Prior to choosing a site for a wind farm, its wind resources must be known. On-site measurement of wind speed, using an anemometer or any other appropriate measuring device or the use of historical meteorological data for the site (if they exist) enhance the knowledge of the site’s wind resources. Typically, the use of 50-year historical data is recommended by Wind Energy Engineering Standards. For the offshore site in study, only the 24-year historical data from the National Oceanic and Atmospheric Administration (NOAA) data base is available. Wind speed determined from NOAA’s error bars is used to plot Rayleigh probability distribution curves for each month of the year, based on the operational limit of the 5MW NREL reference wind turbine. The site’s average wind speed and gust are determined based on average wind energy capture. A Gumbel probability distribution curve is plotted based on the operational range of the wind turbine in study, using NOAA’s error bars for the 24year historical hourly wind gust for the site. This study uses the estimated mean wind speed and mean gust, to implement BEMT simulations to investigate the aerodynamic forces caused by the wind or gust on the blades of the HAWT rotor. The wind power captured and the power coefficient are estimated for each scenario. Empirical formulae are developed for the estimation of the rotor blade airfoil’s chord length in terms of blade element radius and the axial induction factor for each scenario, in terms of blade element radius.
INTRODUCTION
Wind energy was used in propelling sail boats along the Nile River in about 5000BC, in Egypt. Wind mills started being used as prime movers for water pumps in China around 200BC, while vertical axis wind mills were used in grinding grain in the Middle East around the same period. Use of wind energy in Europe commenced in 250AD, when the Persians introduced the technology to the Roman Empire. The Dutch made improvements on the design of wind mills and used them to drain lakes [1]. In the 1800s, settlers in Western United States of America (USA) used wooden wind mills to pump water. Later in the period, wind mills were connected to generators to produce electricity [2]. The US Government was motivated to work with industrial partners in fostering research in wind energy, because of two landmark events, namely; the oil embargo imposed in 1973 by the Organization of Petroleum Exporting Countries (OPEC) and the dethronement of the Shah of Iran in 1979[3]. The US Department of Energy (DOE) in 2008, set a goal for wind energy production in the USA. This goal requires that, 20% of all electricity generated in USA, be from Wind Turbine Power Plants (WTPP). This 20% electricity from wind energy by 2030 report also highlighted improvements to be made on existing technology, in order to meet the set goal. Included in the recommendations for improvements are; improvements on wind turbine (WT) technology, improvement in wind farm siting, manufacturing scale-up and the need to integrate wind energy into the grid [1,3]. Much like in the US, interest in wind energy grew in Europe in the 1970s. By the end of 2008, installed wind energy capacity in Europe stood at; a total of 64.5 GW of onshore wind energy and 1.5GW of offshore wind energy. In the Netherlands, by this time, the installed wind energy capacity stood at; 1.921GW of onshore wind energy and 228MW of offshore wind energy. [4]. By definition; wind is air in motion. A curious mind will pose the following question; “What sets the air in motion?” The differential heating of the earth’s surface by the sun’s radiation causes variations in atmospheric pressure, which in turn give
Site Characterization and the Aerodynamics of An Offshore Wind Power Plant – Statistical, Numerical and Analytical Approaches
W. D. Zhu Mechanical Engineering Department
University of Maryland, Baltimore County Baltimore, MD 21250
rise to the movement of atmospheric air masses; which are the principal causes of the earth’s wind system. High pressure regions indicate changeable windy weather and precipitation [5]. Manwell et al. [6] identified four atmospheric forces that could be considered in the study of the motion of atmospheric air, namely; pressure forces, Coriolis forces caused by the earth’s rotation, inertia forces due to large scale circular motion and frictional forces at the earth’s surface. Geostrophic wind velocity is the upshot of the resultant of the pressure force and the Coriolis force of the wind. This resultant runs parallel to lines of constant pressure. Consult reference [6] for an in-depth treatment of this topic. For many years, micro-wind turbines (MWTs) have been used to supply electricity to remote houses, farm houses and remote communities. MWTs are currently used to supply electricity to cellular phone masts and remote telephone booths [5]. The DOE’s National Renewable Energy Laboratory (NREL) has classified potential wind energy sites based on available wind speed at 80m height. Class 1 sites have mean wind speeds less than 5.9m/s. Class 2 sites have mean wind speeds ranging from 5.9m/s to 6.9m/s; class 3 sites have mean wind speeds ranging from 6.9m/s to 7.5m/s; class 4 sites have mean wind speeds ranging from 7.5m/s to 8.1m/s; class 5 sites have mean wind speeds ranging from 8.1m/s to 8.6m/s; class 6 sites have mean wind speeds ranging from 8.6m/s to 9.4m/s and class seven sites have mean wind speeds greater than or equal to 9.4m/s. Classes 4 through 7 sites are generally feasible for development [2, 7]. NREL’s mean wind speed is based on the Rayleigh probability distribution. Of utmost importance in the design of WTs, the planning of wind farms and the operation of WTPPs are the aerodynamics of the system. Much work has been done in the areas of wind turbine aerodynamics and wind farm aerodynamics, despite the aforementioned, much still has to be done in these areas of study. Rankine considered axial momentum balance in his analysis of a Horizontal Axis Wind Turbine (HAWT). He considered a conical control volume (CV) around the rotor of the HAWT. The rotor of the HAWT was represented by a porous disc of cross sectional area, A, which extracts energy from the air passing through it, by reducing its pressure. Upstream or upwind the WT, the air pressure is above atmospheric due to a slowing down of the airstream. As the airstream passes through the WT, it loses pressure. If the initial wind speed were U, the wind speed at the WT’s inlet will be U(1-a), while the wind speed at the wake of the WT will be U(1-2a). Where, “a” is the interference or axial induction factor [8]. Wang et al. [9] highlighted the difficulty encountered in determining the axial and rotational induction factors respectively; using the Blade Element Momentum Theory (BEMT). It is common practice to use iterative techniques to determine these factors, provided the chord length and angle of twist of respective blade elements, the wind speed, the angular speed of the rotor, the number of turbine rotor blades, blade element airfoil types and the aerodynamics parameters are known [5,9,10]. A knowledge of the induction factor will facilitate the calculation of the aerodynamic forces and the torque on the wind turbine rotor. Normally blade lift forces are responsible for creating the torque on the rotor. Aerodynamic forces generate the primary loads that drive the structural design of the wind turbine. Fluid particle interaction with the WT is multi-scale in nature, ranging from fluctuations in the atmospheric boundary layer (ABL) down to micro-scale turbulent fluctuations in the boundary layer adjacent to the rotor blade’s surface. The stochastic nature of the wind makes the wind entering the WT to be non-uniform, since it varies in both time and space in a manner that is typical of turbulent flows. Wind gust or the buildup of debris on the leading edge of the rotor blade can lead to deleterious changes in the flow over the rotor [1, 5, 7]. The aerodynamic torque decreases with increasing blade pitch angle. When the wind speed changes, only pitch control is used to enhance the wind energy capture and power output of the WT. Wind shear and tower shadow effects produce significant fatigue loads which influence the lives of WTs [11]. Wake interaction with WT downstream or downwind and the turbulent ABL, pose significant modeling problems. Accurate wake modeling is a necessity for accurately predicting the annual electricity production of a wind farm. How both atmospheric turbulence and WT wake affect power output and transient mechanical loading at the WT level, is
somewhat difficult to fathom. Wake momentum deficit is normally compensated by the atmosphere [12]. WT speeds are difficult to control because of the intermittent nature of the wind. Incorporation of a variable ratio gearbox with a fixed speed WT can increase wind energy capture and thus, power generation [6]. The aerodynamic performance of a WT is commonly simulated using BEMT. The WT rotor blade is discretized into a finite number (usually between 10 and 20) of 2D blade elements, with element radii measured from the center of the WT hub to the midpoint of each element. Each blade element is analyzed as a 2D airfoil and the effects of all the blade elements are combined to predict the performance of the WT rotor blades. Appropriate correction factors are applied to the resulting equations for local flow around the hub, generation of tip vortices and wake effects [4, 5, 9, 10, 13, 14, 15]. Details on BEMT will be given in later sections of this paper. BEMT or even Computational Fluid Dynamics (CFD) simulations cannot be implemented without a sound knowledge of a WT’s operating environment. A proper knowledge of the wind pattern of the site proposed for a wind farm is required. In this paper, the site of interest is an offshore site located at the Delaware Bay, earmarked for the Maryland Offshore Wind Farm (MOWF). The wind speed measuring station (Fig. 1) is a buoy owned and operated by the National Oceanic and Atmospheric Administration (NOAA); Station 44009. It is located, 26 nautical miles southeast of Cape May, New Jersey. The buoy is a 3m discus buoy with coordinates at latitude 38.461°N and longitude 74.703°W. The air temperature measuring device is 4m above sea level, the anemometer is 5m above sea level, the barometer is at sea level, the sea temperature measuring device is 0. 6 m below sea level, the watch circle radius is 63m (69yards) and the buoy is located at a point where the sea depth is 30.5m [16]. Wind speed and hourly gust measurements from January, 1984 to November, 2008 are depicted on the error bars shown in figures 2 and 3 respectively. It has been established that, the wind speed and hence the power density follow the Rayleigh probability distribution function [5, 10]. Even the International Electro-Technical Commission (IEC) Standards recommend the use of the Rayleigh probability distribution function for characterizing wind farms [17]. In view of the fact that, NOAA’s data for wind gust for the site in study were measured on hourly intervals, other than at 10 minute intervals, the wind gust data best fits the Gumbel probability distribution curve [5]. The wind turbine to be investigated in this work is an upwind, 3 bladed, 5MW NREL reference HAWT. This offshore WT has a swept radius of 126m, a hub height of 90m, a hub diameter of 3m, a cut-in rotational speed of 6.9RPM and a rated rotational speed of 12.1 RPM. Its cut-in wind speed at 90m hub height is 3m/s, its rated wind speed at hub height is 11.4 m/s and its cut off wind speed is 25m/s [18]. A detailed description of the HAWT is found in reference [18]. This work focuses on the characterization of MOWF using the aforementioned statistical techniques (the average wind speed at 80m height and at the WT hub height, the average hourly wind gust at hub height, the turbulence intensity of the site shall be determined from the NOAA error bars in figures 3 and 4 respectively. Subsequently BEMT simulations will be performed for the wind mill state and the turbulent wake state. Another objective of this work is to develop empirical formulae for the determination of the axial induction factor “a” in terms of blade element radius for the wind mill state and the turbulent wake state respectively, blade element chord length in terms of radius and the determination of aerodynamic forces and the torque on the WT rotor.
Site Characterization As stated in the foregoing section, the data used in this study are 24-year offshore wind and gust data collected by NOAA for the site of interest (figs 2 and 3). The wind speed and gust plotted on the error bars were measured in knots. In order to convert the data from knots to m/s a factor of 0.514444 is used. The wind speed and gust on the NOAA error bars were measured at a height of 5m above sea level; based on these values, wind speed and gust at the WT hub height are estimated using the wind shear formula below;
/ ( / )r rU U h h (1)
Where U is the wind speed at WT hub height, rU is the wind
speed from measured data, h is the height of WT hub above sea
level, rh is the reference height (5m) at which wind speed was
measured and is a friction factor which depends on the surface roughness of the terrain [2, 6, 8, 10]. Counihan’s correlation formula is used to estimate as follows:
2
10 0 10 00.096 log ( ) 0.016(log ( )) 0.24z z (2)
Where, 0z is the surface roughness of the terrain. For calm
open seas, 0z is 2x10-4m and for blown seas, 0z is 5X 10-4m
[8]. In this work a value of 0z =3.5 x 10-4 is used.
The cut-in wind speed for the 5MW NREL reference WT is 3m/s and the cut-off wind speed is 25m/s [18]. Based on the operating range of the reference WT, Rayleigh probability distribution curves are fitted for the monthly wind speed from the NOAA error bar (Fig.2) using the formula below:
2 2( ) 0.5 ( / ) exp ( / 4 )av avp U U U U U (3)
Where U is the wind speed ranging from 3m/s through 25m/s,
avU is the monthly mean wind speed read from the NOAA error
bar (Fig.1) and ( )p U is the probability of occurrence of a wind speed [6, 9]. The power density for each month is estimated based on the Rayleigh distribution and an average monthly power density (PD) is calculated, from which the average wind speed is determined. The power density, PD is given by:
31
2PD U (4)
Where, is the density of air; =1.225kg/m3. Figure 4 below depicts Raleigh distribution curves for the wind speed for each month of the year within the period 1984-2008. The hourly wind gust follows the Gumbel Distribution function, given by:
[( )/ ][( )/ ]( ) (1 / )UU ep U e e
(5)
Each wind gust had the exponent ( ) /U for each month of the year within the period in study, as a result, monthly averages of this exponent were calculated for corresponding wind gust and a Gumbel Distribution curve was plotted as shown in figure 5. Using the power density for the entire operating range of the WT, the average gust was estimated. The turbulence intensity(TI) of the site was estimated using the standard deviation values given in Figure 2 and the estimated wind speed using the formula below:
/ avTI U (6)
Where, is the average standard deviation. Equations (3) through (5) were coded in Engineering Equation Solver (EES) and the resulting curves are shown in Figures 4 and 5 below.
Fig.1-NOAA Station: 44009, Located at Delaware Bay (adopted [16])
Fig.2- Monthly Mean Wind Speed in knots (adopted from [16])
Fig.3- Hourly Wind Gust in Knots(adopted from [16])
Fig.4- Rayleigh Distribution Curves for Monthly Wind Speed
Fig.5 Gumbel Distribution for Wind Gust Wind Turbine Aerodynamics The wind turbine aerodynamics are based on the BEMT. BEMT is a combination of Rankine’s momentum theory and the rotating annular disc or actuator disc theory [6, 8, 10, 14]. Each WT rotor blade is discretized into blade elements possessing different airfoil cross-section as shown in Figure 6. The rotor blade is typically divided into 10 to 20 blade elements. In this work the rotor blade consists of 17 blade elements, with airfoil parameters given in reference [18]. Lift coefficients (Cl) and Drag Coefficients (Cd) are estimated from the plots of angle of attack vs Cl and Cd for the various airfoil sections (shown in Figures 3-1 through 3-6 of reference [18]) that make up the rotor blade. These parameters which have been corrected for 3D effects [18], are determined for angles of attack ranging from 0º to about 60º. The airfoil types that constitute the rotor blades of the 5MW NREL reference WT are; Airfoil DU 40, Airfoil DU 35, Airfoil DU 30, Airfoil DU 25, Airfoil DU21 and Airfoil NACA 64. DU stands for Delft University and NACA stands for National Advisory Committee for Aeronautics. The Ratio of Drag Coefficient to Lift coefficient (Cd/Cl) for the range of angles of attack and respective airfoil type is calculated. Plots of angle of attack versus Cl, Cd and Cd/Cl for each air foil type are made in EES, the resulting curves are cubic splines. Figure 7 below is one such plot for Airfoil DU 35.
Fig.6- Wind Turbine Rotor Discretized into Blade Elements.
Fig.7 Plot of Non-Dimensional Parameters for Airfoil DU 35 For want of space, only the plot of one airfoil type is shown. The values of Cl and Cd and α are determined at points on the curves where Cl is maximum and the ratio of drag coefficient to lift coefficient is low, and not necessarily zero, since in real life, drag always exists. The resulting non-dimensional parameters are used to estimate the aerodynamic forces on the WT rotor as outline here-after. Figure 8 below, is the velocity diagram of a typical blade element. dFL is the lift force on a blade element , dFD is the drag force on the blade element, dFT is the tangential or driving force on the blade element and dFN is the normal force on the blade element. From the geometry of figure 8, the local blade pitch angle of a blade element is given by:
Fig.8 Velocity Diagram of a Blade Element aopted from [6].
The blade element solidity , is given by [6, 9, 10]:
( ) 3 / 2r c r (9)
Where c is the chord length of the blade element. Resolving components of the relative wind speed in the horizontal and vertical directions yields:
(1 ) sinrel
U a U (10)
(1 ') cosrel
r a U (11)
The component 'r a in equation (11) is the contribution of the WT’s wake velocity at the trailing edge of the rotor blade. It acts in the opposite direction to that of the WT rotor [6, 10, 14]. Consult reference [14] for a detailed velocity diagram. Resolving the components of elemental forces in the horizontal and vertical directions yields:
s sinN DLdF dF co dF (12)
sin cosDT LdF dF dF (13)
Dividing equations (12) and (13) respectively by 21
2relU c
yields:
cos sinN L DC C C (14)
sin cosT L D
C C C (15)
Where, CN and CT are the normal and tangential force coefficients respectively and c is the blade element chord length. Stating without proof, the rotational induction factor is given by:
' / (4 sin cos )T T
a C F C (16)
Where, F is the Prandtl’s tip loss factor, given by;
1.5( )1 sin2
cos ( )R r
rF e
(17)
F=1 for the first twelve blade elements, since they are relatively far from the tip of the rotor blade. Equation (17) is applied to the last five blade elements [14]. The axial induction factor for the wind mill state is given in terms of 'a , by:
(1 ') / (4 ' 3)a a a (18a)
For the turbulent wake state, for 0.4a and 0.96TC , the
Glauert’s formula [6] is used to estimate a as follows:
1
21
(0.143 (0.0203 0.6427(0.889 )) )T
a CF
(18b)
Where, TC is the thrust coefficient. TC is given by [10]:
Consult reference [10] for the derivation of equations (14) through (18a). From equation (10) the relative wind speed is given by:
(1 ) / sinrelU U a (19)
The elemental normal and tangential forces are expressed in
terms of relU , , ( )r , c , r and dr as follows:
2( ) ( cos sin )N rel L DdF r U C C crdr (20)
2( ) ( sin cos )T rel L DdF k r U C C crdr (21)
The elemental torque is given by;
2 2( ) ( sin cos )rel L DdT k r U C C cr dr (22)
k is a constant accounting for hub effects, tower shadowing and other irreversibilities. By trial and error, a value of k=0.737 has
been adopted in this paper. Trial values of T
C are chosen for
each blade element, and substituted in equation (18b), to get a corresponding axial induction factor for each blade element. The total torque on the WT rotor is given by the algebraic sum of all the elemental torques [5]. Total torque, T is given by:
17
1
T dT (23)
Power captured, P is expressed as: P T (24)
The Power Coefficient, pC is given by:
2 32 /pC P R U (25)
Some important parameters are calculated using equations (26), (27) and (28) below:
* /N NF dF R (26)
* /T TF dF R (27)
* /r r R (28) Equations 1 through 37 are coded in MATLAB and graphs of
*r against *NF and *TF respectively, are plotted for both
the wind mill state and the turbulent wake state as shown in figures below.
Plots of r against /NdF dr , /TdF dr , a, and c respectively
are made. For the wind mill state, a rotor angular speed of 1.13rads/s and a mean wind speed of 10.13m/s are used; whereas for the turbulent wake state an average gust of 10.97m/s and a rotor angular speed of 1.224rads/s are used in the calculations. The rotor blade pitch angle used in this paper is 15º. The computation time for the wind mill state is 10.99seconds and a
computation time of 11.66seconds is recorded for the turbulent wake state. RESULTS The above relations were coded in MATLAB for the wind mill and the turbulent wake states respectively and each code was run and the resulting graphs are shown in figures 11 through 19.
Fig.9- Normalized Radius versus Normal force per unit Span
Fig.10- Normalized Radius versus Tangential Force per unit Span
Fig. 11- Elemental Normal Force per Unit Element Length
Fig.12- Elemental Tangential Force per Unit Element Length
Fig. 13-Chord Distribution Along the Rotor Blade
Fig. 14- Axial Induction Factor
Fig. 15-Normalized Radius versus Normal force per unit Span
Discussion of Analysis Results The 24-year mean wind speed at the WT hub for the MOWF is estimated to be 10.13m/s while the hourly wind gust is 10.97m/s. A turbulence intensity (TI) of 37% is estimated for the site. The mean wind speed at 80m height is about 10m/s. Based on these findings, the MOWF is a class 7 site in accordance with NREL’s criteria. The plots of normal force per unit span (i.e. Fn*) for both the wind mill state and the turbulent wake state shown in figures 9 and 15 respectively are the results of the BEMT implemented in this work, whereas the plot in figures 20 is the result of CFD simulations based on the actuator line model (ALM) [12] implemented on the 5MW NREL reference WT at a mean wind speed of 8m/s. Figure 22 adopted from reference [10] shows the plot of the same parameter based on the results of ALM and BEMT for an unspecified WT under unspecified site conditions. Based on these four plots, it could be discerned that, the curves do follow a similar trend. The difference between them is in the magnitudes of the normal force per unit span. The BEMT implemented in this work results in lower values of this parameter, whereas the plots from references [10,12] show values which are about ten times higher than those of the former. The plots of elemental normal force per unit element length in figures 12 and 19 for the wind mill and turbulent wake states respectively show values that are higher than those of the reference curves. The higher values are the result of the fact that, a higher mean wind speed was used in the BEMT implemented in this work. The plots of tangential force per unit span (i.e. Ft*) for the wind mill and the turbulent wake states respectively shown in figures 10 and 16 are also the results of the BEMT implemented in this work, while the plot in figure 21 is the result of CFD simulations based on the ALM implemented on the NREL WT in study, at a mean wind speed of 8m/s. Figure 23 which is adopted from reference [10] is a plot of the same parameter based on both the ALM and the BEMT. The curves in figure 23 show drops in the tangential force within the interval 0 10r , a steep rise at about 10r and the curves almost flatten between the interval 10 60r and drop within the interval 60r . The curves in figures 10 and 16 have most of these features, but for the plateau between the interval 10 60r while the curves based on the ALM have the same features except for the depressions in the middle. The values of Ft* shown in figures 10 and 16 are of the same order of magnitude with those in figures 21 and 23 respectively even though the conditions under which the ALM and BEMT schemes resulting in figure 23 are not specified in reference [10]. The higher values of Ft* in figure 16 are evidence of the fact that, a higher mean wind gust was used in the BEMT scheme. Despite the higher mean wind speed, the values of Ft*
obtained for the wind mill state are lower than those in fig. 21. Figures 12 and 19 above, are plots of elemental tangential force per unit element length for the wind mill and turbulent wake
states respectively. The values of /tdF dr for the turbulent
wake state are slightly higher than those of the wind mill state. This slight difference is evidence of the fact that; the WT is less
efficient when in the turbulent wake state than in the wind mill state.
In both the wind mill and turbulent wake states, /tdF dr and
/ndF dr are third order polynomials in r. Equations 29 through
32 depict the situation. Turbulent Wake State
230.2 26.7 909 2834.7/ndF dr r r r (29)
230.2 21.4 721.3 3954.1/tdF dr r r r (30)
Wind Mill State
230.1 15.9 572.9 1017.1/ndF dr r r r (31)
230.1 18.1 628.9 3822/tdF dr r r r (32)
Based on these equations Fn and Ft can be estimated as follows:
( / )h
R
n n
r
F dF dr dr (33)
( / )h
R
t t
r
F dF dr dr (34)
The chord length is a quadratic function of the element radius r as shown in equation (35) below:
20.0014 0.533 3.7096c r r (35)
For the wind mill state, the axial induction factor is a linear function of r as illustrated below;
0.0001 0.3371a r (36) The axial induction factor in the turbulent wake state is a quadratic function of r as shown below:
20.0004 0.0206 0.5619a r r (37)
The total energy captured in the wind mill state is 3.2548MW resulting in a power coefficient of 41% while the total power captured in the turbulent wake state is 3.906MW resulting in a power coefficient of 33.63%. The maximum power captured by the WT in study, based on reference [12] is 2.113MW, resulting in a power coefficient of 54%. Typically power coefficients for most modern commercial HA WTs range from 40% to 50% [1]. CONCLUSION It is clear from the aforementioned that, there exists a functional relationship between the blade element radius and the local chord length of the blade element. There is no gainsaying that,
the empirical formula developed in this work can be used to design an HAWT rotor blade that has the same characteristics as the rotor blades of the 5MW NREL reference WT. In a nutshell, one airfoil shape can be used to generate the entire rotor blade. This will result in a decrease in manufacturing and design efforts. The axial induction factor has been shown to depend on the blade element radius. Empirical formulae developed in the foregoing section will greatly facilitate the estimation of the axial induction factor during BEMT simulations. It is also discernible from the foregoing sections that, the HAWT is more efficient in the wind mill state than in the turbulent wake state. Future work that has to be done includes, BEMT (both steady and unsteady) simulations at various blade pitch angles between 0º and 90º and CFD simulations for various blade pitch angles within the same range. REFERENCES 1. Zayas, J., “Scope of Wind Energy Generation Technologies”, Ch.7, pp7-1 to 7-19, Energy and Power Generation Handbook by Rao, K. R., A.S.M.E. Press 2001. 2. Baldwin, T., Seifert, G.,” Wind Energy in the US,” Ch.8, pp 8-1 to 8-22, Energy and Power Generation Handbook by Rao, K, R., A.S.M.E. Press 2011. 3. Bailey, S. G., Viterna L. A., “Role of NASA in Photovoltaic and Wind Energy”, Ch.6, pp6-17 to 6-21, Energy and Power Generation Handbook by Rao, K.R., A.S.M.E. Press 2011. 4. Eecen, P., “Wind Energy Research in the Netherlands”, Ch.9, pp9-1 to 9-15, Energy and Power Generation Handbook by Rao, K. R., A.S.M.E Press 2011. 5. Taylor, D., “Wind Energy”, Ch.7, pp297 to 354, Renewable Energy (Power for a Sustainable Future), 3e, by Boyle, G., Oxford 2012. 6. Manwell, J., McGowan, J. G., Rogers, A. L., “Wind Energy Explained- Theory, Design and Applications,” 2e, Ch.1 through 3, pp1 through 155, Wiley 2011. 7. Shaltout, M. L., Hall, J. F., Chen, D., “Optimal Control of a Wind Turbine with a Variable Ratio Gearbox for Maximum Energy Capture and Prolonged Gear Life” pp031007-1 t0 031007-7., Journ. Of Sol. Energy Engng., vol. 136, Trans A.S.M.E. Aug., 2014. 8. Ramakumar. R., Butterfield, C. P., “Wind Power,” Ch. 9, pp9-5 t0 9-10, Marks Handbook for M.E., 10e, McGraw Hill 1996. 9. Wang, W., Caro, S., Bennis, F., Mejia, O., R., S.,“A Simplified Morphin Blade for Horizontal Axis Wind Turbines,” pp011018-1 to pp 011018-18, Journ. Of Sol. Energy Engng., vol. 136, Trans A.S.M.E., Feb 2014. 10. Hansen, M. O., L., “Aerodynamics of Wind Turbines”, Ch. 1 through 16, 2e, Earthscan 2008. 11. Dai, J., Liu, D., Hu, Y., Shen. X., “Research on Joint Power and Loads control for Large Scale Directly Driven Wind Turbines”, pp021015-1 to 021015-9, Journ. Of Sol. Energy Engng. Vol. 136, Trans A.S.M.E., May 2014. 12. Jha, P. K., Churchfield, M. J., Moriati, P. J., Schmitz, S., “Guidelines for Volume Force Distribution Within Actuator Line Modeling of Wind Turbines and Large Eddy Simulations- Type Grid”, ppo31003-1 to 031003-11, Journ. Of Sol. Energy Engng., Vol. 136, Trans. A.S.M.E., Aug 2014.
13. Song, Q., Lubitz, W. D., “Design and Testing of a New Small Wind Turbine Blade,” pp034502-1 to 034502-4, Journ. Of Sol. Energy Engng., Vol. 136, Trans. A.S.M.E, Aug 2014. 14. Kulunk, E.,” Aerodynamics of Wind Turbines, “Fundamentals and Advanced Topics in Wind Power by Carriveau, R., Intech 2011. www.intechopen.com. Website was accessed on Sept 9, 2015. 15. Ali, M. H.,” Wind Energy Systems Solutions for Power Quality and Stabilization” Ch.2, pp17-25, CRC Press 2012. 16. www.ndbc.noaa.gov/masdes.shtml, “Website was accessed on Sept 28, 2015”. 17. Ning, S. A., Damiani, R., Moriarti, P. J., “Objectives and Constraints for Wind Turbine Optimization”, pp041010-1 to 041010-11, Journ. Of Sol. Energy Engng, Vol 136, Trans. A.S.M.E., Nov 2014. 18. Jonkman, J., Butterfield, S., Musial, W., Scott, G., “Definition of a 5-MW Reference Wind Turbine for Offshore System Development”, NREL Technical Report # NREL/TP-500-38060, Feb 2009.
NOMENCLATURE
a Axial Induction Factor
a’ Rotational Induction Factor
U Mean Wind Speed- m/s
Urel Relative Wind Speed- m/s
Ω Wind Turbine Rotor speed- rad/s
Relative Wind Angle- °
p Local Blade Pitch Angle- °
op Blade Pitch Angle- °
T Blade Element Angle of Twist- ° ∝ Angle of Attack- ° Fn Elemental Normal Force-N
Ft Elemental Tangential or Driving Force- N
T Elemental Torque- N-m
Fn* Elemental Normal Force per unit Span- N/m
Ft*
r r*
R
rh
Elemental Tangential Force per unit Span- N/m Element Center Radius from Hub Center- m Normalized Element Radius- Dimensionless Swept Radius of WT Rotor Blade- m Rotor Hub Radius- m
