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A novel adaptive blade concept for large-scale wind turbines. Part I: Aeroelastic behaviour
Energy xxx (2014) 1e10
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A novel adaptive blade concept for large-scale wind turbines. Part I: Aeroelastic behaviour M. Capuzzi*, A. Pirrera*, P.M. Weaver Advanced Composites Centre for Innovation and Science, Aerospace Engineering Department, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 October 2013 Received in revised form 20 March 2014 Accepted 14 April 2014 Available online xxx
This two-part paper introduces a novel aeroelastic approach to the design of large-scale wind turbine blades. By suitably tailoring the blade's elastic response to aerodynamic pressure, the turbine's Annual Energy Production is shown to increase, while simultaneously alleviating extreme loading conditions due to gusts. In Part I, we use a current blade as the baseline for an aerodynamic analysis aimed at maximising the turbine's yielded power. These results are then used to identify ideal aeroelastic behaviour. In Part II, we exploit material and structural bend-twist couplings in the main spar to induce appropriate differential blade twist, section by section, while bending flap-wise. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Wind turbine blade design Aeroelastic tailoring Yielded power maximisation
1. Introduction and rationale In recent years, the cost of energy produced by alternative supplies has steadily decreased. This, together with several other socio-economical reasons, has made alternative energies increasingly competitive and, hence, a viable alternative to more traditional sources such as carbon, oil or nuclear power [1e6]. This trend is confirmed by industry growth figures. The wind energy industry, in particular, has grown and is predicted to grow steadily, both in terms of investments and installed capacity [7]. From an engineering perspective, the growth in this sector raises some interesting challenges as it creates the drive to build larger, more durable rotors that produce more energy, in a cheaper, more cost efficient way [8,9]. The rationale for moving towards larger rotors is that, with current designs, the power generated by wind turbines is theoretically proportional to the square of the blade length [9]. Furthermore, taller wind turbines operate at higher altitudes and, on average, at greater wind speeds. Hence, in general, a single rotor can produce more energy than two rotors with half the area. Having said this, larger blades are heavier, more expensive and increasingly prone to greater aerodynamic and inertial forces. In fact, it has been shown that they exhibit a cubic relationship
* Corresponding authors. E-mail addresses: [email protected] (M. Capuzzi), alberto.pirrera@ bristol.ac.uk (A. Pirrera).
between length and mass [9], meaning that material costs, inertial and self-weight effects grow faster that the energy output as the blade size increases (see Fig. 1). In this scenario, the demand for improvements in blade design is evident. The notion of increasingly mass efficient turbines, which are also able to harvest more energy, is indeed immediately attractive. The aim and rationale of our effort are set out in the next section while the current state-of-the-art is discussed in Section 1.2. 1.1. Design drivers and aim of the work The power curve of a modern variable-speed wind turbine is typically characterised by distinctive operating conditions. These are the cut-in, rated and cut-out wind speeds and are shown in Fig. 2. Wind speeds above and below rated correspond to different operating regimes, in which the aerodynamic couple acting on the rotor and its angular speed are controlled to meet specific requirements. Below rated speed they can increase to maximise the yielded power, as the components of the turbine do not operate at their structural limit. Conversely, above rated, the angular speed and the couple are generally set by structural integrity reasons (e.g. limited fatigue loads). In summary, a wind turbine blade is designed to maximise its aerodynamic performances below rated speed and to withstand extreme loads above it. This work presents a novel adaptive blade concept that, for the first time to the authors' knowledge, satisfies both these design drivers, exploiting aeroelastic tailoring principles to improve the performance of current blades.
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Nomenclature a
a
aopt
CD CL c D Drj F fhub ftip L
dimensionless induced flow speed (induced speed divided by undisturbed wind speed) angle of attack angle of attack that maximises the component T of the aerodynamic force drag coefficient lift coefficient chord of the airfoil drag force spanwise width of blade element j aerodynamic force resultant hub loss factor tip loss factor lift force
In particular, by suitably tailoring the blade's elastic response to aerodynamic pressure, the turbine's Annual Energy Production (AEP) is shown to increase, while also alleviating extreme loading conditions due to gusts. This is done by purposefully designing bend-twist coupling into the main spar, so as to have the blade sections twist appropriately while bending flap-wise. Specifically, the angles of attack of the blade's aerodynamic sections are designed to adapt to different wind speeds in order to maximize energy harvesting and gust load alleviation, respectively, below and above rated conditions. 1.2. Background Owing to the increased mass and loads associated with larger wind turbine blades, prior research has focused on reducing either weight or aerodynamic forces. For instance, Refs. [11e14] performed structural optimisations aimed at minimising the mass of some, or all, of the turbine's components. Other authors [15e20] looked at the possibility of alleviating extreme aerodynamic loads (i.e. gust loads), in order to relax prevailing design constraints by passive adaptive concepts. Similarly, Refs. [21,22] considered flexible and morphing airfoil sections as a means for load alleviation and improved energy production, respectively. Here, we only report on studies in which load alleviation is obtained in a passive adaptive manner, i.e. by exploiting the capabilities that structural anisotropy and geometrically induced couplings provide. For example, Refs. [15e20] designed the main spar's
Fig. 1. Blade mass vs. rotor radius. Adapted from Ref. [10].
N Nblades Nel
u f
R r rhub rtip
r
T
q
qopt V0 V1
aerodynamic force normal to the rotor plane number of blades in the rotor number of blade elements in the aerodynamic mesh angular speed of the rotor inflow angle rotor's radius radial coordinate in the rotor plane radial coordinate of the hub section radial coordinate of the tip section air density aerodynamic force tangential to the rotor plane and perpendicular to the radial direction geometric twist of a blade's section geometric twist of a blade's section that maximises T undisturbed wind speed resultant flow speed at a blade's section.
torsional and bend-twist stiffnesses to induce a rotation towards feather (nose-down) of the blade's sections, thereby reducing the angles of attacks (AOA) and, consequently, the aerodynamic forces acting on the profiles. For a given blade length, this approach provides benefits, but has proven to be detrimental in terms of Annual Energy Production (AEP) [18]. Indeed, on the one hand, alleviating the gust-induced loads above rated wind speed damps the power oscillations, the structural vibrations and allows the reduction of the ultimate design load due to the 50 year gust. On the other hand, below rated speed, i.e. when the system does not operate at its design limit and power maximisation is the main goal, the same working principle causes a power loss. It must be noted, by allowing the blade length to increase, the power loss can be overcome at the expense of the benefits to the load. At the limit, in which the adaptive and classic designs have the same ultimate load, the power yielded by the former is greater. In all of the aforementioned studies the elastically induced twist has a monotonic distribution that increases along the length of the blade, running from root to tip. The required coupling is achieved by using unbalanced composite laminates in some cases [16e18], or with swept blades in some others [15,19,20]. Some researchers also explored the opportunity of towards stall bend-induced twist (nose-up). A notable example is given by Ref. [23]. In this case, stiffness coupling causes a decrease of the sections' twist, which is more pronounced traversing from the blade's root to tip. Strictly speaking, this work was concerned with constant speed wind turbines, but its conclusions can be generalized: such a solution, despite enhancing the AEP, gives a notable increase of gust-induced and fatigue loads. To conclude, it is noted that an adaptive blade that improves both yielded power and extreme loads requirements has not yet
Fig. 2. Typical trend for the power curve of a pitch controlled wind turbine.
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been proposed. This goal provides the main focus of the present work. The details of the proposed approach are set out in Section 2.
3
elastically induced twist contribution to the total twist should be considered. This being the case, the designer has three degrees of freedom to set, as opposed to two in typical current designs. Summarising, for the sake of clarity:
2. The novel adaptive approach Total twist ¼ pre-twist þ pitch angle Generally speaking, the aerodynamic design of a blade is characterised by geometric and control features such as -
the the the the the
blade length, section's thickness-to-chord ratio, section's pre-twist and chord distributions, airfoil shape along the length, pitch angle and angular speed control laws.
If all of these parameters, except the pre-twist and the pitch angle, were to be considered as given design variables, the power yielded by the turbine (standard nomenclature and geometric features in Fig. 3) would depend only on the total twist distribution (note, this is the sum of pre-twist and pitch angle. It determines the sections' AOA and hence the torque acting on the rotor). Conceptually, in typical designs, the AEP can be maximised by choosing the pre-twist to be optimal at a given wind speed, and then controlling the pitch to regain part of the power loss at different wind speeds. In aeroelastic approaches, the aerodynamic profile of the blade is no longer considered as torsionally rigid. As a consequence, the
in classic designs and Total twist ¼ pre-twist þ pitch angle þ elastically induced twist in aeroelastic designs. In this work, by adopting an aeroelastic approach, the turbine's AEP and its variation as a function of the total twist, is studied. Then, the blade's bend-twist coupling is set so as to maximize the power yielded below rated wind speed, by allowing the AOAs of the sections along the blade length to adapt to different wind speeds. Similarly to previous concepts described in the literature, the adaptation consists of a nose-down rotation of the sections, but in this case, the elastically induced twist is no longer a monotonic function of the radial position. Upon bending, moving from root to tip, the induced twist, at first decreases the AOAs, then, outboard, the trend is inverted and the AOAs increase again. It is noted that, despite the inversion of the twist rate in the second half of the blade, all the sections move towards feather. As a
Fig. 3. Parts and nomenclature in a conventional wind turbine. Adapted from Ref. [24].
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result, this concept retains some of the load alleviation capabilities of the designs proposed in Refs. [15e20] even if it is somewhat diminished. The reason that the suggested induced twist distribution increases the yielded power is essentially due to aerodynamic effects and will be detailed in the following sections. The novel structural design is the topic of Part II companion paper. 3. Foundational aerodynamic study In this section, we present an aerodynamic study aimed at optimising the total twist distribution at several operating conditions, spanning from cut-in to rated wind speed. At each of these operating conditions the optimised twist yields maximum power output. The blade characteristics were made available from an industrial partner. The values refer to an existing large-scale variable-speed WT, which is pitch controlled to twist towards feather. In the remainder of this paper, all of these data, except those defining the total twist, are considered as given design parameters. The reference WT is three-bladed. The aerodynamic model and the optimisation method are detailed in Sections 3.1 and 3.2, respectively. 3.1. Aerodynamic modelling The aerodynamic model adopted in this work is based on the Blade Element Momentum (BEM) theory as described, for instance, in Ref. [25]. The flow around the airfoil and relevant forces, for this model, are shown in Fig. 4a and b (symbols are introduced where used). An in-house MATLAB® model has been developed to estimate the nondimensional component of induced flow perpendicular to the rotor plane, denoted by a in Fig. 4a. The model is described in A. The tangential component, a0 has been neglected. Our model also includes standard engineering corrections, such as tip and hub loss factors. Furthermore, to model the turbulent windmill state, the aerodynamic tool has been complemented with a Buhl correction [27]. This is obtained by modifying the classical Glauert empirical relationship, which extends BEM applicability to conditions where the dimensionless induced speed, a, is greater than 0.5. Buhl's modification is a numerical expedient that allows
Glauert's correction to be used when tip and hub loss factors are employed. The implementation of this correction enables the model to be used for the optimisation of the blade's twist distribution. Indeed, in this way, the model was able to give solutions even when a is greater than 0.5. In terms of accuracy, we note that optimal power outputs never correspond to these turbulent windmill conditions, therefore the use of Buhl's correction is expected to have little or no effect on the optimum twist distributions. This conclusion is also confirmed by the results that are presented later. The reason that the correction is implemented is that it allows the model to be used over a wide range of twist values, as is required for the twist optimisation study. 3.1.1. Validation For verification purposes, the power output calculated by our aerodynamic model for the baseline WT has been validated against WT_PERF [28]. A comparison of the results is shown in Fig. 5. The power curves are shown for the wind speeds between cut-in and rated (3.5e15 m/s) and they show adequate agreement. Both software require an aerodynamic mesh, hence the blade has been segmented into 13 elements. Such refinement produced satisfactory converged results. The values and distributions of the orthogonal induced speed have also been successfully validated. Furthermore, the effect of neglecting a0 on the power estimation under conventional flow conditions was found to be negligible. These results are not shown for the sake of brevity. 3.2. Yielded power optimisation The total twist distributions that maximise the power output at different operating conditions are found by performing an exhaustive search. This search was conducted within a preassigned domain of realistic twist values, independently for each element of the aerodynamic mesh and at operating conditions corresponding to wind speed increments of 0.5 m/s in the interval from cut-in to rated speed. In the next section, the qualitative nature of the results is anticipated by reasoning on the fundamental BEM equations and
Fig. 4. Flow (a) and forces (b) on the blade section. Adapted from Ref. [26].
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the optimum twist as a function of wind speed and radial position for the operating conditions below rated. We start the analysis by differentiating Eq. (2) with respect to V0. Then,
vq vf va vf ¼ ¼ vV0 vV0 vf vV0
1
va vf
vf : vV0
(4)
Generally speaking, in order to maximise CT, we seek an aerodynamic profile at approximatively its maximum efficiency, i.e. in the interval of AOAs around the point that maximises the ratio CL/CD. This is the case for any inflow angle, hence, ideally for varying f, we seek a q value at each section to maintain a ¼ aopt xaðmaxðCL =CD ÞÞ. With reference to Eq. (4), this suggests Fig. 5. Comparison between power curves: WT_Perf and author's model results.
the optimisation's input data. Numerical results are then presented in Section 3.4 and shown to confirm expectations. For the sake of clarity, it is noted that during the power optimisation procedure all of the blade features, except for the sections' total twist, are treated as given parameters and kept constant. Furthermore, our work deals with static aeroelasticity and only considers the effect of static twist variations on the turbine's yielded power. Flap-wise vibrations and twist dynamics also have an effect on the power performance, but dynamic effects have so far been neglected and will be the subject of future analyses. This approach does not limit the generality of the results presented here, and reflects a modus operandi commonly practised in the wind energy industry, i.e. the use of steady power models for the preliminary aerodynamic blade design. In fact, several commercial tools are available for this type of procedure. 3.3. Critical model analysis As mentioned in Section 3.1, within the framework of BEM assumptions, the aerodynamic field on the blade section can be sketched as shown in Fig. 4a. The operating condition is fully determined by assigning the wind speed V0 and the angular speed control law uðV0 Þ. As with the BEM model, selecting the total twist q at a distance r from the rotor's centre determines the nondimensional induced flow a, which is basically a function of the thrust developed on the blade element. This, in turn, gives the relationship
f ¼ tan1
V0 ð1 aÞ ur
(1)
and
f ¼ q þ a;
vaopt ≪1; vf
(5)
and substituting in Eq. (4), we have
vqopt ¼ vV0
1
vaopt vf
vf vf x : vV0 vV0
(6)
This means that the optimum total twist variation reflects the distribution of inflow angle. The latter quantity can be studied by differentiating Eq. (1). By so doing, we obtain
vf v V ð1 aÞ ¼ tan1 0 vV0 vV0 ur r vu va ¼ ð1 aÞ u V uV : 0 0 vV0 vV0 u2 r 2 þ V02 ð1 aÞ2 (7) The qualitative behaviour of this function is understood as follows. First, in optimal conditions, a can be assumed to be smaller than one and almost constant with V0dthis is clear considering the BEM fundamentals. Secondly, for modern wind turbines, the variation of angular speed with V0 below rated is typically described by the curve in Fig. 6. Hence, for wind speeds within the interval between cut-in to rated vu=vV0 x0, we deduce that vf=vV0 is positive and a decreasing function of the radial location. By virtue of Eq. (6), this also holds true for vqopt =vV0. Ultimately, it can be concluded that, below rated but well above the cut-in speed, the results of the aerodynamic optimisation should give an optimum total twist which increases as a function of the wind speed. Furthermore, this increase is expected to be accentuated from tip to root. On the other hand, for operating conditions closer to cut-in, the term vu=vV0 in Eq. (7) cannot be
(2)
determines the inflow angle f and the AOA a. Here, with reference to Fig. 4a, we recall that a0 is neglected. The forces acting on the section under consideration are shown in Fig. 4b, where, with customary notation, L and D are lift and drag, F is the force resultant, and T and N are its components on-to and normal-to the rotor plane, respectively. Finally, the tangential component T is expressed, in dimensionless form, as
CT ¼ CL sin f CD cos f:
(3)
Since the aerodynamic field is determined by q, it is evident that at each operating condition there will be a q ¼ qopt that maximises CT and hence provides maximum power output. This consideration, together with Eqs. (1)e(3) facilitate prediction of the variation of
Fig. 6. Typical distributions of angular speed with wind speed for a variable-speed WT.
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neglected. Therefore, vf=vV0 may be negative and, consequently, qopt could decrease with V0. 3.4. Aerodynamic optimisation results Here, the results of the aerodynamic optimisation, described in the previous sections, are presented. The optimum total twist distribution, at different radial locations, is shown as a function of the operating conditions in Fig. 7. As anticipated in Section 3.3, on the right-hand side of the plot the curves increase monotonically. Furthermore, their gradients decrease with the radial position (moving from root outboard). At lower wind speeds the curves become more irregular and, mostly, their slope inverts. 4. Optimum adaptive behaviour: target curves Based on the aerodynamic study presented in Section 3, the present aim is to identify a distribution of induced elastic twist that realises the shape adaptation necessary to maintain the optimal total twist profile at all of the operating conditions. In other words, an aeroelastic concept is sought where the blade's twist distribution follows the curves shown in Fig. 7. As mentioned in Section 2, the total twist distribution has three parts. These are the pre-twist, the pitch angle and the elastic twist. If the pre-twist is chosen to match qopt at a given operating condition, its values can then be obtained as the intersections of the curves shown in Fig. 7 with the vertical line identifying the chosen wind speed. Henceforth, this wind speed is referred to as the design wind speed. For any other operating condition, in an attempt to follow the optimal curves closely, the total twist can then be adjusted using pitch control. This, however, changes its values by the same amount at all of the radial locations, thus forcing a deviation from optimal conditions. This can be seen from Fig. 7, where the optimum total twist is observed to change with a different rate depending on the radial location. This approach for the aerodynamic design entails a loss of power but, in principle, it is similar to the one used in conventional turbines (in general, to be strictly accurate, the pre-twist is not chosen to be optimal at the design wind speed, but to be a suitable compromise over the entire range of operating conditions). This power loss can be partially overcome by exploiting an elastically induced twist, as it allows the total twist to vary with the aerodynamic load and notably, differentially, along the blade length.
Fig. 7. Optimum twist values as a function of wind speeds, at different fixed radial positions.
By further analysing Fig. 7 it is noted that, given a pre-twist, if the optimal curves were to be accompanied with an elastic contribution, the latter would have to change sign where the curves change from negative to positive gradient. This need arises because, for increasing wind speed, the elastic twist should first (where the curves' slope is negative) be nose-up to decrease the total twist; then nose-down to increase it. This deformation mechanism cannot be achieved passively, as it would require the blade's bend-twist coupling at a given radial location to change sign depending on the wind speed. In the present work, in order to design an adaptive behaviour which allows for both increased power output and reduced gust loads, we define Adaptive Target Curves. These are modified optimum total twist curves that can be followed adaptively, i.e. by only adding an elastic twist contribution to a set pre-twist. These curves are shown in Fig. 8, where, for the sake of clarity only four radial locations are considered. They are obtained from the optimum total twist curves by imposing a horizontal tangent where the slope is not constantly positive. The target curves are achievable because they require the blade sections to only twist nose-down for all operating conditions. Such a combination of pre- and elastic twist allows the optimal power curves to be followed closely in the upper half of the operating wind speed range. The power that is lost in the first half can then be partially recovered by prescribing a suitable pitch variation that realises the required nose-up rotation of the blade sections. The target curves are shown in an alternative way in Fig. 9. In this case, the target twist distribution is presented as a function of the blade's radial coordinate at different wind speeds. Again, only a few curves are shown for clarity. This representation is useful for several reasons. Firstly, it gives a clear picture of the geometry of the target twist along the blade. Secondly, it shows clearly that the distance between the target curves changes along the blade length, which is fundamentally the justification for an aeroelastically tailored design. Indeed, the differential change of the curves' shape
Fig. 8. Twist curves, optimum and suboptimal solutions. Twist values are shown at fixed radial positions (where R is the radius of the turbine) and for a variable speed of wind within the below rated range.
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With reference to the baseline blade, let us consider the wind speed V0 ¼ 15 m/s. As this is the design speed, the pre-twist must be chosen to match the corresponding qopt curve, which is indicated in Fig. 10 with a dotted line. At different operating conditions the total twist can be modified, with a power loss, by pitching the blade. For instance, and still referring to Fig. 10, the total twist at V0 ¼ 9 m/s should follow the target curve indicated with a dashed line. However, since pitching the blade corresponds to a vertical translation of the twist curves, the best compromise in terms of power output is realised by the solid line. It is noted that, in this case, i.e. for torsionally rigid blades, the aerodynamic design is based on the optimal total twist curves of Fig. 7, rather than on the target curves (of Figs. 8 and 9). In addition, we note that, in general, the blade's pre-twist does not necessarily have to be chosen to follow the qopt of the design operating condition. (In fact, our baseline blade represents a practical compromise: its pre-twist does not follow any of the optimum curves.) Nonetheless, regardless of the technique adopted to set the pre-twist distribution, the example illustrated here shows all of the limitations of classic designs. These, in fact, are inherently due to the way that optimum curves change with V0 and to the torsional rigidity of classic blades. 5.2. Aeroelastically tailored approach for the aerodynamic design of the blade Fig. 9. Suboptimal twist distributions along the blade's axis, for fixed wind speeds.
can only be achieved via an elastic twist deformation, as pitching the blade corresponds to a rigid vertical translation of the fixed pretwist distribution. Lastly, it shows that the target curves only move upward for increasing wind speeds, which is the reason that they can be matched by adding a nose-down contribution to the initial pre-twist. Conversely, if the unmodified qopt curves were to be plotted in Fig. 9, for increasing wind speeds, they would, at first, shift downwards and then upwards again. This, as already mentioned, is a behaviour that is not structurally feasible (for linear responses, at least), because it would require the sections' stiffness coefficients to change sign. 5. Adaptive behaviour design In Section 4, by defining target curves, we have identified the twist deformation required for optimisation of yielded power. In this section, we fine-tune pre-twist, pitch and elastically induced twist in a combination that realises the desired aeroelastic behaviour. To further clarify the differences between the proposed approach and conventional design methods and for a better appreciation of its advantages/limitations, this section is divided in to two parts. In Section 5.1 a blade design that does not rely on induced deformations is presented; in Section 5.2 a fully aeroelastically tailored design is shown. In both sections, we compare and contrast the total twist designed into the blade with that prescribed by the target curves.
In this section, the aeroelastic design, that realises the sought adaptive behaviour, is presented. First, reconsider the operating conditions used in Section 5.1. As shown in Section 4, the target curves were used rather than the optimum total twist distributions. These are shown as the upper plot in Fig. 11. The total twist variation required for the structure to adapt from one condition to the other is shown in the lower plot in this figure. This variation is reproduced by the dashed curve in Fig. 12, where we note that the variation could be realised by combining a nose-up elastically induced twist with a nose-down pitch. In this figure, the nose-up elastic twist and the nose-down pitch are represented by the dotted line and by its vertical distance from the dashed curve, respectively. Despite its feasibility, this adaptive solution was disregarded, as it does not satisfy the pre-established power and load requirements, simultaneously. Indeed, as mentioned in Section 1.2, a nose-up adaptation implies an increase in gust-induced loads.
5.1. Torsionally rigid blade's aerodynamic design In the most simplistic approach, when a blade's structure is such that the aeroelastic contribution to the total twist is negligible, its design can be based upon the choice of a ‘design operating condition'. This is usually a wind speed that yields high power output and occurs with reasonable frequency. Such conditions are normally found in the upper part of the below rated wind speed range.
Fig. 10. Matching of optimum twist distributions with the classic approach.
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Fig. 11. Required variation of twist in order to move from one optimum twist distribution to another.
In the current approach, the total twist variation is achieved by defining a pre-twist distribution and by designing nose-down, bend-twist coupling into the blade. However, it is noted that no realistic distribution of nose-down elastic twist will be able to reproduce the dashed curve of Fig. 12 exactly. Indeed, since the root is the fixed end of the structure, the induced twist value at this point is zero. Due to this practical constraint, the target curves are matched exactly only on the outboard portion of the blade. This is shown qualitatively by the solid line in Fig. 12. This curve represents a nose-down rotation of the blade sections, which increases moving outboard and then follows the dashed line after reaching it. In summary, in our aeroelastically tailored design we invert the gradient of the elastically induced twist distribution halfway along the blade.
Fig. 12. Ideal twist variation and feasible induced elastic twist distribution.
Materials and structural considerations that meet such aeroelastic behaviour are discussed in Part II of this paper. Before concluding, we show that the increasing-decreasing spanwise elastic twist qualitatively affects the aerodynamic design of the blade. As already considered in Section 5.1, the rated wind speed is the ‘design operating condition'. With an aeroelastic approach, blade sections can be designed to follow the relative target curve with a combination of pre-twist and elastically induced twist. For lower wind speeds, the latter decreases according to the solid curve shown in Fig. 12. The result is a blade design that behaves as indicated by the upper plot in Fig. 13. The design's target curve (dotted line) at rated speed is matched exactly. At cut-in (dashed line), by prescribing an increasing-decreasing elastically induced twist distribution, the target curve is matched only in the second half. In the first half, the total twist of the design deviates from the target curve. Comparing this design with that of Fig. 10 it is apparent that, overall, the target curves are followed more closely. This, in turn, gives the blade superior energy harvesting capabilities. (It is worth emphasizing that the outermost half of the blade yields approximately 80% of the total power.) Furthermore, these are achieved with a nose-down aeroelastic adaptation, which also ensures load alleviation, even if somewhat attenuated in comparison to previous aeroelastically tailored designs with monotonic distributions of elastic twist. In conclusion, Fig. 13 depicts the design philosophy of the proposed aeroelastic concept and it shows the required variation of elastically induced twist. It is noted that, due to the stiffness properties of realistic blades, the elastic twist at cut-in is generally negligible. This considerably simplifies the structural design that will be detailed in Part II, because it means that a blade is required that achieves the elastic twist distribution prescribed for rated speed, rather that one realising the twist variation between cut-in and rated.
Fig. 13. Aeroelastic design, improved matching between optimum twist distributions relatively to cut-in and rated conditions.
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6. Conclusion
Nj ¼ In part I of this article, a new aeroelastic approach for the aerodynamic design of a wind turbine blade is introduced. In the proposed method, the blade's torsional deformation is exploited to change its total twist distribution, hence its sections' angle of attack, at different operating conditions. The aeroelastic design is based on an aerodynamic study of the total twist distribution aimed at maximising the yielded power. Results were presented as total twist curves varying as functions of the radial position along the blade and of the wind speed. They show that the turbine's power output cannot be maximised with pitch control only, because the optimum total twist varies differentially, but also that the ideal adaptive behaviour is not feasible from a structural point of view. Initial results have subsequently been modified to define the ‘target twist curves', i.e. total twist distributions that are possible by passive structural adaptation. Ultimately, by considering target curves and structural constraints, such as the clamped condition for the blade root, an elastically induced twist distribution was identified that induces a nose-down rotation of the blade, with the magnitude of this rotation having an increasing-decreasing trend along the blade length. This solution matches the target curves on the outermost half of the blade, thus giving superior power harvesting properties, while, on the other hand, it retains gust load alleviation capability. In part II, we introduce the structural design, with which we embody and realise the passive behaviour identified here. Additionally, we assess the increase of yielded power in terms of Annual Energy Production.
Acknowledgments The authors wish to thank Chris Payne and Tomas Vronsky of Vestas Technology R&D for their technical support.
Appendix A. Algorithm for the determination of a The first step in the procedure to calculate the distribution of induced flow along the blade is to define an aerodynamic mesh. To this end, the blade's span is divided into a finite number of longitudinal elements of length Drj , with j ¼ 1; 2; …; Nel . Next, the undisturbed wind speed, V0, the angular speed of the rotor, u, and the rotor's radius, R, are assigned. Furthermore, in order to define the blade elements' aerodynamic properties, the in-house MATLAB® tool requires the following geometric parameters, defined as functions of the radial coordinate r: -
Airfoils (NACA 6-series for the baseline blade), Chord, c, of the aerodynamic section, Thickness-to-chord ratio of the blade's cross section, Geometric twist, q, of the blade's section, plus the following aerodynamic quantities, depending on the specific airfoil and on its AOAs a: - CL ðaÞ with a2½p; p, - CD ðaÞ with a2½p; p.
Two modelsddetailed belowdare then used to calculate the thrust produced by each blade element. Finally, the induced flow is determined with an iterative process that varies aj until the formulations give the same result [25]. The first thrust equation is based on the Blade Element Model and gives
9
2 r NBlades cj Drj V02 1 aj þ u2 rj2 CL aj cos fj 2 þ CD aj sin fj ;
where NBlades is the number of blades in the rotor and 1
aj ¼ tan
fj ¼ tan1
! V0 1 aj qj ; urj ! V0 1 aj : urj
The second derives from the Actuator Disk Theory and gives
Nj ¼
fhub ftip 4rprj V02 Drj
( 1 aj aj ; if a < 0:4 K1 a2j þ K2 aj þ K3 ; if a 0:4
where fhub and ftip are the hub and tip loss factors,
fhub ¼
ftip ¼
0
1
@
A
NBlades rj rhub B 2 2 rj sin fj C 1 B C; e cos
p
0
1
@
A
NBlades rtip rj B 2 2 rj sin fj C C; cos1 Be
p
and the values of K1, K2 and K3 are determined as prescribed in Ref. [27]. That is, so that the quadratic function
PðaÞ ¼ K1 a2 þ K2 a þ K3 satisfies the conditions
Pð0:4Þ ¼ 0:24;
Pð1Þ ¼ 0:5;
dPð0:4Þ ¼ 0:2: da
References [1] Wind energy generation costs, fact sheet 04. Renewable UK; 2010. Technical report. [2] Projected costs of generating electricity 2010 edition. International Energy Agency; 2010. Technical report. [3] 20% wind energy by 2030: increasing wind energy's contribution to U.S. electricity supply. US Department of Energy; 2008. Technical report, DOE/GO102008-102567. [4] Kyoto protocol to the United Nations framework convention on climate change. United Nations; 1998. Technical report. [5] Meeting the energy challenge; a white paper on energy. Department of Trade and Industry, HM Gov; 2007. Technical report. [6] Renewables obligation: annual report 2008e09. OFGEM; 2010. Technical report. [7] Ashwill TD. Innovative design approaches for large wind turbine blades: final report. Technical report. Sandia National Laboratories; 2004. [8] World market update 2009 (forecast 2010e2014). BTM Consult ApS; 2010. Technical report. [9] Ashwill TD. Materials and innovation for large blade structures: research opportunities in wind energy technology. 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 4e7 May 2009, Palm Springs, California, AIAA Paper 2009-2407; 2009. [10] Ashwill TD. Blade technology innovations for utility-scale turbines. Technical report. Wind Energy Department, Sandia National Labs; 2006. [11] Jackson KJ, Zuteck MD, Van Dam CP, Standish KJ, Berry D. Innovative design approaches for large wind turbine blades. Wind Energy 2005;8(2):141e71. [12] Berggreen C, Branner K, Jensen JF, Schultz JP. Application and analysis of sandwich elements in the primary structure of large wind turbine blades. J Sandw Struct Mater 2007;9(6):525e52.
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[13] Pirrera A, Capuzzi M, Buckney N, Weaver PM.. Optimization of wind turbine blade spars. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 23e26 April 2012, Honolulu, Hawaii, AIAA Paper 2012-1500; 2012. [14] Buckney N, Green SD, Pirrera A, Weaver PM. Structural efficiency of a wind turbine blade. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 23e26 April 2012, Honolulu, Hawaii, AIAA Paper 2012-1502; 2012. [15] Liebst BS. Wind turbine gust load alleviation utilizing curved blades. J Propuls 1986;2(4):371e7. [16] Veers PS, Lobitz DW, Bir G. Aeroelastic tailoring in wind-turbine blade applications. Technical report. Sandia National Laboratories; 1998. [17] Lobitz DW, Veers PS. Aeroelastic behavior of twist-coupled hawt blades. In: Aerospace sciences meeting and exhibit, 36th, and 1998 ASME Wind Energy Symposium, Reno, NV, Jan. 12e15, 1998, Collection of technical papers (A9816844 03-44); 1998. [18] Lobitz DW, Laino DJ. Load mitigation with twist-coupled hawt blades. In: Aerospace sciences meeting and exhibit, 37th, and 1999 ASME wind energy symposium, Reno, NV, Jan. 11e14, 1999, Collection of technical papers (A9917151 03-44); 1999. [19] Zuteck MD. Adaptive blade concept assessment: curved platform induced twist investigation. Technical report. Sandia National Laboratories; 2002.
[20] Larwood S, Zuteck MD. Swept wind turbine blade aeroelastic modeling for loads and dynamic behavior. AWEA windpower 2006, Pittsburgh, PA; 4e7 June 2006. [21] Hoogedoorn E, Jacobs GB, Beyene A. Aero-elastic behavior of a flexible blade for wind turbine application: a 2D computational study. Energy 2010;35(2): 778e85. [22] Puterbaugh M, Beyene A. Parametric dependence of a morphing wind turbine blade on material elasticity. Energy 2011;36:466e74. [23] Kooijman HJT. Bending-torsion coupling of a wind turbine rotor blade. ECN; 1996. Technical report ECN-I-96-060. [24] Hau E. Wind turbines: fundamentals, technologies, application. In: Economics. 2nd ed. Springer; 2006. [25] Ingram G. Wind turbine blade analysis using the blade element momentum method. Durham University; 2011. Version 1.1. Technical report. [26] Lanzafame R, Messina M. Fluid dynamics wind turbine design: critical analysis, optimization and application of bem theory. Renew Energy 2007;32(14): 2291e305. [27] Buhl ML. A new empirical relationship between thrust coefficient and induction factor for the turbulent windmill state. Technical report NREL/TP-50036834. National Renewable Energy Laboratory; 2005. [28] NWTC Design Codes (WT_Perf by Marshall Buhl); 2011. Available from: http://wind.nrel.gov/designcodes/simulators/wtperf/.
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
A novel adaptive blade concept for large-scale wind turbines. Part I: Aeroelastic behaviour M. Capuzzi*, A. Pirrera*, P.M. Weaver Advanced Composites Centre for Innovation and Science, Aerospace Engineering Department, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 October 2013 Received in revised form 20 March 2014 Accepted 14 April 2014 Available online xxx
This two-part paper introduces a novel aeroelastic approach to the design of large-scale wind turbine blades. By suitably tailoring the blade's elastic response to aerodynamic pressure, the turbine's Annual Energy Production is shown to increase, while simultaneously alleviating extreme loading conditions due to gusts. In Part I, we use a current blade as the baseline for an aerodynamic analysis aimed at maximising the turbine's yielded power. These results are then used to identify ideal aeroelastic behaviour. In Part II, we exploit material and structural bend-twist couplings in the main spar to induce appropriate differential blade twist, section by section, while bending flap-wise. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Wind turbine blade design Aeroelastic tailoring Yielded power maximisation
1. Introduction and rationale In recent years, the cost of energy produced by alternative supplies has steadily decreased. This, together with several other socio-economical reasons, has made alternative energies increasingly competitive and, hence, a viable alternative to more traditional sources such as carbon, oil or nuclear power [1e6]. This trend is confirmed by industry growth figures. The wind energy industry, in particular, has grown and is predicted to grow steadily, both in terms of investments and installed capacity [7]. From an engineering perspective, the growth in this sector raises some interesting challenges as it creates the drive to build larger, more durable rotors that produce more energy, in a cheaper, more cost efficient way [8,9]. The rationale for moving towards larger rotors is that, with current designs, the power generated by wind turbines is theoretically proportional to the square of the blade length [9]. Furthermore, taller wind turbines operate at higher altitudes and, on average, at greater wind speeds. Hence, in general, a single rotor can produce more energy than two rotors with half the area. Having said this, larger blades are heavier, more expensive and increasingly prone to greater aerodynamic and inertial forces. In fact, it has been shown that they exhibit a cubic relationship
* Corresponding authors. E-mail addresses: [email protected] (M. Capuzzi), alberto.pirrera@ bristol.ac.uk (A. Pirrera).
between length and mass [9], meaning that material costs, inertial and self-weight effects grow faster that the energy output as the blade size increases (see Fig. 1). In this scenario, the demand for improvements in blade design is evident. The notion of increasingly mass efficient turbines, which are also able to harvest more energy, is indeed immediately attractive. The aim and rationale of our effort are set out in the next section while the current state-of-the-art is discussed in Section 1.2. 1.1. Design drivers and aim of the work The power curve of a modern variable-speed wind turbine is typically characterised by distinctive operating conditions. These are the cut-in, rated and cut-out wind speeds and are shown in Fig. 2. Wind speeds above and below rated correspond to different operating regimes, in which the aerodynamic couple acting on the rotor and its angular speed are controlled to meet specific requirements. Below rated speed they can increase to maximise the yielded power, as the components of the turbine do not operate at their structural limit. Conversely, above rated, the angular speed and the couple are generally set by structural integrity reasons (e.g. limited fatigue loads). In summary, a wind turbine blade is designed to maximise its aerodynamic performances below rated speed and to withstand extreme loads above it. This work presents a novel adaptive blade concept that, for the first time to the authors' knowledge, satisfies both these design drivers, exploiting aeroelastic tailoring principles to improve the performance of current blades.
http://dx.doi.org/10.1016/j.energy.2014.06.044 0360-5442/© 2014 Elsevier Ltd. All rights reserved.
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Nomenclature a
a
aopt
CD CL c D Drj F fhub ftip L
dimensionless induced flow speed (induced speed divided by undisturbed wind speed) angle of attack angle of attack that maximises the component T of the aerodynamic force drag coefficient lift coefficient chord of the airfoil drag force spanwise width of blade element j aerodynamic force resultant hub loss factor tip loss factor lift force
In particular, by suitably tailoring the blade's elastic response to aerodynamic pressure, the turbine's Annual Energy Production (AEP) is shown to increase, while also alleviating extreme loading conditions due to gusts. This is done by purposefully designing bend-twist coupling into the main spar, so as to have the blade sections twist appropriately while bending flap-wise. Specifically, the angles of attack of the blade's aerodynamic sections are designed to adapt to different wind speeds in order to maximize energy harvesting and gust load alleviation, respectively, below and above rated conditions. 1.2. Background Owing to the increased mass and loads associated with larger wind turbine blades, prior research has focused on reducing either weight or aerodynamic forces. For instance, Refs. [11e14] performed structural optimisations aimed at minimising the mass of some, or all, of the turbine's components. Other authors [15e20] looked at the possibility of alleviating extreme aerodynamic loads (i.e. gust loads), in order to relax prevailing design constraints by passive adaptive concepts. Similarly, Refs. [21,22] considered flexible and morphing airfoil sections as a means for load alleviation and improved energy production, respectively. Here, we only report on studies in which load alleviation is obtained in a passive adaptive manner, i.e. by exploiting the capabilities that structural anisotropy and geometrically induced couplings provide. For example, Refs. [15e20] designed the main spar's
Fig. 1. Blade mass vs. rotor radius. Adapted from Ref. [10].
N Nblades Nel
u f
R r rhub rtip
r
T
q
qopt V0 V1
aerodynamic force normal to the rotor plane number of blades in the rotor number of blade elements in the aerodynamic mesh angular speed of the rotor inflow angle rotor's radius radial coordinate in the rotor plane radial coordinate of the hub section radial coordinate of the tip section air density aerodynamic force tangential to the rotor plane and perpendicular to the radial direction geometric twist of a blade's section geometric twist of a blade's section that maximises T undisturbed wind speed resultant flow speed at a blade's section.
torsional and bend-twist stiffnesses to induce a rotation towards feather (nose-down) of the blade's sections, thereby reducing the angles of attacks (AOA) and, consequently, the aerodynamic forces acting on the profiles. For a given blade length, this approach provides benefits, but has proven to be detrimental in terms of Annual Energy Production (AEP) [18]. Indeed, on the one hand, alleviating the gust-induced loads above rated wind speed damps the power oscillations, the structural vibrations and allows the reduction of the ultimate design load due to the 50 year gust. On the other hand, below rated speed, i.e. when the system does not operate at its design limit and power maximisation is the main goal, the same working principle causes a power loss. It must be noted, by allowing the blade length to increase, the power loss can be overcome at the expense of the benefits to the load. At the limit, in which the adaptive and classic designs have the same ultimate load, the power yielded by the former is greater. In all of the aforementioned studies the elastically induced twist has a monotonic distribution that increases along the length of the blade, running from root to tip. The required coupling is achieved by using unbalanced composite laminates in some cases [16e18], or with swept blades in some others [15,19,20]. Some researchers also explored the opportunity of towards stall bend-induced twist (nose-up). A notable example is given by Ref. [23]. In this case, stiffness coupling causes a decrease of the sections' twist, which is more pronounced traversing from the blade's root to tip. Strictly speaking, this work was concerned with constant speed wind turbines, but its conclusions can be generalized: such a solution, despite enhancing the AEP, gives a notable increase of gust-induced and fatigue loads. To conclude, it is noted that an adaptive blade that improves both yielded power and extreme loads requirements has not yet
Fig. 2. Typical trend for the power curve of a pitch controlled wind turbine.
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been proposed. This goal provides the main focus of the present work. The details of the proposed approach are set out in Section 2.
3
elastically induced twist contribution to the total twist should be considered. This being the case, the designer has three degrees of freedom to set, as opposed to two in typical current designs. Summarising, for the sake of clarity:
2. The novel adaptive approach Total twist ¼ pre-twist þ pitch angle Generally speaking, the aerodynamic design of a blade is characterised by geometric and control features such as -
the the the the the
blade length, section's thickness-to-chord ratio, section's pre-twist and chord distributions, airfoil shape along the length, pitch angle and angular speed control laws.
If all of these parameters, except the pre-twist and the pitch angle, were to be considered as given design variables, the power yielded by the turbine (standard nomenclature and geometric features in Fig. 3) would depend only on the total twist distribution (note, this is the sum of pre-twist and pitch angle. It determines the sections' AOA and hence the torque acting on the rotor). Conceptually, in typical designs, the AEP can be maximised by choosing the pre-twist to be optimal at a given wind speed, and then controlling the pitch to regain part of the power loss at different wind speeds. In aeroelastic approaches, the aerodynamic profile of the blade is no longer considered as torsionally rigid. As a consequence, the
in classic designs and Total twist ¼ pre-twist þ pitch angle þ elastically induced twist in aeroelastic designs. In this work, by adopting an aeroelastic approach, the turbine's AEP and its variation as a function of the total twist, is studied. Then, the blade's bend-twist coupling is set so as to maximize the power yielded below rated wind speed, by allowing the AOAs of the sections along the blade length to adapt to different wind speeds. Similarly to previous concepts described in the literature, the adaptation consists of a nose-down rotation of the sections, but in this case, the elastically induced twist is no longer a monotonic function of the radial position. Upon bending, moving from root to tip, the induced twist, at first decreases the AOAs, then, outboard, the trend is inverted and the AOAs increase again. It is noted that, despite the inversion of the twist rate in the second half of the blade, all the sections move towards feather. As a
Fig. 3. Parts and nomenclature in a conventional wind turbine. Adapted from Ref. [24].
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M. Capuzzi et al. / Energy xxx (2014) 1e10
result, this concept retains some of the load alleviation capabilities of the designs proposed in Refs. [15e20] even if it is somewhat diminished. The reason that the suggested induced twist distribution increases the yielded power is essentially due to aerodynamic effects and will be detailed in the following sections. The novel structural design is the topic of Part II companion paper. 3. Foundational aerodynamic study In this section, we present an aerodynamic study aimed at optimising the total twist distribution at several operating conditions, spanning from cut-in to rated wind speed. At each of these operating conditions the optimised twist yields maximum power output. The blade characteristics were made available from an industrial partner. The values refer to an existing large-scale variable-speed WT, which is pitch controlled to twist towards feather. In the remainder of this paper, all of these data, except those defining the total twist, are considered as given design parameters. The reference WT is three-bladed. The aerodynamic model and the optimisation method are detailed in Sections 3.1 and 3.2, respectively. 3.1. Aerodynamic modelling The aerodynamic model adopted in this work is based on the Blade Element Momentum (BEM) theory as described, for instance, in Ref. [25]. The flow around the airfoil and relevant forces, for this model, are shown in Fig. 4a and b (symbols are introduced where used). An in-house MATLAB® model has been developed to estimate the nondimensional component of induced flow perpendicular to the rotor plane, denoted by a in Fig. 4a. The model is described in A. The tangential component, a0 has been neglected. Our model also includes standard engineering corrections, such as tip and hub loss factors. Furthermore, to model the turbulent windmill state, the aerodynamic tool has been complemented with a Buhl correction [27]. This is obtained by modifying the classical Glauert empirical relationship, which extends BEM applicability to conditions where the dimensionless induced speed, a, is greater than 0.5. Buhl's modification is a numerical expedient that allows
Glauert's correction to be used when tip and hub loss factors are employed. The implementation of this correction enables the model to be used for the optimisation of the blade's twist distribution. Indeed, in this way, the model was able to give solutions even when a is greater than 0.5. In terms of accuracy, we note that optimal power outputs never correspond to these turbulent windmill conditions, therefore the use of Buhl's correction is expected to have little or no effect on the optimum twist distributions. This conclusion is also confirmed by the results that are presented later. The reason that the correction is implemented is that it allows the model to be used over a wide range of twist values, as is required for the twist optimisation study. 3.1.1. Validation For verification purposes, the power output calculated by our aerodynamic model for the baseline WT has been validated against WT_PERF [28]. A comparison of the results is shown in Fig. 5. The power curves are shown for the wind speeds between cut-in and rated (3.5e15 m/s) and they show adequate agreement. Both software require an aerodynamic mesh, hence the blade has been segmented into 13 elements. Such refinement produced satisfactory converged results. The values and distributions of the orthogonal induced speed have also been successfully validated. Furthermore, the effect of neglecting a0 on the power estimation under conventional flow conditions was found to be negligible. These results are not shown for the sake of brevity. 3.2. Yielded power optimisation The total twist distributions that maximise the power output at different operating conditions are found by performing an exhaustive search. This search was conducted within a preassigned domain of realistic twist values, independently for each element of the aerodynamic mesh and at operating conditions corresponding to wind speed increments of 0.5 m/s in the interval from cut-in to rated speed. In the next section, the qualitative nature of the results is anticipated by reasoning on the fundamental BEM equations and
Fig. 4. Flow (a) and forces (b) on the blade section. Adapted from Ref. [26].
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5
the optimum twist as a function of wind speed and radial position for the operating conditions below rated. We start the analysis by differentiating Eq. (2) with respect to V0. Then,
vq vf va vf ¼ ¼ vV0 vV0 vf vV0
1
va vf
vf : vV0
(4)
Generally speaking, in order to maximise CT, we seek an aerodynamic profile at approximatively its maximum efficiency, i.e. in the interval of AOAs around the point that maximises the ratio CL/CD. This is the case for any inflow angle, hence, ideally for varying f, we seek a q value at each section to maintain a ¼ aopt xaðmaxðCL =CD ÞÞ. With reference to Eq. (4), this suggests Fig. 5. Comparison between power curves: WT_Perf and author's model results.
the optimisation's input data. Numerical results are then presented in Section 3.4 and shown to confirm expectations. For the sake of clarity, it is noted that during the power optimisation procedure all of the blade features, except for the sections' total twist, are treated as given parameters and kept constant. Furthermore, our work deals with static aeroelasticity and only considers the effect of static twist variations on the turbine's yielded power. Flap-wise vibrations and twist dynamics also have an effect on the power performance, but dynamic effects have so far been neglected and will be the subject of future analyses. This approach does not limit the generality of the results presented here, and reflects a modus operandi commonly practised in the wind energy industry, i.e. the use of steady power models for the preliminary aerodynamic blade design. In fact, several commercial tools are available for this type of procedure. 3.3. Critical model analysis As mentioned in Section 3.1, within the framework of BEM assumptions, the aerodynamic field on the blade section can be sketched as shown in Fig. 4a. The operating condition is fully determined by assigning the wind speed V0 and the angular speed control law uðV0 Þ. As with the BEM model, selecting the total twist q at a distance r from the rotor's centre determines the nondimensional induced flow a, which is basically a function of the thrust developed on the blade element. This, in turn, gives the relationship
f ¼ tan1
V0 ð1 aÞ ur
(1)
and
f ¼ q þ a;
vaopt ≪1; vf
(5)
and substituting in Eq. (4), we have
vqopt ¼ vV0
1
vaopt vf
vf vf x : vV0 vV0
(6)
This means that the optimum total twist variation reflects the distribution of inflow angle. The latter quantity can be studied by differentiating Eq. (1). By so doing, we obtain
vf v V ð1 aÞ ¼ tan1 0 vV0 vV0 ur r vu va ¼ ð1 aÞ u V uV : 0 0 vV0 vV0 u2 r 2 þ V02 ð1 aÞ2 (7) The qualitative behaviour of this function is understood as follows. First, in optimal conditions, a can be assumed to be smaller than one and almost constant with V0dthis is clear considering the BEM fundamentals. Secondly, for modern wind turbines, the variation of angular speed with V0 below rated is typically described by the curve in Fig. 6. Hence, for wind speeds within the interval between cut-in to rated vu=vV0 x0, we deduce that vf=vV0 is positive and a decreasing function of the radial location. By virtue of Eq. (6), this also holds true for vqopt =vV0. Ultimately, it can be concluded that, below rated but well above the cut-in speed, the results of the aerodynamic optimisation should give an optimum total twist which increases as a function of the wind speed. Furthermore, this increase is expected to be accentuated from tip to root. On the other hand, for operating conditions closer to cut-in, the term vu=vV0 in Eq. (7) cannot be
(2)
determines the inflow angle f and the AOA a. Here, with reference to Fig. 4a, we recall that a0 is neglected. The forces acting on the section under consideration are shown in Fig. 4b, where, with customary notation, L and D are lift and drag, F is the force resultant, and T and N are its components on-to and normal-to the rotor plane, respectively. Finally, the tangential component T is expressed, in dimensionless form, as
CT ¼ CL sin f CD cos f:
(3)
Since the aerodynamic field is determined by q, it is evident that at each operating condition there will be a q ¼ qopt that maximises CT and hence provides maximum power output. This consideration, together with Eqs. (1)e(3) facilitate prediction of the variation of
Fig. 6. Typical distributions of angular speed with wind speed for a variable-speed WT.
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neglected. Therefore, vf=vV0 may be negative and, consequently, qopt could decrease with V0. 3.4. Aerodynamic optimisation results Here, the results of the aerodynamic optimisation, described in the previous sections, are presented. The optimum total twist distribution, at different radial locations, is shown as a function of the operating conditions in Fig. 7. As anticipated in Section 3.3, on the right-hand side of the plot the curves increase monotonically. Furthermore, their gradients decrease with the radial position (moving from root outboard). At lower wind speeds the curves become more irregular and, mostly, their slope inverts. 4. Optimum adaptive behaviour: target curves Based on the aerodynamic study presented in Section 3, the present aim is to identify a distribution of induced elastic twist that realises the shape adaptation necessary to maintain the optimal total twist profile at all of the operating conditions. In other words, an aeroelastic concept is sought where the blade's twist distribution follows the curves shown in Fig. 7. As mentioned in Section 2, the total twist distribution has three parts. These are the pre-twist, the pitch angle and the elastic twist. If the pre-twist is chosen to match qopt at a given operating condition, its values can then be obtained as the intersections of the curves shown in Fig. 7 with the vertical line identifying the chosen wind speed. Henceforth, this wind speed is referred to as the design wind speed. For any other operating condition, in an attempt to follow the optimal curves closely, the total twist can then be adjusted using pitch control. This, however, changes its values by the same amount at all of the radial locations, thus forcing a deviation from optimal conditions. This can be seen from Fig. 7, where the optimum total twist is observed to change with a different rate depending on the radial location. This approach for the aerodynamic design entails a loss of power but, in principle, it is similar to the one used in conventional turbines (in general, to be strictly accurate, the pre-twist is not chosen to be optimal at the design wind speed, but to be a suitable compromise over the entire range of operating conditions). This power loss can be partially overcome by exploiting an elastically induced twist, as it allows the total twist to vary with the aerodynamic load and notably, differentially, along the blade length.
Fig. 7. Optimum twist values as a function of wind speeds, at different fixed radial positions.
By further analysing Fig. 7 it is noted that, given a pre-twist, if the optimal curves were to be accompanied with an elastic contribution, the latter would have to change sign where the curves change from negative to positive gradient. This need arises because, for increasing wind speed, the elastic twist should first (where the curves' slope is negative) be nose-up to decrease the total twist; then nose-down to increase it. This deformation mechanism cannot be achieved passively, as it would require the blade's bend-twist coupling at a given radial location to change sign depending on the wind speed. In the present work, in order to design an adaptive behaviour which allows for both increased power output and reduced gust loads, we define Adaptive Target Curves. These are modified optimum total twist curves that can be followed adaptively, i.e. by only adding an elastic twist contribution to a set pre-twist. These curves are shown in Fig. 8, where, for the sake of clarity only four radial locations are considered. They are obtained from the optimum total twist curves by imposing a horizontal tangent where the slope is not constantly positive. The target curves are achievable because they require the blade sections to only twist nose-down for all operating conditions. Such a combination of pre- and elastic twist allows the optimal power curves to be followed closely in the upper half of the operating wind speed range. The power that is lost in the first half can then be partially recovered by prescribing a suitable pitch variation that realises the required nose-up rotation of the blade sections. The target curves are shown in an alternative way in Fig. 9. In this case, the target twist distribution is presented as a function of the blade's radial coordinate at different wind speeds. Again, only a few curves are shown for clarity. This representation is useful for several reasons. Firstly, it gives a clear picture of the geometry of the target twist along the blade. Secondly, it shows clearly that the distance between the target curves changes along the blade length, which is fundamentally the justification for an aeroelastically tailored design. Indeed, the differential change of the curves' shape
Fig. 8. Twist curves, optimum and suboptimal solutions. Twist values are shown at fixed radial positions (where R is the radius of the turbine) and for a variable speed of wind within the below rated range.
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With reference to the baseline blade, let us consider the wind speed V0 ¼ 15 m/s. As this is the design speed, the pre-twist must be chosen to match the corresponding qopt curve, which is indicated in Fig. 10 with a dotted line. At different operating conditions the total twist can be modified, with a power loss, by pitching the blade. For instance, and still referring to Fig. 10, the total twist at V0 ¼ 9 m/s should follow the target curve indicated with a dashed line. However, since pitching the blade corresponds to a vertical translation of the twist curves, the best compromise in terms of power output is realised by the solid line. It is noted that, in this case, i.e. for torsionally rigid blades, the aerodynamic design is based on the optimal total twist curves of Fig. 7, rather than on the target curves (of Figs. 8 and 9). In addition, we note that, in general, the blade's pre-twist does not necessarily have to be chosen to follow the qopt of the design operating condition. (In fact, our baseline blade represents a practical compromise: its pre-twist does not follow any of the optimum curves.) Nonetheless, regardless of the technique adopted to set the pre-twist distribution, the example illustrated here shows all of the limitations of classic designs. These, in fact, are inherently due to the way that optimum curves change with V0 and to the torsional rigidity of classic blades. 5.2. Aeroelastically tailored approach for the aerodynamic design of the blade Fig. 9. Suboptimal twist distributions along the blade's axis, for fixed wind speeds.
can only be achieved via an elastic twist deformation, as pitching the blade corresponds to a rigid vertical translation of the fixed pretwist distribution. Lastly, it shows that the target curves only move upward for increasing wind speeds, which is the reason that they can be matched by adding a nose-down contribution to the initial pre-twist. Conversely, if the unmodified qopt curves were to be plotted in Fig. 9, for increasing wind speeds, they would, at first, shift downwards and then upwards again. This, as already mentioned, is a behaviour that is not structurally feasible (for linear responses, at least), because it would require the sections' stiffness coefficients to change sign. 5. Adaptive behaviour design In Section 4, by defining target curves, we have identified the twist deformation required for optimisation of yielded power. In this section, we fine-tune pre-twist, pitch and elastically induced twist in a combination that realises the desired aeroelastic behaviour. To further clarify the differences between the proposed approach and conventional design methods and for a better appreciation of its advantages/limitations, this section is divided in to two parts. In Section 5.1 a blade design that does not rely on induced deformations is presented; in Section 5.2 a fully aeroelastically tailored design is shown. In both sections, we compare and contrast the total twist designed into the blade with that prescribed by the target curves.
In this section, the aeroelastic design, that realises the sought adaptive behaviour, is presented. First, reconsider the operating conditions used in Section 5.1. As shown in Section 4, the target curves were used rather than the optimum total twist distributions. These are shown as the upper plot in Fig. 11. The total twist variation required for the structure to adapt from one condition to the other is shown in the lower plot in this figure. This variation is reproduced by the dashed curve in Fig. 12, where we note that the variation could be realised by combining a nose-up elastically induced twist with a nose-down pitch. In this figure, the nose-up elastic twist and the nose-down pitch are represented by the dotted line and by its vertical distance from the dashed curve, respectively. Despite its feasibility, this adaptive solution was disregarded, as it does not satisfy the pre-established power and load requirements, simultaneously. Indeed, as mentioned in Section 1.2, a nose-up adaptation implies an increase in gust-induced loads.
5.1. Torsionally rigid blade's aerodynamic design In the most simplistic approach, when a blade's structure is such that the aeroelastic contribution to the total twist is negligible, its design can be based upon the choice of a ‘design operating condition'. This is usually a wind speed that yields high power output and occurs with reasonable frequency. Such conditions are normally found in the upper part of the below rated wind speed range.
Fig. 10. Matching of optimum twist distributions with the classic approach.
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M. Capuzzi et al. / Energy xxx (2014) 1e10
Fig. 11. Required variation of twist in order to move from one optimum twist distribution to another.
In the current approach, the total twist variation is achieved by defining a pre-twist distribution and by designing nose-down, bend-twist coupling into the blade. However, it is noted that no realistic distribution of nose-down elastic twist will be able to reproduce the dashed curve of Fig. 12 exactly. Indeed, since the root is the fixed end of the structure, the induced twist value at this point is zero. Due to this practical constraint, the target curves are matched exactly only on the outboard portion of the blade. This is shown qualitatively by the solid line in Fig. 12. This curve represents a nose-down rotation of the blade sections, which increases moving outboard and then follows the dashed line after reaching it. In summary, in our aeroelastically tailored design we invert the gradient of the elastically induced twist distribution halfway along the blade.
Fig. 12. Ideal twist variation and feasible induced elastic twist distribution.
Materials and structural considerations that meet such aeroelastic behaviour are discussed in Part II of this paper. Before concluding, we show that the increasing-decreasing spanwise elastic twist qualitatively affects the aerodynamic design of the blade. As already considered in Section 5.1, the rated wind speed is the ‘design operating condition'. With an aeroelastic approach, blade sections can be designed to follow the relative target curve with a combination of pre-twist and elastically induced twist. For lower wind speeds, the latter decreases according to the solid curve shown in Fig. 12. The result is a blade design that behaves as indicated by the upper plot in Fig. 13. The design's target curve (dotted line) at rated speed is matched exactly. At cut-in (dashed line), by prescribing an increasing-decreasing elastically induced twist distribution, the target curve is matched only in the second half. In the first half, the total twist of the design deviates from the target curve. Comparing this design with that of Fig. 10 it is apparent that, overall, the target curves are followed more closely. This, in turn, gives the blade superior energy harvesting capabilities. (It is worth emphasizing that the outermost half of the blade yields approximately 80% of the total power.) Furthermore, these are achieved with a nose-down aeroelastic adaptation, which also ensures load alleviation, even if somewhat attenuated in comparison to previous aeroelastically tailored designs with monotonic distributions of elastic twist. In conclusion, Fig. 13 depicts the design philosophy of the proposed aeroelastic concept and it shows the required variation of elastically induced twist. It is noted that, due to the stiffness properties of realistic blades, the elastic twist at cut-in is generally negligible. This considerably simplifies the structural design that will be detailed in Part II, because it means that a blade is required that achieves the elastic twist distribution prescribed for rated speed, rather that one realising the twist variation between cut-in and rated.
Fig. 13. Aeroelastic design, improved matching between optimum twist distributions relatively to cut-in and rated conditions.
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6. Conclusion
Nj ¼ In part I of this article, a new aeroelastic approach for the aerodynamic design of a wind turbine blade is introduced. In the proposed method, the blade's torsional deformation is exploited to change its total twist distribution, hence its sections' angle of attack, at different operating conditions. The aeroelastic design is based on an aerodynamic study of the total twist distribution aimed at maximising the yielded power. Results were presented as total twist curves varying as functions of the radial position along the blade and of the wind speed. They show that the turbine's power output cannot be maximised with pitch control only, because the optimum total twist varies differentially, but also that the ideal adaptive behaviour is not feasible from a structural point of view. Initial results have subsequently been modified to define the ‘target twist curves', i.e. total twist distributions that are possible by passive structural adaptation. Ultimately, by considering target curves and structural constraints, such as the clamped condition for the blade root, an elastically induced twist distribution was identified that induces a nose-down rotation of the blade, with the magnitude of this rotation having an increasing-decreasing trend along the blade length. This solution matches the target curves on the outermost half of the blade, thus giving superior power harvesting properties, while, on the other hand, it retains gust load alleviation capability. In part II, we introduce the structural design, with which we embody and realise the passive behaviour identified here. Additionally, we assess the increase of yielded power in terms of Annual Energy Production.
Acknowledgments The authors wish to thank Chris Payne and Tomas Vronsky of Vestas Technology R&D for their technical support.
Appendix A. Algorithm for the determination of a The first step in the procedure to calculate the distribution of induced flow along the blade is to define an aerodynamic mesh. To this end, the blade's span is divided into a finite number of longitudinal elements of length Drj , with j ¼ 1; 2; …; Nel . Next, the undisturbed wind speed, V0, the angular speed of the rotor, u, and the rotor's radius, R, are assigned. Furthermore, in order to define the blade elements' aerodynamic properties, the in-house MATLAB® tool requires the following geometric parameters, defined as functions of the radial coordinate r: -
Airfoils (NACA 6-series for the baseline blade), Chord, c, of the aerodynamic section, Thickness-to-chord ratio of the blade's cross section, Geometric twist, q, of the blade's section, plus the following aerodynamic quantities, depending on the specific airfoil and on its AOAs a: - CL ðaÞ with a2½p; p, - CD ðaÞ with a2½p; p.
Two modelsddetailed belowdare then used to calculate the thrust produced by each blade element. Finally, the induced flow is determined with an iterative process that varies aj until the formulations give the same result [25]. The first thrust equation is based on the Blade Element Model and gives
9
2 r NBlades cj Drj V02 1 aj þ u2 rj2 CL aj cos fj 2 þ CD aj sin fj ;
where NBlades is the number of blades in the rotor and 1
aj ¼ tan
fj ¼ tan1
! V0 1 aj qj ; urj ! V0 1 aj : urj
The second derives from the Actuator Disk Theory and gives
Nj ¼
fhub ftip 4rprj V02 Drj
( 1 aj aj ; if a < 0:4 K1 a2j þ K2 aj þ K3 ; if a 0:4
where fhub and ftip are the hub and tip loss factors,
fhub ¼
ftip ¼
0
1
@
A
NBlades rj rhub B 2 2 rj sin fj C 1 B C; e cos
p
0
1
@
A
NBlades rtip rj B 2 2 rj sin fj C C; cos1 Be
p
and the values of K1, K2 and K3 are determined as prescribed in Ref. [27]. That is, so that the quadratic function
PðaÞ ¼ K1 a2 þ K2 a þ K3 satisfies the conditions
Pð0:4Þ ¼ 0:24;
Pð1Þ ¼ 0:5;
dPð0:4Þ ¼ 0:2: da
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Please cite this article in press as: Capuzzi M, et al., A novel adaptive blade concept for large-scale wind turbines. Part I: Aeroelastic behaviour, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.06.044