Nowadays, all the modern megawatt-class wind turbines make use of pitch control to optimise the rotor performance and control the turbine. However, for kilowatt-range machines, stall-regulated solutions are still attractive and largely used for their simplicity and robustness. In the design phase, the aerodynamics plays a crucial role, especially concerning the selection/design of the necessary airfoils. This is because the airfoil performance is supposed to guarantee high wind turbine performance but also the necessary machine control capabilities. In the present work, the design of a new airfoil dedicated to stall machines is discussed. The design strategy makes use of a numerical optimisation scheme, where a gradient-based algorithm is coupled with the RFOIL code and an original Bezier-curves-based parameterisation to describe the airfoil shape. The performances of the new airfoil are compared in free- and fixed-transition conditions. In addition, the performance of the rotor is analysed, comparing the impact of the new geometry with alternative candidates. The results show that the new airfoil offers better performance and control than existing candidates do.
Looking back in wind turbine history, pitch-regulated machines gradually substituted stall-regulated systems. In fact, the possibility to optimise the power production for each wind condition by regulating the pitch angle of the blade, proved to be a key feature to maximise the annual energy production (AEP) of the wind turbines. Nowadays, all the modern megawatt-class wind turbines are by default pitch-regulated and several innovations are implemented by industry to improve the pitch performance (e.g. individual pitch control, fine regulation mechanisms/algorithms) and extract more power.
In apparent contradiction with megawatt machines, however, small and medium kilowatt wind turbines are still largely stall-regulated machines. The reasons for this are easy to give. The advantages of the pitch system in fact come at some costs. The first is the literal cost of the pitch system and its maintenance. Secondly, the pitch system increases the general complexity of the system, together with the development costs and the issues related to the system robustness/reliability. Extra components, such as onboard anemometers and pitch bearings are necessary to operate the pitch of the blade correctly. All these costs and complications can be very relevant for small machines, and it explains why a robust and easy-to-maintain solution is preferred even with some AEP sacrifice.
From the design point of view, the stall-regulated machines still offer a challenging task, especially concerning the aerodynamics of the blade that is supposed to ensure the power performance but also provide the machine control. In practice, the design of the blade should obviously aim to maximise the AEP, but it is also the only component to keep the turbine under control, stopping it when necessary. To do so, the stall and post-stall characteristics of the airfoils play a crucial role. From this angle, the selection/design of the airfoils and the blade shape design are more delicate than in pitch-regulated turbines.
The present work focuses on the design of a new airfoil specifically designed for stall-regulated turbines. The next section illustrates the design of the new airfoil in comparison with existing geometries. Then, its impact on the overall turbine performance is discussed.
The selection of the proper airfoils is very relevant to achieve satisfactory wind turbine performance. Depending on the area of the blade, the requirements change quite a lot; in fact, the outer sections are optimised for high aerodynamic performance, while the inner sections are designed to provide a low weight and structural integrity for the blade.
The focus of the present investigation is the outer region of the blade, so
the airfoils should have high aerodynamic efficiency (
Regarding the blade construction, it must be buildable and lightweight to save production costs, so the airfoils adopted should not have critical features which may compromise those aspects (e.g. too thin trailing edge, very concave complex areas). Inevitably, there is interaction between weight minimisation and annual energy production optimisation, where the first would lead, for instance, to a large thickness distribution to accommodate a structurally efficient spar and maximise the section's moment of inertia, while the second would tend to reduce the airfoil thickness to reduce the drag.
A complete discussion can be found in Grasso (2011).
In addition to what has been presented in the previous paragraph, special considerations should address the peculiarity of stall-regulated wind turbines. As mentioned, the big challenge of these machines is their control. While the pitch-regulated turbines can change the pitch angle of the blades, to optimise the performance for each wind speed, the stall-regulated turbines are much simpler and rely only on the aerodynamics of the airfoils. This increases the complexity of the airfoil design.
First of all, the airfoils of stall-regulated turbines work in quite a wide range of angles of attack, so a sound performance comes from the fact that they achieve high aerodynamic efficiency over the angle of attack range. This is an important element to properly set up the design process. In fact, a design point close to stall would be desirable to obtain the best AEP performance, and the margin must be carefully calibrated and reduced compared to the values for pitch-regulated machines. The stall mechanism stops the turbine when the loads are becoming too large; postponing the stall could lead to excessive forces on the blades and the other components of the turbine. Furthermore, the capability to control the machine, slowing down the rotor and avoiding over-power issues depends on the airfoil stall and post-stall behaviour. In fact, a slope of the lift curve that is excessively “flat” could be insufficient to control the turbine (and so prevent over-power), while a sharp stall would make it more difficult to re-start the machine and would cause sudden changes in the loads faced by the blades. In addition to this, the airfoil post-stall response is fundamental to avoid stall-induced vibrations, which is one of the main issues to address in designing stall-regulated machines.
When a wind turbine blade vibrates, the aerodynamic forces have an additional component originating in the vibration velocity. Such a component can, with good approximation, be considered proportional to the vibration velocity; thus, it actually acts as a viscous damping force, usually denoted as “aerodynamic damping” (see Petersen et al., 1998; Rasmussen at al., 1993; Rasmussen, 1994). When the airfoils are in stall conditions, the slope of the lift curve becomes negative and can cause a local negative aerodynamic damping in the lift direction.
Power curve
As an example, a descending airfoil will see an increasing angle of attack that will cause a lower value of lift coefficient; this will be equivalent to having a component of the aerodynamic force promoting the descent of the airfoil, thus acting as a negative damping force.
If global aerodynamic damping of the blade is both negative and larger (in magnitude) than the structural damping, any disturbance can cause divergent oscillations which can dramatically increase fatigue loads and can even lead to rapid failure in the worst case.
This phenomenon is usually referred to as “stall-induced vibrations” and represents a key issue for stall-regulated wind turbines, which work in stalled conditions for a significant part of their lifetime.
Stall-induced vibrations have to be regarded as instabilities of the blades that can take place due to any initial disturbance. A sharp stall leads to a lower damping force and so to larger vibrations. On the other hand, a flat lift curve beyond the stall could be insufficient to control the turbine.
Low stall-induced vibrations and power control represent two conflicting requirements which make the design of a stall-regulated wind turbine a highly complex challenge. Finding a good compromise between these two aspects has been one of the main efforts in this work.
During the preliminary design phase, a simplified expression of the aerodynamic damping of the blade has been used to predict the dynamic behaviour of the blades without the need of any aeroelastic analysis, to make the design as fast as possible.
The linearised approach presented by Petersen et al. (1998) has been applied to obtain a simplified expression for the local aerodynamic damping on the different sections of the blades, using only quasi-steady, 2-D aerodynamics of the airfoils. Then, a simplified modal approach has been implemented to evaluate the aerodynamic damping of the complete blade, obtaining a damping coefficient (DC) used as an index of eventual oscillation amplitude. The use of this damping coefficient has been validated with several cases of wind turbines obtained during the optimisation process, giving always results coherent with the behaviour of the blades evaluated through aeroelastic analysis.
From the expression of the local damping coefficient in the out-of-plane
direction (that usually is very close to the flap-wise direction), it is
possible to see that a gentle stall of the airfoils along the blade (which
means a small value of the absolute value
The typical effect of using an airfoil with a smoother stall in the outer half of the blade is shown in Fig. 1, in terms of power curve and modal aerodynamic DC. It can be seen how a gentle slope of lift coefficient curve of the airfoils (Airfoil 2) results in a reduction in the absolute value of DC with the related stall-induced vibrations but in less power control at high wind speeds.
So overall, it is important that the stall margin is reduced, but with gentle and continuous stall. To limit the problem of power control, the airfoils along the blade should have a low lift coefficient beyond stall and a drag coefficient that is as high as possible.
To meet the challenging scenario, these characteristics must be achieved both in clean and rough conditions. This introduces more complexity for the designer. In fact, special attention should be paid to ensuring that the characteristics of the lift curve do not change significantly with regard to stall and post-stall behaviour.
During the rotor design, the “rough” power curve is considered because it is the most conservative in terms of overall performances and power control. The “clean” power curve is considered because it is the most conservative for extreme and fatigue loads (due to higher stall-induced vibrations caused by a more abrupt stall).
Multidisciplinary design optimisation (MDO) (see Fletcher, 1987) has been adopted in this work. In fact, when compared to a traditional design technique (e.g. inverse design), MDO leads to a more accurate and computational time-saving design product, while covering constraints coming from different disciplines. Based on the authors' experience (see Bizzarrini et al., 2011; Grasso, 2012), a gradient-based algorithm (Zhou et al., 1999) has been preferred to control the design procedure, where the popular tool RFOIL (van Rooij, 1996) is used to evaluate the aerodynamic performance of the airfoil.
RFOIL is a modified version of XFOIL (Drela, 1989) featuring an improved prediction around the maximum lift coefficient and capabilities of predicting the effect of rotation on airfoil characteristics. In fact, numerical stability improvement is obtained by using the Schlichting velocity profiles for the turbulent boundary layer instead of the Swafford velocity profiles (Schlichting and Gersten, 2017). Furthermore, the shear lag coefficient in Green's lag entrainment equation of the turbulent boundary-layer model is adjusted, and the deviation from the equilibrium flow is coupled to the shape factor of the boundary layer.
Figures 2 and 3 show a comparison between the two codes against S814 airfoil (Somers and Tangler, 1997) wind tunnel data (Somers and Tangler, 1994). As can be observed, RFOIL accuracy for the stall region is significantly better than XFOIL, and, as mentioned in the previous chapters, stall is quite a crucial parameter in this case. Additional validation tests can be found in Grasso (2011) and van Rooij (1996).
Lift curve for the S814 airfoil. Numerical experimental comparison. Reynolds number: 1 million; free transition.
Drag curve for the S814 airfoil. Numerical experimental comparison. Reynolds number: 1 million; free transition.
The geometry of the airfoil is parameterised (Grasso, 2008) with a
combination of four Bezier curves (see Prautzsch et al., 2002, Barsky, 199,
and Beach, 1991, for general information about Bezier curves) of third order
distributed along the airfoil contour (Fig. 4). Each Bezier curve covers one
quarter of the shape, with 13 control points free to move in chord and
normal-to-the-chord directions (i.e. 26 design variables). To appreciate and
understand the choice of four Bezier curves, the reader should consider that
a third-order polynomial is needed to describe inflection points; however, a higher degree can lead to wavy shapes. Dividing the airfoil contour into four
pieces is a smart move to divide the complexity of the parameterisation and
ease the control of the shape. This formulation is C
Airfoil shape parameterisation scheme. From Grasso, 2008.
The blade in development has only two airfoils (one main and one in the inner
part, excluding the blending area at the very root of the rotor) in order to
simplify the blade construction. The first one is a 30 % thickness
airfoil which is used at the maximum chord station, while the second one is a
25 % thickness airfoil which extends from half of the blade span to
the tip. A blending area connects these two airfoils. This work focuses on
the main airfoil design where the main target is the aerodynamic efficiency
(
As already mentioned, this aspect plays a crucial role in the present work. From an optimisation point of view, several options in terms of constraints and design points to be included are possible. Some of them are discussed here. High lift performance may lead to sharp stall behaviour; a constraint limiting the maximum lift coefficient can be quite a natural choice. However, limiting the lift coefficient at a specific angle of attack may not be sufficient since there will be no control on different angles. The risk would then be that the stall angle could be delayed or occur earlier, making the constraint (technically satisfied) completely ineffective. The same constraint could be then assigned simultaneously for several angles of attack around the expected stall angle range. This will gain little more confidence but it will add complexity to the optimisation problem and increase the computational costs. Even more dangerous, the risk of limiting the design space too much and driving the solution to local optima would increase. Anyway there will still not be any guarantee about post-stall characteristics, which would still require specific constraint(s). A better and more accurate approach could be to evaluate the full polar at each design iteration and retrieve the information about the maximum lift coefficient and post-stall (via, for instance, the lift slope value). In this way, the number of constraints will reduce to just two, which would fully describe the stall behaviour while keeping the mathematical complexity of the optimisation problem low. However, the computational time would rise because the full polar needs to be calculated for any iteration. On top of that, the same approach should be used in rough conditions to make sure that the airfoil has comparable characteristics in both cases.
S819 and S821 shapes.
Although the latest approach would be the most accurate, a different and more
practical solution has been adopted in the present work, which should still have a good level of accuracy. A combination of constraints focused on the maximum
lift coefficient (< 1.4) and moment coefficient
(>
The airfoil thickness (
Considering existing airfoils, the S821 and the S819 have been used as a reference (Somers, 1993; Tangler et al., 1995; Somers, 1998) because of their good characteristics in terms of insensitivity to roughness and post-stall behaviour. Figure 5 shows the shapes, while Figs. 6–8 show the aerodynamic performance of these airfoils in free and fixed transition, as calculated with the RFOIL code. The Reynolds number used for the simulations is 1 million, in accordance with the average real Reynolds number value expected for a 60 kW range machine. All the simulations in fixed transitions (representative of rough condition) presented in this work prescribe a transition at 5 % of the chord on the suction side and 10 % of the chord on the pressure side. It should be noted that the stall and post-stall behaviour is soft but monotonically decreasing in the indicated angle of attack range. In addition, it should be noted that there is a relatively small margin between the design point and the stall; for stall-regulated turbines, this is an important feature to avoid excessive loads once the design condition has been passed (e.g. in case of wind gust).
Lift curves for S819 and S821 airfoils. Free- and fixed-transition
data;
Aerodynamic efficiency curves for S819 and S821 airfoils. Free- and
fixed-transition data;
Moment coefficient for S819 and S821 airfoils. Free- and fixed-transition data;
So the ideal airfoil is a 25 % thick shape (similar to the S821, which is
24 % thick) with an
With these parameters in mind, three airfoils have been developed to offer better performance than the reference geometries. The airfoils have been preliminarily named A, B and C and are all 25 % thick (the shapes are not shown because of confidentiality issues). Their aerodynamic characteristics, evaluated with RFOIL, are illustrated in Figs. 9 and 10.
The airfoil A has more camber than the other airfoils since the constraint on the moment coefficient discussed above has not been used in order to check the validity of the assumption. This is evident from the lift curve. It achieves better efficiency in clean conditions. However, its behaviour is very sensitive to the roughness; in fixed transition the efficiency drops significantly and the lift curve changes completely, making the control of the wind turbine impossible. The differences are smaller for the airfoil B, but the post-stall characteristics of the lift curve make the control of the turbine difficult. The airfoil C (from now on, called G25sx6) is instead a good compromise between good performance and good control properties. The lift curve is in practice almost unchanged from free to fixed transition, as result of adopting the constraint on the moment coefficient and lift coefficient. In addition, the stall angle of attack is unchanged. In terms of efficiency, the G25sx6 exhibits the best performance in fixed transition and quite a flat plateau in both free and fixed transition. As mentioned, this is quite convenient for stall-regulated turbines because the airfoil will operate in a range of angles of attack rather than a specific value like in the pitch-controlled machines. Combining lift and efficiency performance, the stall margin is almost unchanged between free and fixed transition.
Lift curve of the new airfoils. Free- and fixed-transition data;
Aerodynamic efficiency curve of the new airfoils. Free- and fixed-transition data;
Comparing the G25sx6 with the S821 airfoil (Figs. 11 and 12) a similar value of efficiency in free transition can be seen, but better performance in fixed transition despite the G25sx6 being thicker (25 %) than the S821 (24 %) is observed.
In addition, the efficiency curves keep a good level over a wider range of angles of attack, and the stall margin is reduced, which is an advantage for stall-regulated wind turbines (i.e. avoiding excessive loads in case of wind gust).
Lift curve of the new airfoil. Free- and fixed-transition data;
Aerodynamic efficiency curve of the new airfoil. Free- and fixed-transition data;
This section presents some of the details of the optimisation process for the
G25sx6 airfoil. As mentioned in the previous paragraph, the
Evolution of the objective function during the design process. Optimal solution highlighted by the circle.
Evolution of the constraints during the design process. The blue region corresponds to the feasible domain, while the red one corresponds to the unfeasible domain.
Chord distribution adopted during the blade design.
In order to assess the value of the new airfoil, its impact on wind turbine performance has been evaluated with a numerical analysis. This step is important to give a complete overview of the new airfoil effects but is actually necessary to make sure that the optimisation problem has been correctly set up and the constraints are effective in preventing or limiting stall-induced vibration since only the airfoil side of the problem has been investigated after being separated from the rotor response.
A 60 kW stall-regulated wind turbine has been used as reference and the S821
and G25sx6 airfoils have been adopted as the main airfoil. The reference wind
turbine is a three-blade machine designed to produce energy at sites
characterised by a very low mean wind speed (4 m s
Figure 16 shows the power curves for the blade optimised based on the S821 airfoil and G25sx6 airfoil. The blade element momentum (BEM)-based (Hansen, 2007) tool WT_Perf (Buhl, 2004a, b) developed by the National Renewable Energy Laboratory (NREL) has been used for these analyses.
The blade geometry has been adjusted to consider the actual airfoils adopted. Normally, this includes chord and twist; however, in this case, the same chord distribution has been used (Fig. 15) since preliminary analyses showed little impact on overall performance.
As already mentioned, the G25sx6 is 1 % thicker than the S821; this ensures a higher moment of inertia of each section implying a lower weight of the blade. From a preliminary analysis, the weight of the blade can be reduced by about 5 %.
Both free- and fixed-transition conditions have been included, as representative of clean and rough blade conditions. According to the results, there are no symptoms of stall-induced vibration. This was not expected to happen anyway, but since the airfoil design has been performed in fixed transition, the performance in clean conditions could have been subject to the risk of stall-induced vibration.
Effect of the new airfoil on the wind turbine power curve.
Angle of attack distribution along the blade.
The power curves related to free and fixed transition in Fig. 16 refer to different values of the blade pitch, which is the value necessary to achieve the desired peak power in each case.
Since in fixed transition the lift coefficient (particularly the maximum lift coefficient) is lower than in free transition, a larger pitch angle will be necessary to reach the desired peak power. At the same time, a higher wind speed is needed to reach the same peak power.
Figure 17 shows the angle of attack distribution along the blade
at 5 m s
Impact of the new airfoil on the wind turbine AEP.
CFD power curve vs. Wt_Perf power curve implementing aerodynamic curves of inner airfoils extracted from CFD.
Considering the overall AEP (see Table 1), the new
airfoil provides a considerable gain in free (
The findings illustrated so far are based on BEM assumptions and WT_Perf accuracy. In particular, the flow at the root is a critical point. In fact, lift and drag coefficients of root airfoils of a rotating blade are affected by the so-called “stall delay” phenomenon (Himmelskamp, 1947; Guntur, 2011; Herráez, 2014); so the two-dimensional aerodynamic curves of these airfoils need to be adjusted at high angles of attack before being used in a BEM code like Wt_Perf to consider rotational effects. In this work, lift and drag coefficients of the inner airfoils (approximately from root to 20 % of the blade) have been extrapolated from a computational fluid dynamics (CFD) analysis of a rotating blade following the inverse BEM method reported in Guntu and Słrensen (2014), while two-dimensional aerodynamic coefficients obtained by using RFOIL have been used for the airfoils along the outer half of the blade, where rotational effects can be neglected (Tangler, 2005). This method is useful to speed-up the wind turbine optimisation process because it allows us to modify the outer part of the blade, which is most influential for the performances and behaviour of the whole system, simply by using two-dimensional aerodynamic airfoil characteristics.
One of the preliminary blades designed during this work has been used as a reference to validate the method. Despite the fact that the design was intended to produce
a 60 kW machine, the actual results ended in a rejected design since it failed
to be controllable. This fact, however, made the design an interesting test
case for validation because of two distinct peaks in the power curve. Figure
18 shows the comparison between the power curve predicted with CFD analysis
in steady operating conditions and the power curve obtained with the method
used in this work. STAR-CCM software has been used, with the
Despite the fact that the pitch-controlled wind turbines cover the complete large-megawatt
machines market, stall-regulated solutions are still diffused for small power
production. A new airfoil specifically designed for this class of wind
turbines has been developed and presented in this work. Compared to existing
geometries, the new airfoil can increase the annual energy production of the
machine, both in clean and rough conditions. In terms of rotor performance,
the new airfoil brings an evident benefit to the punctual power production
and to the overall AEP (
The data are not publicly available as they refer to the
characteristics/performance of a new industrial product which is currently
under development and the data are therefore confidential. The mathematical
models used in the present work are third-party tools and can be accessed via
the following links: RFOIL,
The authors declare that they have no conflict of interest.
This article is part of the special issue “The Science of Making Torque from Wind (TORQUE) 2016”. It is a result of the The Science of Making Torque from Wind (TORQUE 2016), Munich, Germany, 5–7 October 2016.