropic. When the large eddy and the small eddy are treated in the same way, unsatisfactory predictions are not surprising. This is the situation happening in RANS. Although the RANS methods are popular in the wind turbine aerodynamics communities. However, some drawbacks and weakness of the RANS methods on their inherent incapability of capturing massive flow separation and vortex shedding have been clearly highlighted [32]. LES [30, 31], however, is an approach that tries to solve this problem by dealing with large and small eddies separately. The variables in LES are decomposed by a spatial filter operation into two parts: the resolved and the modeled. Unlike RANS, they are not the mean value and the fluctuation [32]. The resolved corresponds to the unsteady fields with large scales, whereas the modeled (or the sub-grid scale) relates to the universal small eddies. After filtering the governing equations, several new terms called sub-grid-scale (SGS) stresses arise. The SGS stresses are the results of the small eddies and their interactions with the large scales, which need to be modeled. This makes the computational cost of LES considerable large, compared with RANS [41]. The Smagorinsky model [33] computes the eddy viscosity and the sub-grid kinetic energy as: 8 2 e > e ¼ C ρ Δ μ S > μ t > > < 2 (1.30) k ¼ Ck Δ2 Se > qffiffiffiffiffiffiffiffiffiffi > > > : Se ¼ Seij Seij where Seij is the density-weighted strain rate tensor, Cμ and Ck are the model coefficients, which are computed by a dynamic procedure proposed by Germano et al. [34]. A good review on RANS and LES studies of wind turbine aerodynamics can be found in Refs. [30–32]. The LES approach [41] could be widely implemented in the near future due to its demanding computational expense. The main challenge of LES is to obtain good resolution of wall-bounded layer at high Reynolds number. Approximately 90% of the computational grids is distributed over the near-wall regions as Re > 105. To reduce the high computational cost, a hybrid RANS-LES method was proposed in wind turbine aerodynamics communities. It is a technique to bridge the gap between the less accurate RANS and more computational costly LES approach. The hybrid method could be a remedy to wind turbines in complex flow conditions involving with flow separation and vortex shedding. The application of the hybrid method to wind turbine aerodynamics is reviewed and discussed in Ref. [32].
1.4 Betz limit In 1920s, Albert Betz (1885–1968) predicted the ideal and frictionless efficiency of a wind turbine by applying linear momentum theory on a simple
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one-dimensional model [11, 20]. The model consists of a rotor represented by a uniform “actuator disk” confined in the assumed control volume. The control volume is defined by the surface and the cross sections of a stream tube in which the fluid passes through the rotor disk. The rotor “actuator disk” creates a pressure discontinuity of fluid flowing through it. A schematic illustration of the simplified model is shown in Fig. 1.8. This analysis based on the actuator disk model adopts the following assumptions: l
l l l
The fluid flow is ideal across the control volume, meaning that it is steady, homogenous, inviscid, incompressible and irrotational. There is an infinite number of blades, thus fits the actuator disk description. Both flow and thrust are uniform across the disk area. Undisturbed ambient static pressure is assumed for the static pressure far upstream and downstream of the rotor disk.
In order to attain the net force on the contents of the control volume, the conservation of linear momentum is applied. The net force is equal in magnitude but in opposite direction to the thrust, Fthrust, which is the force exerted on the turbine by the wind flow. For one-dimensional, incompressible and timeinvariant flow, as a linear momentum is conserved, the thrust can be obtained from the change in momentum of air flow. Fthrust ¼ V1 ðρAV Þ1 V4 ðρAV Þ4
(1.31)
where the subscript is indicating cross section location as labeled in Fig. 1.8. ρ is the air density, A is the cross sectional area of the rotor disk and V is the air velocity of the flow. _ where m_ is the As the flow is assumed to be steady, ðρAV Þ1 ¼ ðρAV Þ4 ¼ m, mass flow rate. Hence the thrust Fthrust can be written as: Fthrust ¼ m_ ðV1 V4 Þ
(1.32)
FIG. 1.8 Control volume for actuator disk model of wind turbine. V is air velocity; 1, 2, 3 and 4 indicate locations.
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As no work is done on either side of the turbine disc, the Bernoulli function is applied to the two parts of control volume, upstream and downstream of the disk. On the upstream side of the disk: 1 1 p1 + ρv21 ¼ p2 + ρv22 2 2
(1.33)
where p is the pressure and the subscript is denotes location. Meanwhile, on the downstream side of the disk: 1 1 p3 + ρv23 ¼ p4 + ρv24 2 2
(1.34)
As it is assumed that the pressures far upstream and far downstream are equal (p1 ¼ p4), and the velocity remains the same after fluid passes the disk (V2 ¼ V3), the thrust can also be expressed with the different pressure between sides of the disk: Fthrust ¼ A2 ðP2 P3 Þ
(1.35)
Using Eq. (1.33) and. (1.34) to solve for (p2 p3) and substituting into Eq. (1.35) will give: 1 Fthrust ¼ ρA2 V12 V42 2
(1.36)
The thrust values from Eq. (1.35) and (1.36) should be equal, thus 1 V2 ¼ ð V1 + V 4 Þ 2
(1.37)
This means the fluid velocity are the rotor disk will be the average of the upstream and downstream velocities, as required by continuity and momentum. An axial induction factor, a, is defined to express the fractional decrease in wind velocity between the free stream and the rotor disk: a¼
V 1 V2 V1
(1.38)
The maximum possible value of a is a ¼ 1/2, as it requires V3 to decrease to zero. Therefore, the thrust at the turbine plane can be written as: 1 Fthrust ¼ ρAV12 ½4að1 aÞ 2
(1.39)
The power coefficient, defined as the ratio of power extracted to the total power available, can be defined in terms of a also: Cp ¼ 4að1 aÞ2
(1.40)
Fig. 1.9 shows the plot of power coefficient Cp at different values of the axial induction factor. It can be seen that power coefficient reaches a maximum value
General introduction to wind turbines Chapter
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FIG. 1.9 Power coefficient for an ideal Betz wind turbine model as axial induction factor varied.
of 0.593, which is known as the Betz limit for an ideal frictionless turbine. This theoretical maximum efficiency is difficult to be achieved practically for many reasons, such as: l l l l l
Pressure distribution at the rotor disc is not uniform. Viscous effect will lead to an aerodynamic drag. Vortices formed at the blades tips will lead to energy losses. Mechanical losses due to shaft friction. Other mechanical and electrical losses in the gearbox, generator, etc.
It is worth noting that Betz’s analysis on wind turbine efficiency is not limited to any particular type of wind turbines [21]. Fig. 1.10 shows the relationships between the turbine power coefficient and the tip speed ratios for different types of wind turbines. It shows power coefficient Cp as a function of the ratio of the turbine blade tip speed RΩ to wind speed V. Here ω is the angular velocity of the wind turbine blades and R is the radius. It can be seen from this graph that an ideal propeller-type wind turbine approaches the Betz limit, as ΩR/V approaches infinity. However, the power coefficient of real wind turbines reaches a maximum at some finite value of ΩR/V and then drops beyond that. It is obvious that the ‘best-efficient’ wind turbine is the high-speed HWAT, and that is why you see this type of wind turbines being implemented all around the world. For different wind turbine designs, the maximum power coefficient is achieved at different tip speed ratios [22]. This means the suitability of wind turbine design to a particular working environment must be considered [23, 24]. The above theoretical limitations are seen in practical wind turbines. A well optimized lift-based turbine such as the Pinson Cycloturbine has a peak CP of
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Wind turbines and aerodynamics energy harvesters
FIG. 1.10 The power coefficient as a function of tip speed ratio for different wind turbine machines designs. Note that in some previous publications [21], the efficiency curves of the American multiblade and the Savonius designs were inadvertently switched. (Adapted from M. Ragheb, A.M. Ragheb, Wind Turbines Theory-the Betz Equation and Optimal Rotor Tip Speed Ratio, INTECH Open Access Publisher, 2011.)
0.4 [25]. In contrast, cP for Savonious (drag-based) devices does not exceed 0.2 [26]. However, when selecting a turbine for deployment, one does not merely make a decision on the basis of its CP. For example, Blackwell, et al. [27] mentions that the less efficient Savonius turbine may find more applications in developing countries. Bos [28], when assessing the feasibility of the WindNok drag-based turbine, uses a weighted objectives method that includes suitability for Do-It-Yourself installation and likelihood of approval from authorities. Oy Windside Production Ltd. [29] uses a helical Savonius design as the basis for their highly durable products intended for implementing in harsh remote environments such as Antarctica where its simplicity, low cut-in wind speed, high survival wind speed are overriding factors.
1.5 Concluding remarks In summary, wind power as a promising renewable energy source is overviewed. It has great potential to be harnessed via optimally designed wind turbines. The fundamental concepts and classifications in wind turbine industries are then explained. There are two typical wind turbines basing on its axis of rotation. One is HAWT (horizontal axis wind turbine) and VAWT (vertical axis) with different power performance curves. As far as the turbine location
General introduction to wind turbines Chapter
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is concerned, wind turbines can be classified as on-shore and off-shore. The aerodynamics characteristics and turbulence models involved in studying wind turbines are then provided. Finally, the discussion on the Betz limit is included to show that the maximum power coefficient of a wind turbine is 59.3% in theory. This limit provide a guidance on optimising the design and performance of wind turbines. It was confirmed that all wind turbines applied in practice for power generation are found to be associated with a power coefficient below the Betz limit.
References [1] World Energy Outlook 2015, International Energy Agency (IEA), 2015. [2] D. Abbott, Keeping the energy debate clean: how do we supply the world’s energy needs? Proc. IEEE 98 (1) (2010) 42–66. [3] P. Ren, Renewables 2015 global status report, REN21 Secretariat, Paris, France, 2015. [4] N.M. Han, Experimental and Numerical Evaluation of the Performance of Electromagnetic Miniature Energy Harvesters Driven by Air Flow, PhD thesis, Nanyang Technological University, Singapore, 2017. [5] Medium-Term Renewable Energy Market Report 2015: Market Analysis and Forecasts to 2020, International Energy Agency (IEA), 2015. [6] Global Wind Report 2015—Annual market update, Global Wind Energy Council, 2015. [7] Global Wind Energy Outlook 2014, Global Wind Energy Council, 2014. [8] W. Tong, Wind Power Generation and Wind Turbine Design, Wit Press, 2010. [9] A. Hemami, Wind Turbine Technology, Cengage Learning, 2012. [10] S. Mathew, Wind Energy: Fundamentals, Resource Analysis and Economics, Springer, 2006. [11] Y.A. Cengel, J.M. Cimbala, Fluid Mechanics Fundamentals and Applications, fourth ed., McGraw Hill Eduction, New York, 2017. [12] E. Hau, Wind Turbines Fundamentals, Technologies, Application, Economics, Springer, 2000. [13] M.O.L. Hansen, Aerodynamics of Wind Turbines, fourth ed., Earthscan from Routledge, 2015. [14] P. Jamieson, Innovation in Wind Turbine Design, Wiley, 2011. [15] H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, second ed., Prentice Hall, 2007. [16] S. Murakami, A. Mochida, Y. Hayashi, Examining the k-ε model by means of a wind tunnel test and large eddy simulation around a cube, J. Wind Eng. Ind. Aerodyn. 35 (1990) 87–100. [17] P. Durbin, B. Pettersson Reif, Statistical Theory and Modeling for Turbulent Flows, second ed., Wiley, Chichester, 2010. [18] F.R. Menter, Two-equation eddy viscosity turbulence models for engineering applications, AIAA J. 32 (8) (1994) 1598–1605. [19] D.C. Wilcox, Reassessment of the scale-determining equation for advanced turbulence models, AIAA J. 26 (11) (1988) 1299–1310. [20] J.F. Manwell, J.G. McGowan, A.L. Rogers, Wind Energy Explained: Theory, Design and Application, John Wiley & Sons, 2010. [21] F.R. Eldridge, Wind Machines, Van Nostrand Reinhold Co., 1980 [22] M. Ragheb, A.M. Ragheb, Wind Turbines Theory-the Betz Equation and Optimal Rotor Tip Speed Ratio, INTECH Open Access Publisher, 2011. [23] S. Roy, U.K. Saha, Review on the numerical investigations into the design and development of Savonius wind rotors, Renew. Sust. Energ. Rev. 24 (2013) 73–83.
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[24] J. Kumbernuss, C. Jian, J. Wang, H. Yang, W. Fu, A novel magnetic levitated bearing system for vertical Axis wind turbines (VAWT), Appl. Energy 90 (1) (2012) 148–153. [25] R. Noll, N.D. Ham, H.M. Drees, N.L. B, 1 kW High Reliability Wind System Development, United States Department of Energy, Rocky Flats, 1982. [26] U.K. Saha, M.J. Rajkumar, On the performance analysis of Savonius rotor with twisted blades, Renew. Energy 31 (2006) 1776–1788. [27] B.F. Blackwell, R.E. Sheldahl, L.V. Feltz, Wind Tunnel Performance Date for Two- and Three-Bucket Savonius Rotors, Sandia Laboratories, Albuquerque, 1977. [28] J.E. Bos, Feasibility Study of the WindNok, TU Delft, Delft, 2010. [29] Windside Wind Turbine, [Online]. Available: http://www.windside.com/products, 2012. Accessed 20 June 2012. [30] D. Mehta, A.H. van Zuijlen, B. Koren, J.G. Holierhoek, H. Bijl, Large eddy simulation of wind farm aerodynamics: a review, J. Wind Eng. Ind. Aerodyn. 133 (1) (2014) 1–17. [31] R.C. Storey, J.E. Cater, S.E. Norris, Large eddy simulation of turbine loading and performance in a wind farm, Renew. Energy 95 (1) (2016) 31–42. [32] J. The, H. Yu, A critical review on the simulations of wind turbine aerodynamics focusing on hybrid RANS-LES methods, Energy 138 (1) (2017) 257–289. [33] J. Smagorinsky, General circulation experiments with the primitive equations, Mon. Weather Rev. 91 (3) (1963) 99–164. [34] M. Germano, U. Piomelli, P. Moin, W. Cabot, A dynamic localization model for large-eddy simulation of turbulent flows, Phys. Fluids 3 (1991) 1760–1765. [35] P. Spalart, S. Allmaras, A one-equation turbulence model for aerodynamic flows, in: 30th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, 1992. [36] J.Y. You, D.O. Yu, O.J. Kwon, Effect of turbulence models on predicting HAWT rotor blade performances, J. Mech. Sci. Technol. 27 (12) (2013) 3703–3711. [37] Y. Song, J.B. Perot, CFD simulation of the NREL phase VI rotor, Wind Eng. 39 (3) (2015) 299–309. [38] M. Nini, V. Motta, G. Bindolino, A. Guardone, Three-dimensional simulation of a complete vertical Axis wind turbine using overlapping grids, J. Comput. Appl. Math. 270 (2014) 78–87. [39] K. Pope, V. Rodrigues, R. Doyle, A. Tsopelas, R. Gravelsins, G.F. Naterer, et al., Effects of stator vanes on power coefficients of a zephyr vertical axis wind turbine, Renew. Energy 35 (5) (2010) 1043–1051. [40] M. Elkhoury, T. Kiwata, K. Nagao, T. Kono, F. Elhajj, Wind tunnel experiments and delayed detached eddy simulation of a thress bladed micro vertical axis wind turbine, Renew. Energy 129 (2018) 63–74. [41] G.E. Seach Chyr, Enhancement of Wind Turbine Performance by Installation above a Bluff Body, Ph.D. thesis, Nanyang Technological University, Singapore, 2014.
Further reading [42] N. Sedaghatizadeh, M. Arjomandi, R. Kelso, B. Cazzolato, M.H. Ghayesh, Modelling of wind turbine wake using large eddy simulation, Renew. Energy 115 (2018) 1166–1176.
General introduction to wind turbines Chapter outline 1.1 Wind: a renewable energy sources 1.2 Wind turbine basic concepts and classifications 1.3 Aerodynamics and turbulence
1.1
1 4 8
1.4 Betz limit 1.5 Concluding remarks References Further reading
14 18 19 20
Wind: A renewable energy sources
Energy is an essential part of human life, and affecting many sectors including residence, transportation, agriculture, commercial and industrial activities, etc. Due to rapidly increasing demand for power generation, heat production and transport fuels manufacture, the world primary energy demand is increased by 55% between 1990 and 2013. It is projected to grow by 45% under the current policies scenario. This continues the implementation of existing energy measures and policies; 32% under the new policies scenario, which assumes more cautious policies implementation are proposed. And approximately 12% is expected under the 450 scenario, which has achieved 50% probability of limiting global temperature increase within 2 °C [1]. The strong growth in energy demand has triggered increased concern for energy security and environment sustainability. Together with constantly growing demand, it has shaped a new craving for alternative energy sources that are able to supply for escalating energy demand with minimal impact on the environment. As the global energy demand keeps increasing, the supply of fossil fuels is diminishing. The price of energy continues to rise. To keep up with the global energy demand, most of alternative energy sources being considered are renewable ones, including solar, wind, wave, biomass, geothermal and hydro energies [2]. Renewable energy supplied around 19.1% of energy consumption globally in 2013, as shown in Fig. 1.1, and contributed 22.8% of global electricity generation by the end of 2014 (see Fig. 1.2). Renewable energies’ contributions in terms of global energy consumption and electricity generation both maintain a strong growth for many decades [3]. Considering the total primary energy Wind Turbines and Aerodynamics Energy Harvesters. https://doi.org/10.1016/B978-0-12-817135-6.00001-6 © 2019 Elsevier Inc. All rights reserved.
1
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FIG. 1.1 Estimated renewable energy share of global final energy consumption, 2013. (Adapted from P. Ren, Renewables 2015 global status report, REN21 Secretariat, Paris, France, 2015.)
FIG. 1.2 Estimated renewable energy share of global electricity production, end-2014. (Adapted from P. Ren, Renewables 2015 global status report, REN21 Secretariat, Paris, France, 2015.)
demand, the share of renewable energies holds at about 15% throughout the period to 2040 under the current policies scenario; increases to 19% in 2040 under the New Policies Scenario; and has to reach nearly 30% to achieve goals set under the 450 Scenario [1]. The importance of renewable energy is clearly demonstrated. Among various renewable energy sources, wind energy and hydropower are the most dominant energy sources in terms of energy generation. Wind energy becomes the most widely implemented non-hydro electricity-generating renewable energy source globally (see Fig. 1.3) [4]. Examining wind energy industry by regions, it reveals that OECD (Organization for Economic Co-operation and Development) Europe is the leading player in offshore wind generation industry, while OECD Americas, OECD Europe and China are all very active in onshore wind power industry [5]. Due to the fact that these different countries are driven by the major motivations such as preserving environmental sustainability and reducing greenhouse
General introduction to wind turbines Chapter
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FIG. 1.3 Estimated renewable energy share of global electricity production, end-2014. (Adapted from N.M. Han, Experimental and Numerical Evaluation of the Performance of Electromagnetic Miniature Energy Harvesters Driven by Air Flow (Ph.D. thesis), Nanyang Technological University, Singapore, 2017.)
200000
500000
400000
Global Cumulative Installed Wind Capacity(MW) Global Annual Installed Wind Capacity(MW) 150000
300000 100000 200000 50000 100000
0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Global Annual Installed Wind Capacity(MW)
Global Cumulative Installed Wind Capacity(MW)
gases emission, global wind power generation shows a rapid growth during the past two decades, as shown in Fig. 1.4 [6]. Under such high growth rate, the global cumulative wind capacity is expected to reach 1,684,074 MW under new policy scenario by the year 2050. And the corresponding capacity under moderate scenario and advanced scenario are 2,672,231 MW and 4,042,475 MW, respectively (see Fig. 1.5) [7]. In this book, we concentrate on wind turbines (miniature, bladeless, off-shore, or on-shore) and the spin-off application of aerodynamic energy harvesters used to generate electricity. Although the wind is ‘free’ and renewable, modern wind turbines are more expensive and suffer from one obvious drawback in comparison with other power generation devices: they produce electrical power only when the wind is blowing. Thus the power output of
0
Year
FIG. 1.4 (A) Global annual installed wind capacity 2000–2015. (B) Global cumulative installed wind capacity 2000–2015. (Adapted from Global Wind Report 2015—Annual market update, Global Wind Energy Council, 2015.)
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Wind turbines and aerodynamics energy harvesters
FIG. 1.5 Global cumulative wind power capacity projection (GW). (Adapted from Global Wind Energy Outlook 2014, Global Wind Energy Council, 2014.)
a wind turbine is inherently unsteady. Furthermore, the wind turbines need to be located where the wind blows, which is often far from traditional power grids, requiring construction of new high-voltage power lines. This is especially true for off-shore wind turbines. Nevertheless, wind turbines are expected to play an ever-increasing role in the global supply of energy for the future. In the following sections, the basic concepts and classifications of wind turbines are introduced first. The aerodynamics characteristics including turbulence model and Betz limit of wind turbines are then discussed.
1.2 Wind turbine basic concepts and classifications Wind power has been used in the past in a few different ways, such as sailing, windmills and wind turbine, etc. In modern days, a large-scale wind turbine is an energy-converting device that transforms the wind energy into mechanical energy and in turn into electrical energy [8]. Wind energy is kinetic energy of flowing air. The amount of available wind kinetic energy depends on two factors, air mass and air flow speed V. Instead of measuring air mass, it is more convenient to measure air density, thus it is more practical to find wind power (Eq. 1.1) [9]. If we define the disk area (swept area) A of a wind turbine as the area normal to the wind flow direction swept out by the blades as they are rotat˙ available in the blade swept area is detering, then the available wind power w mined as the rate of change of the wind kinetic energy: w_ available ¼
dðmV 2 =2Þ ρAV 3 ðAir densityÞðDisk=swept areaÞðWind speedÞ3 ¼ ¼ 2 2 dt (1.1)
It is apparent that the available wind power is proportional to the swept/disk area and also proportional to the cube of the wind speed. Doubling the wind
General introduction to wind turbines Chapter
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5
speed (for example choosing a region where the turbine can be exposed to higher-speed wind) or the turbine blade diameter will lead to 8 or 4 times as much available wind power. Additionally, wind power density is another comprehensive index to evaluate various wind turbines at different locations for comparison. It is the available wind power in moving air through a unit area of perpendicular cross-sectional plane within a period [8] as defined in Eq. (1.2) with a unit of W/m2. It can be used to evaluate the effectiveness of wind energy harvester in utilisation of space. Wind power density ¼ ẇavailable =A ¼
ðAir densityÞðWind speedÞ3 2
(1.2)
Eq. (1.2) reveals that (1) The wind power density is linearly proportional to the air density. Colder air has a larger wind power density than warmer air blowing at the same speed. However, this density effect is typically insignificant. (2) The wind power density is proportional to the cube of the wind speed. Doubling the wind speed increases the wind power density by a factor of 800%. This is the main reason why wind farms are located where wind speed is high! Eq. (1.2) provides an instantaneous value on wind power density. It is known that the wind speed various dramatically throughout the day and through the year! For this, it is a general practice to define the average wind power density as 1 Average wind powerdensity ¼ w_ available =A ¼ ρavg V 3 αe 2
(1.3)
where αe is the energy patter factor. It is a correction factor, which is related to the annual average wind speed V (basing on hourly average) and the total number N ¼ 8760 of hours in a year. αe is defined as 1 XN 3 V (1.4) αe ¼ n¼1 n NV From an engineering point of view, if the average wind power density is <100 W/m2, then the location is considered poor for construction of wind turbine. A good location is associated with 400 W/m2 and best location is above 700 W/m2. There are other factors affecting the choice of a wind turbine site selection. These include (1) atmospheric turbulence intensity, terrain, obstacles (trees, building et al.), environmental impact et al. Further details can be found in Ref. [20]. For comparison and analysis purposes, we define the aerodynamic efficiency of a wind turbine as Cp ¼
w_ rotor shaft output w_ rotor shaft output ¼ w_ available ρAV 3 =2
(1.5)
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Wind turbines and aerodynamics energy harvesters
It describes the fraction of available wind power that is extracted by the turbine blades. Cp is commonly known as the power coefficient. It is not complicated to calculate the maximum possible power coefficient for a wind turbine. This will be introduced in the following chapter. Typically, wind turbines can be classified by its axis of rotation, such as horizontal axis wind turbines (HAWT) and vertical axis one (VAWT). HAWTs are those whose axes of rotation are horizontal or nearly horizontal to the ground and almost parallel to the wind direction [9]. Most of the commercial wind turbines are HAWTs [10, 11]. Those include the most commonly seen propeller turbines, which are lift-type that work based on the lift force on the blades [9]. Unlike vertical axis wind turbines (VAWTs), HAWTs are preferred in electricity generation due to relatively higher energy conversion efficiencies [11]. There are a number of advantages involved in HAWTs [10]: l
l
l l
l
HAWT is one of the most stable and commercially applied wind turbine designs. HAWT produces electrical power resulted from relatively lower cut-in wind speed and involves with a higher energy conversion efficiency. It is possible to utilise them at higher elevation using taller towers. HAWT performs better under fluctuating wind speed due to better angle of attack control. There is easier furling by turning the HAWT’s rotor away from wind stream.
Unfortunately, there are some inherent drawbacks as well [10]: l l l l
HAWTs require yaw drives to turn the turbine toward oncoming wind. Stronger structural support is needed for a heavy generator and a gearbox. Installation and maintenance costs are higher due to a greater tower height. Taller towers are detrimental to wind farms’ visual acceptability.
In contrast, when a wind turbine’s axis of rotation is vertical to the ground and nearly perpendicular to the wind direction, the turbine is classified as an example of VAWT [9, 10]. Compared with HAWTs, VAWTs are involved with the following distinct features [10]: l l
l l
VAWT is insensitive to the wind direction, thus no yaw control is necessary. Structural requirement is less stringent as heavy components like gearbox and generators can be placed as close as to the ground level. Maintenance is easier at ground level. Pitch control is not required for VAWTs.
However, VAWTs are not so popular commercially due to some major disadvantages [10] as following: l
l
Generally, VAWTs are not able to be self-starting. Hence additional motor may be required. VAWTs are closer to the ground, where wind speed is lower than higher elevations.
General introduction to wind turbines Chapter
l
l
1
7
Efficiency is limited as the blades have to pass through aerodynamically dead zones in a complete cycle. Guy wires may be required to support the structure, and may cause inconveniences for installation and maintenance.
Most of wind energy industry share is contributed by large-scale wind turbines, which are generally HAWTs. VAWTs also attract increasing attention for their utilisation as small- to medium-scale wind energy harvesting units [11]. An alternative way to classify wind turbines is by the mechanism that provides torque to the rotating shaft: lift or drag. By now, none of the VAWT designs or drag-type designs have achieved the efficiency or success of the lift-type HAWT. This is the main reason why the majority of wind turbines being built around the world are of this type. Every wind turbine has a characteristic power performance curve. A typical one is illustrated in Fig. 1.6, in which electrical power output is plotted as a function of wind speed V at the height of the turbine axis. We can identify 3 key locations on the wind-speed scale: l
l
l
Cut-in speed is the minimum wind speed at which useful power can be produced. Rated speed is the wind speed that delivers the rated power, typically the maximum power Cut-out speed is the maximum wind speed at which the wind turbine is designed to produce power. At wind speeds greater than the cut-out speed, the turbine blades are sopped by some type of braking mechanism to avoid damage and for safety issues. The short section of the dashed red line indicates the power that would be produced if the cut-out were not implemented.
FIG. 1.6 Typical wind turbine power performance curve with the definitions of cut-in, rated and cut-out speeds.
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Wind turbines and aerodynamics energy harvesters
The wind turbine classification can also be done basing on (1) the relative position of wind turbine, (2) the wind turbine capacity, (3) the type of generator used, (4) the power supply mode, and (5) the turbine location [8] for example, onshore and off-shore. Further details can be found in Ref. [20].
1.3 Aerodynamics and turbulence In order to convert wind kinetic energy into mechanical energy more efficiently, modern wind turbine rotors [12–14] are generally made into airfoils’ shape as shown schematically in Fig. 1.7. Due to the airfoil curvature, air flowing along upper curvature will be at a higher velocity due to a longer path travelled by air particles compared with lower streamlines. Based on Bernoulli’s theorem, the higher velocity is compensated by a reduction in pressure. The pressure difference between the two surfaces of the airfoil will generate a lift force, L (see Fig. 1.7). Meanwhile, there will be a drag force D acting on the airfoil exerted by air flow. The net force F on the airfoil will be the resultant force of drag and lift forces [9, 10]. The lift is the force perpendicular to direction of oncoming airflow. And it is formed due to pressure difference between the upper and lower airfoil surfaces [11]. In contrast, drag force is the force being parallel to the direction of oncoming air flow [11]. It is formed partially due to the unequal pressure on the airfoil surfaces, and partially due to the viscous friction forces on the surfaces. To describe these forces, lift (CL) and drag coefficient (CD) and momentum (CM) coefficients are widely used in the literature. They are defined as: CL ¼
FL FD FM , CD ¼ ,CM ¼ 1=2ρv2 c 1=2ρc2 c 1=2ρv2 c2
FIG. 1.7 Cross-sectional view of airfoil.
(1.6)
General introduction to wind turbines Chapter
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where ρ is the air density, v is the air flow velocity and c is the chord length. FL, FD, and FM are the lift, drag force, and momentum, respectively. The tip speed ratio (λ) is another important parameter of wind turbine, and it is defined as the ratio of the blade tip tangential speed ωR to the speed of fluid flow V. Its definition can be expressed as: λ¼
ωR V
(1.7)
where ω is the angular velocity of the wind turbine rotor, R is the radius of the turbine rotor and v is the wind speed. Eq. (1.7) expressed with Reynolds number will give: λ¼
ωR ðμRe=ρDh Þ
(1.8)
where DH is the hydraulic diameter of the wind turbine in meter. μ is fluid dynamic viscosity. Generally a higher tip speed ratio indicates the wind turbine is associated with a higher efficiency, but a higher level of noise will be produced as well. Re is Reynolds number, which is typically applied to determine the flow conditions: laminar or turbulent. Since most of wind turbines are operated under turbulent flow conditions [15, 16]. It is necessary to introduce some fundamental concepts related to turbulence. Turbulence is a condition in fluid flow where the velocity, pressure and other flow properties at given points in the turbulent region change stochastically with time. The Reynolds number (Re) of a fluid flow is defined as: Re ¼
ρVL μ
(1.9)
where: ρ: the density of the fluid, V: characteristic velocity of the flow, L: characteristic length of the flow, μ: the dynamic viscosity of the fluid. Re determines whether it is turbulent, with the onset of turbulent flow marked by a value of Re higher than a critical value. Due to the randomness of turbulent flow, it is not easily represented by simple formulae. The common practice in CFD is to decompose the flow properties, represented generally by φ (t), into a steady mean value Φ with a fluctuating component φ’(t) superimposed on it, a technique known as Reynolds decomposition is given as: φðtÞ ¼ Φ + φ0 ðtÞ
(1.10)
Consider the instantaneous continuity and Navier–Stokes momentum equations [15] with a velocity vector u, comprising the Cartesian components u, v and w: div u ¼ 0
(1.11)
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Wind turbines and aerodynamics energy harvesters
∂u 1 ∂P + div ðuuÞ ¼ + ν div ð grad uÞ ∂t ρ ∂x
(1.12)
∂v 1 ∂P + div ðvuÞ ¼ + ν div ð grad vÞ ∂t ρ ∂y
(1.13)
∂w 1 ∂P + div ðwuÞ ¼ + ν div ð grad wÞ ∂t ρ ∂z
(1.14)
Applying Reynolds decomposition (Eq. 1.11) to the velocity vector u and its components and pressure P: u ¼ U + u0 ,u ¼ U + u0 , v ¼ V + v0 ,w ¼ W + w0 and p ¼ P + p0 From Eqs. (1.12)–(1.14), for the case of an incompressible flow, div U ¼ 0
(1.15)
Applying Reynolds decomposition to the momentum equations and re-arranging so that the Reynolds stress terms are grouped together: 2 3 02 ∂ ρu0 v0 ∂ ρu0 w0 5 ∂U 1 ∂P 1 4∂ ρu + + + div ðUUÞ ¼ + ν div ð grad U Þ + ∂y ∂z ∂x ∂t ρ ∂x ρ
(1.16) 2 3 ∂ ρv0 2 ∂ ρv0 w0 5 ∂V 1 ∂P 1 4∂ ρu0 v0 + + + div ðVUÞ ¼ + ν div ð grad V Þ + ∂x ∂z ∂y ∂t ρ ∂y ρ (1.17) 3 2 ∂ ρw0 2 ∂ ρv0 w0 ∂W 1 ∂P 1 4∂ ρu0 w0 5 + + + div ðWUÞ ¼ + ν div ð grad W Þ + ∂z ∂x ∂y ∂t ρ ∂z ρ (1.18)
The above four equations are known as the Reynolds-averaged NavierStokes (RANS) equations. Equations for time-averaged scalar properties with similar extra turbulent terms can be derived in the same manner. These additional terms are then modelled with turbulence models. Equations for compressible flow are slightly different due to the need to consider non-constant density. However, since the wind turbine aerodynamics research involves incompressible flow in most cases, compressible flow is not elaborated here. To handle the Reynolds stresses, Boussinesq proposed the use of turbulent viscosity or eddy viscosity μt in the usual Newtonian viscosity equation using the mean flow velocities: ∂Ui ∂Uj (1.19) + τij ¼ ρu0i u0j ¼ μt ∂xj ∂xi
General introduction to wind turbines Chapter
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where i and j represent two perpendicular Cartesian directions. In the literature, there are many turbulence models available, such as 1-equation Spalart-Allmaras (SA) [40] model, 2-equation k-ε, k-ω, SST k-ω and 7-equation Reynolds stress model (RSM). In RSM, the Reynolds stresses ρu00i u00j are directly computed. The transport of the Reynolds stress equation can be illustrated as: Rate change of Transport by Rate of Transport by Rate of + ¼ + the Reynolds stress convection production diffusion dissipation +
Transport due to turbulent Transport due + pressure strain interaction to rotation
On the right hand side, the diffusion, the dissipation, and the pressure-strain interaction terms are needed to be modeled. For the pressure-strain term, the linear pressure-strain model, quadratic pressure-strain model, and the stress omega model are widely used. As this model considers the anisotropic nature of turbulence, it has six additional partial differential equations and one additional transport equation for the six independent Reynolds stresses, which turns it into a seven-equation model. However, the additional equations and the highly coupled equations also mean a significant increase in the computational cost, which may be comparable with LES. The 1-equation SA model was developed for airfoil predictions [35]. It has been applied to the well-known NREL phase VI HAWT rotor [36, 37]. It has been shown [36, 37] that the SA closure model cannot re-matches the surface distribution and reproduce the flow separation accurately. SA model has also been attempted to simulation aerodynamic loads on VAWTs [38, 39]. However, the numerical and experimental results on predicting near wake velocity profiles are found to be dramatically different for a 3-bladed H-rotor. These findings confirm that the SA turbulence model is not applicable to simulate VAWT. Although all length scales of turbulence in steady or unsteady mode may be simulated in RANS (Reynolds-averaged Navier-Stokes) methods, the 2equation models, especially, k-ε model are widely used and validated [15]. In this model, the turbulent kinetic energy k and the rate of dissipation of turbulent kinetic energy ε are used to obtain the eddy viscosity μt as follows: μt ¼ ρCμ
k2 ε
The two equations for solving k and ε are: ∂ðρkÞ μ + div ðρkUÞ ¼ div t grad k + 2μt Sij Sij ρε σk ∂t ∂ðρεÞ μ ε ε2 + div ðρεUÞ ¼ div t grad ε + C1ε 2μt Sij Sij C2ε ρ σε k ∂t k
(1.20)
(1.21) (1.22)
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Wind turbines and aerodynamics energy harvesters
where Sij Sij is the dot product of the rate of deformation tensor of the mean flow. The five constants in Eq. (1.20) to Eq. (1.22) are obtained by fitting data from a wide range of turbulent flows as follows: Cμ ¼ 0:09; σ k ¼ 1:00; σ e ¼ 1:30; C1ε ¼ 1:44; C2ε ¼ 1:92 Summing the normal Reynolds stress terms in Eqs. (1.16)–(1.18), it is found that it is exactly equal to twice the negative of turbulent kinetic energy per unit 2 2 2 0 0 0 volume: ρ u + v + w ¼ 2ρk. Hence assuming isotropic behaviour of the normal Reynolds stresses, each of them is given a value of (2ρk)/3. However, it is to be noted that this assumption is not always accurate. This method is expressed in the modified Boussinesq expression: ∂Ui ∂Uj 2 ρkδij + (1.23) τij ¼ ρu0 i u0 j ¼ μt ∂xj ∂xi 3 where σij, the Kronecker delta, is 1 if i ¼ j and zero if i 6¼ j. Although the k-ε model is widely used, it does not perform well in unconfined flows, flows with large strains (such as those over curved surfaces), rotating flows and flows in non-circular ducts. As reported by Murakami [16] et al., its key shortcoming arises from the inability of the term for turbulence kinetic energy production to take on negative values, thus over-predicting the turbulence level in front of a forward facing step bluff body. Due to this overprediction, the observed re-circulating flow above the bluff body is also not reproduced by the model. Hence, the k-ε model is not recommended for flows with separation. For the present research involving a cross flow turbine, the blades undergo full circles of angle of attack variation during normal operation, hence flow separation is inevitable. A technique for reducing the problem of excessive turbulence prediction according to Durbin and Reif [17] is to impose bounds on the turbulent viscosity, for example, by limiting it to: Cμ k2 αk , (1.24) μt ¼ min ε j Sj pffiffiffi with α 1= 6. For the flows encountered in the present research, the Shear Stress Transport (SST) k-ε model of Menter [15, 18] is more appropriate. This model arose from the original k-ε model of Wilcox [15, 19]. In this model, the turbulence frequency ω (originally named the specific dissipation rate by Wilcox) is defined as: ω ¼ ε=k
(1.25)
μt ¼ ρk=ω
(1.26)
Thus the eddy viscosity is:
General introduction to wind turbines Chapter
The transport equations for solving k and ω are:
∂ðρkÞ μt grad k + Pk β∗ ρkω + div ðρkU Þ ¼ div μ + σk ∂t
1
13
(1.27)
2 ∂Ui δij is the rate of production of turbulent kinetic where Pk ¼ 2μt Sij Sij ρk 3 ∂xj energy, and Sij Sij is the dot product of the rate of deformation tensor of the mean flow.
∂ðρωÞ μ 2 ∂Ui δij + div ðρωU Þ ¼ div μ + t grad ω + γ 1 2ρSij Sij ρω σω ∂xj ∂t 3 β1 ρω2 (1.28) However, the model is very dependent on the proper setting of ω at the free stream boundary condition. Thus Menter developed the SST model. The model uses the standard k-ε model (which is less sensitive to assumed values in the free stream) in the fully turbulent region far from the wall and transformation into a k-ω model in the near wall region. The k-equation is unchanged from Wilcox’s model but the transformed ω-equation is as follows:
∂ðρωÞ μ 2 ∂Ui δij + div ðρωU Þ ¼ div μ + t grad ω + γ 2 2ρSij Sij ρω σ ω,1 ∂xj ∂t 3 ρ ∂k ∂ω 2 β2 ρω + 2 σ ω, 2 ω ∂xk ∂xk (1.29) To limit over prediction of shear stress in adverse pressure gradient boundary layers, limiters on the eddy viscosity μt and rate of production of turbulent kinetic energy Pk are employed. Blending functions give a smooth transition between the far field and near wall. More recently, Menter improved the SST model with revised model constants as follows: σ k ¼ 1:0; σ ω,1 ¼ 2:0; σ ω,2 ¼ 1:17; γ 2 ¼ 0:44; β2 ¼ 0:083; β∗ ¼ 0:09; Additionally, CFX also incorporates the curvature correction technique of Spalart and Shur [15], thus making the solver more suitable for the aerodynamics research on a rotating wind turbine turbine. RANS turbulence models use a single model to describe the whole range of turbulence. In many aerodynamics engineering problems, the numerical predictions are acceptable. However, the results of RANS have also revealed that perfect predictions with a single model for various applications seem to be formidable. One reason contributing to that is the different characteristic of turbulence with different scales. For example, the behaviour of large eddies whose energy comes from the main flow is highly dependent on macroscopic features, i.e. the flow domain geometries and boundary conditions. In other words, they
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Wind turbines and aerodynamics energy harvesters
are anisotropic. In contrast, the small-scale eddies have a universal behaviour and hence are almost isotropic. When the large eddy and the small eddy are treated in the same way, unsatisfactory predictions are not surprising. This is the situation happening in RANS. Although the RANS methods are popular in the wind turbine aerodynamics communities. However, some drawbacks and weakness of the RANS methods on their inherent incapability of capturing massive flow separation and vortex shedding have been clearly highlighted [32]. LES [30, 31], however, is an approach that tries to solve this problem by dealing with large and small eddies separately. The variables in LES are decomposed by a spatial filter operation into two parts: the resolved and the modeled. Unlike RANS, they are not the mean value and the fluctuation [32]. The resolved corresponds to the unsteady fields with large scales, whereas the modeled (or the sub-grid scale) relates to the universal small eddies. After filtering the governing equations, several new terms called sub-grid-scale (SGS) stresses arise. The SGS stresses are the results of the small eddies and their interactions with the large scales, which need to be modeled. This makes the computational cost of LES considerable large, compared with RANS [41]. The Smagorinsky model [33] computes the eddy viscosity and the sub-grid kinetic energy as: 8 2 e > e ¼ C ρ Δ μ S > μ t > > < 2 (1.30) k ¼ Ck Δ2 Se > qffiffiffiffiffiffiffiffiffiffi > > > : Se ¼ Seij Seij where Seij is the density-weighted strain rate tensor, Cμ and Ck are the model coefficients, which are computed by a dynamic procedure proposed by Germano et al. [34]. A good review on RANS and LES studies of wind turbine aerodynamics can be found in Refs. [30–32]. The LES approach [41] could be widely implemented in the near future due to its demanding computational expense. The main challenge of LES is to obtain good resolution of wall-bounded layer at high Reynolds number. Approximately 90% of the computational grids is distributed over the near-wall regions as Re > 105. To reduce the high computational cost, a hybrid RANS-LES method was proposed in wind turbine aerodynamics communities. It is a technique to bridge the gap between the less accurate RANS and more computational costly LES approach. The hybrid method could be a remedy to wind turbines in complex flow conditions involving with flow separation and vortex shedding. The application of the hybrid method to wind turbine aerodynamics is reviewed and discussed in Ref. [32].
1.4 Betz limit In 1920s, Albert Betz (1885–1968) predicted the ideal and frictionless efficiency of a wind turbine by applying linear momentum theory on a simple
General introduction to wind turbines Chapter
1
15
one-dimensional model [11, 20]. The model consists of a rotor represented by a uniform “actuator disk” confined in the assumed control volume. The control volume is defined by the surface and the cross sections of a stream tube in which the fluid passes through the rotor disk. The rotor “actuator disk” creates a pressure discontinuity of fluid flowing through it. A schematic illustration of the simplified model is shown in Fig. 1.8. This analysis based on the actuator disk model adopts the following assumptions: l
l l l
The fluid flow is ideal across the control volume, meaning that it is steady, homogenous, inviscid, incompressible and irrotational. There is an infinite number of blades, thus fits the actuator disk description. Both flow and thrust are uniform across the disk area. Undisturbed ambient static pressure is assumed for the static pressure far upstream and downstream of the rotor disk.
In order to attain the net force on the contents of the control volume, the conservation of linear momentum is applied. The net force is equal in magnitude but in opposite direction to the thrust, Fthrust, which is the force exerted on the turbine by the wind flow. For one-dimensional, incompressible and timeinvariant flow, as a linear momentum is conserved, the thrust can be obtained from the change in momentum of air flow. Fthrust ¼ V1 ðρAV Þ1 V4 ðρAV Þ4
(1.31)
where the subscript is indicating cross section location as labeled in Fig. 1.8. ρ is the air density, A is the cross sectional area of the rotor disk and V is the air velocity of the flow. _ where m_ is the As the flow is assumed to be steady, ðρAV Þ1 ¼ ðρAV Þ4 ¼ m, mass flow rate. Hence the thrust Fthrust can be written as: Fthrust ¼ m_ ðV1 V4 Þ
(1.32)
FIG. 1.8 Control volume for actuator disk model of wind turbine. V is air velocity; 1, 2, 3 and 4 indicate locations.
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Wind turbines and aerodynamics energy harvesters
As no work is done on either side of the turbine disc, the Bernoulli function is applied to the two parts of control volume, upstream and downstream of the disk. On the upstream side of the disk: 1 1 p1 + ρv21 ¼ p2 + ρv22 2 2
(1.33)
where p is the pressure and the subscript is denotes location. Meanwhile, on the downstream side of the disk: 1 1 p3 + ρv23 ¼ p4 + ρv24 2 2
(1.34)
As it is assumed that the pressures far upstream and far downstream are equal (p1 ¼ p4), and the velocity remains the same after fluid passes the disk (V2 ¼ V3), the thrust can also be expressed with the different pressure between sides of the disk: Fthrust ¼ A2 ðP2 P3 Þ
(1.35)
Using Eq. (1.33) and. (1.34) to solve for (p2 p3) and substituting into Eq. (1.35) will give: 1 Fthrust ¼ ρA2 V12 V42 2
(1.36)
The thrust values from Eq. (1.35) and (1.36) should be equal, thus 1 V2 ¼ ð V1 + V 4 Þ 2
(1.37)
This means the fluid velocity are the rotor disk will be the average of the upstream and downstream velocities, as required by continuity and momentum. An axial induction factor, a, is defined to express the fractional decrease in wind velocity between the free stream and the rotor disk: a¼
V 1 V2 V1
(1.38)
The maximum possible value of a is a ¼ 1/2, as it requires V3 to decrease to zero. Therefore, the thrust at the turbine plane can be written as: 1 Fthrust ¼ ρAV12 ½4að1 aÞ 2
(1.39)
The power coefficient, defined as the ratio of power extracted to the total power available, can be defined in terms of a also: Cp ¼ 4að1 aÞ2
(1.40)
Fig. 1.9 shows the plot of power coefficient Cp at different values of the axial induction factor. It can be seen that power coefficient reaches a maximum value
General introduction to wind turbines Chapter
1
17
FIG. 1.9 Power coefficient for an ideal Betz wind turbine model as axial induction factor varied.
of 0.593, which is known as the Betz limit for an ideal frictionless turbine. This theoretical maximum efficiency is difficult to be achieved practically for many reasons, such as: l l l l l
Pressure distribution at the rotor disc is not uniform. Viscous effect will lead to an aerodynamic drag. Vortices formed at the blades tips will lead to energy losses. Mechanical losses due to shaft friction. Other mechanical and electrical losses in the gearbox, generator, etc.
It is worth noting that Betz’s analysis on wind turbine efficiency is not limited to any particular type of wind turbines [21]. Fig. 1.10 shows the relationships between the turbine power coefficient and the tip speed ratios for different types of wind turbines. It shows power coefficient Cp as a function of the ratio of the turbine blade tip speed RΩ to wind speed V. Here ω is the angular velocity of the wind turbine blades and R is the radius. It can be seen from this graph that an ideal propeller-type wind turbine approaches the Betz limit, as ΩR/V approaches infinity. However, the power coefficient of real wind turbines reaches a maximum at some finite value of ΩR/V and then drops beyond that. It is obvious that the ‘best-efficient’ wind turbine is the high-speed HWAT, and that is why you see this type of wind turbines being implemented all around the world. For different wind turbine designs, the maximum power coefficient is achieved at different tip speed ratios [22]. This means the suitability of wind turbine design to a particular working environment must be considered [23, 24]. The above theoretical limitations are seen in practical wind turbines. A well optimized lift-based turbine such as the Pinson Cycloturbine has a peak CP of
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Wind turbines and aerodynamics energy harvesters
FIG. 1.10 The power coefficient as a function of tip speed ratio for different wind turbine machines designs. Note that in some previous publications [21], the efficiency curves of the American multiblade and the Savonius designs were inadvertently switched. (Adapted from M. Ragheb, A.M. Ragheb, Wind Turbines Theory-the Betz Equation and Optimal Rotor Tip Speed Ratio, INTECH Open Access Publisher, 2011.)
0.4 [25]. In contrast, cP for Savonious (drag-based) devices does not exceed 0.2 [26]. However, when selecting a turbine for deployment, one does not merely make a decision on the basis of its CP. For example, Blackwell, et al. [27] mentions that the less efficient Savonius turbine may find more applications in developing countries. Bos [28], when assessing the feasibility of the WindNok drag-based turbine, uses a weighted objectives method that includes suitability for Do-It-Yourself installation and likelihood of approval from authorities. Oy Windside Production Ltd. [29] uses a helical Savonius design as the basis for their highly durable products intended for implementing in harsh remote environments such as Antarctica where its simplicity, low cut-in wind speed, high survival wind speed are overriding factors.
1.5 Concluding remarks In summary, wind power as a promising renewable energy source is overviewed. It has great potential to be harnessed via optimally designed wind turbines. The fundamental concepts and classifications in wind turbine industries are then explained. There are two typical wind turbines basing on its axis of rotation. One is HAWT (horizontal axis wind turbine) and VAWT (vertical axis) with different power performance curves. As far as the turbine location
General introduction to wind turbines Chapter
1
19
is concerned, wind turbines can be classified as on-shore and off-shore. The aerodynamics characteristics and turbulence models involved in studying wind turbines are then provided. Finally, the discussion on the Betz limit is included to show that the maximum power coefficient of a wind turbine is 59.3% in theory. This limit provide a guidance on optimising the design and performance of wind turbines. It was confirmed that all wind turbines applied in practice for power generation are found to be associated with a power coefficient below the Betz limit.
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[24] J. Kumbernuss, C. Jian, J. Wang, H. Yang, W. Fu, A novel magnetic levitated bearing system for vertical Axis wind turbines (VAWT), Appl. Energy 90 (1) (2012) 148–153. [25] R. Noll, N.D. Ham, H.M. Drees, N.L. B, 1 kW High Reliability Wind System Development, United States Department of Energy, Rocky Flats, 1982. [26] U.K. Saha, M.J. Rajkumar, On the performance analysis of Savonius rotor with twisted blades, Renew. Energy 31 (2006) 1776–1788. [27] B.F. Blackwell, R.E. Sheldahl, L.V. Feltz, Wind Tunnel Performance Date for Two- and Three-Bucket Savonius Rotors, Sandia Laboratories, Albuquerque, 1977. [28] J.E. Bos, Feasibility Study of the WindNok, TU Delft, Delft, 2010. [29] Windside Wind Turbine, [Online]. Available: http://www.windside.com/products, 2012. Accessed 20 June 2012. [30] D. Mehta, A.H. van Zuijlen, B. Koren, J.G. Holierhoek, H. Bijl, Large eddy simulation of wind farm aerodynamics: a review, J. Wind Eng. Ind. Aerodyn. 133 (1) (2014) 1–17. [31] R.C. Storey, J.E. Cater, S.E. Norris, Large eddy simulation of turbine loading and performance in a wind farm, Renew. Energy 95 (1) (2016) 31–42. [32] J. The, H. Yu, A critical review on the simulations of wind turbine aerodynamics focusing on hybrid RANS-LES methods, Energy 138 (1) (2017) 257–289. [33] J. Smagorinsky, General circulation experiments with the primitive equations, Mon. Weather Rev. 91 (3) (1963) 99–164. [34] M. Germano, U. Piomelli, P. Moin, W. Cabot, A dynamic localization model for large-eddy simulation of turbulent flows, Phys. Fluids 3 (1991) 1760–1765. [35] P. Spalart, S. Allmaras, A one-equation turbulence model for aerodynamic flows, in: 30th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, 1992. [36] J.Y. You, D.O. Yu, O.J. Kwon, Effect of turbulence models on predicting HAWT rotor blade performances, J. Mech. Sci. Technol. 27 (12) (2013) 3703–3711. [37] Y. Song, J.B. Perot, CFD simulation of the NREL phase VI rotor, Wind Eng. 39 (3) (2015) 299–309. [38] M. Nini, V. Motta, G. Bindolino, A. Guardone, Three-dimensional simulation of a complete vertical Axis wind turbine using overlapping grids, J. Comput. Appl. Math. 270 (2014) 78–87. [39] K. Pope, V. Rodrigues, R. Doyle, A. Tsopelas, R. Gravelsins, G.F. Naterer, et al., Effects of stator vanes on power coefficients of a zephyr vertical axis wind turbine, Renew. Energy 35 (5) (2010) 1043–1051. [40] M. Elkhoury, T. Kiwata, K. Nagao, T. Kono, F. Elhajj, Wind tunnel experiments and delayed detached eddy simulation of a thress bladed micro vertical axis wind turbine, Renew. Energy 129 (2018) 63–74. [41] G.E. Seach Chyr, Enhancement of Wind Turbine Performance by Installation above a Bluff Body, Ph.D. thesis, Nanyang Technological University, Singapore, 2014.
Further reading [42] N. Sedaghatizadeh, M. Arjomandi, R. Kelso, B. Cazzolato, M.H. Ghayesh, Modelling of wind turbine wake using large eddy simulation, Renew. Energy 115 (2018) 1166–1176.