A brief review on wind turbine aerodynamics - ScienceDirect

THEORETICAL & APPLIED MECHANICS LETTERS 2, 062001 (2012)

A brief review on wind turbine aerodynamics Tongguang Wanga) Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

(Received 15 July 2012; accepted 25 September 2012; published online 10 November 2012) Abstract This article briefly reviews wind turbine aerodynamics, which follows an explanation of the aerodynamic complexity. The aerodynamic models including blade momentum theory, vortex wake model, dynamic stall and rotational effect, and their applications in wind turbine aerodynamic performance prediction are discussed and documented. Recent progress in computational fluid dynamics for wind turbine is addressed. Wind turbine aerodynamic experimental studies are c 2012 The Chinese Society of Theoretical and Applied Mechanics. also selectively introduced. [doi:10.1063/2.1206201] Keywords aerodynamics, wind turbines, computational fluid dynamics, rotational argumentation, dynamic stall I. INTRODUCTION

Wind energy as a renewable and inexhaustible source of energy is now the fastest growing energy technology worldwide. Only in China side, the total installed wind turbine capacity was more than 63 GW by the end of 2011, which has brought China to the leading position in wind application over the world since 2010. There are, however, still many key issues to be solved in the aerodynamics as the basis of wind turbine design. The wind turbine aerodynamics is extremely complicated. First, as both wind speed and wind direction can change frequently and very rapidly and wind turbines always experience high turbulence and wind shear, wind turbines operate in extremely unsteady circumstances. Second, unlike the case of flow over a fixed wing, which can often be analyzed by linear aerodynamics, the flow past a wind turbine is never what aerodynamicists consider to be linear. This presents significant problems in modeling since numerical simulations need to be iterative in character and experimental observations of highly nonlinear phenomena are often difficult to interpret because of their complexity. Third, wind turbines may suffer more severe interactions. For a downwind turbine, the tower produces a dynamic wake which the rotor blade passes through every revolution. A wind turbine in a wind farm operates in complex wakes produced by other turbines. Fourth, blade angle of attack may be very high. In addition to dynamic inflow, a wind turbine encounters both deep static stall and dynamic stall much more frequently than a fixed wing. Finally, there exist difficulties in experiment. For field tests, the extremely unsteady operational environment not only requires the data acquisition system to have an appropriate dynamic response but also makes the collected data difficult to resolve appropriately into individual aspects. For wind tunnel experiments, the wind tunnel wall interference remains a major difficulty in obtaining reliable data. a) Corresponding

author. Email: [email protected].

Due to the similarities in their flowfields many aerodynamic analysis and design methods for wind turbines were transformed with appropriate modifications from helicopter and propeller researches. Nowadays wind turbine aerodynamics is a worldwide field of research and greatly helps the development of the wind industry at large. In this paper, a very brief review of wind turbine aerodynamics is presented with emphasis on aerodynamic models, computational fluid dynamics, and experiments. II. BLADE ELEMENT MOMENTUM THEORY AND OPTIMAL ROTOR A.

Blade element momentum theory

The basic and classical theory for understanding the wind turbine aerodynamics is the one-dimensional momentum theory first developed by Rankine and Froude, which was then extended by Glauert to 2D flow including rotational motion in the wake.1 The rotor is modeled by an actuator disc which is divided into concentric aerodynamically independent annular control volumes (CV) or streamtubes. This actuator disc is based on the assumptions that the flow is incompressible, inviscid, and axisymmetric and that the number of blades is infinite. Applying the mass conservation, axial and angular momentum balances and energy conservation to a CV, the following equations can be obtained V · dA = 0, (1) CV ρux V · dA = T − ρ dA · ex , (2) CV CV rut ρV · dA = Q, (3) CV 1 2 p + ρ [[V ]] V · dA = P, (4) 2 CV where V = (ux , ur , ut ) denotes the velocity vectors in the axial, radius, and tangential directions, dA is the

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Theor. Appl. Mech. Lett. 2, 062001 (2012)

a σ(Cl cos φ + Cd sin φ) , = 1−a 8 sin2 φ a σ(Cl sin φ − Cd cos φ) = , 1−a 8 sin φ cos φ

(5) (6)

where a and a are the axial and tangential induction factors defined as a = (V0 − V )/V and a = ω/Ω, respectively. V0 is the freestream velocity, V is the axial velocity at the rotor, ω is the angular velocity of the wake just behind the rotor, Ω is the angular velocity of the rotor; φ is the inflow angle, σ is the rotor solidity, Cl and Cd are the lift coefficient and drag coefficient, respectively. A limitation of the BEM theory is that when axial induction factor is greater than 0.5, there would be negative flow in the wake. This contravenes the RankineFroude flow theory and therefore the classic momentum theory breaks down. To overcome this problem, several thrust coefficient formulas for large induced velocity states have been proposed on the basis of experimental investigations.3 The BEM method with modification often predicts the gross performance of wind turbines with acceptable accuracy at a cost of high dependence on empirical 2D airfoil data. BEM methods are applied not only in wind turbine designs but also in static performance calculations. Meanwhile BEM methods have also been extended to some unsteady applications by correcting 2D experimental data to account for dynamic stall and three-dimensional (3D) rotational effects.4,5 The upgraded models are successfully embodied into some well-known codes AERODYN5 and BLADED.6

0.6 Power coefficient CP

area vector normal to the CV, ρ is the air density, r is the local radius, T is the thrust, Q is the torque and P is the rotor power extracted from the wind. The second term on the right hand is the axial component of the force exerted by the pressure on the CV, which is not equal to zero but is negligible due to its little effect on the power calculation.2 The combination of Eqs. (1)–(4) can easily yield the expressions of both power and thrust, but can neither finally determine the rotor aerodynamic performance nor obtain the blade aerodynamic configuration. These limitations can be overcome by introduction of the blade element method dividing the blade into small elements that act independently of surrounding elements and operate aerodynamically as two-dimensional airfoils whose aerodynamic forces can be calculated based on the local flow conditions. The combination of the momentum theory and the blade element approach sets up the socalled blade element momentum (BEM) theory which involves an iterative process to determine the aerodynamic forces and also the induced velocities at the rotor

Experiment FVM CFD

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Fig. 1. Power coefficient with tip speed ratio.6

an optimal rotor must have maximum power coefficient. The Rankine-Froude flow theory gives the rotor power coefficient CP =

2P = 4a(1 − a)2 , AρV03

(7)

when a = 1/3, the maximum value of CP can be obtained as 16/27≈0.593, which is the well-known Betz limit, giving an extremely significant theoretical upper limit without regard to any losses resulting from wake rotation, viscosity, and infinite blade number assumption, etc. Because of its simplicity and high efficiency, BEM theory is widely used and wind turbine researchers have been accumulating rich experiences on BEM methods. Therefore, wind turbine aerodynamic designs are almost based on BEM theory. A recent attempt to design a high-performance 1.5 MW wind turbine blade has been made by Wang et al.6–8 based on Pareto optimal theory for multiobjective optimization, taking maximum annual energy production and minimum blade mass as the optimization objectives. The design acquires comprehensively optimal solutions rather than a single aerodynamically optimum solution which are obtained usually from the conventional single-objective optimizations. This blade design has been tested through aerodynamic calculation, aeroelastic validation, aeroacoustic calculation and wind tunnel experiment. A 1/16-scale model of this blade was tested in a 12 m × 16 m wind tunnel, demonstrating that the maximum power coefficient for the scaled model was as high as 0.492. Moreover, both the computational fluid dynamics (CFD) method and a free-vortex method (FVM) were applied to calculate the aerodynamic performance with the maximum power coefficient 0.505 and 0.528 (Fig. 1), respectively, for the full-scale blade. III.

VORTEX WAKE METHOD

B. Optimal rotor

The ultimate aim of wind turbine design is to capture energy from wind as much as possible. Therefore,

Another alternative for wind turbine aerodynamic prediction is the so-called vortex wake methods. These methods directly calculate the induced velocity via

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Biot-Savart law from the bound vortices on the blade and the trailing vortex in the wake which are represented by lifting line, lifting surface or vortex lattice model. Vortex methods are commonly categorized into three types as rigid wake model, prescribed wake model and free wake model. The difficulty with the rigid wake model9 is that expansion of the wake is not taken into account and thus the blade load calculations might not be accurate enough. To remedy this weakness, the prescribed wake model uses experimental data or other numerical results to locate the wake position.10–12 In the free wake calculation the vortex motion is calculated directly from the effects of all the other components of the wake vortex system and the effects of the blades at every time step.13–16 Free wake analyses are fundamentally better suited to the complex flow fields generated by wind turbines and avoid the difficulty of prescribing a wake geometry, but doing so introduces more computational expense. Prescribed vortex wake methods have been tried to use in wind turbine design.17 They are progressively replaced by free vortex models. A recently developed free vortex method applies a relaxation factor in every short period iterative step to allow free distortion of the vortex wake and free rolling-up of the tip vortex with an introduction of vortex core whose vortical strength dissipates with time to obtain convergent and appropriate results (Fig. 2).13 Vortex wake methods are reckoned to be more accurate than BEM method and should play a major role in future engineering applications with the increase of computer power.

IV. AIRFOIL AERODYNAMIC DATA A. Static data

Reliable airfoil aerodynamic data as input are prerequisite to obtain accurate results from both BEM method and vortex wake method. Usually the airfoil aerodynamic coefficients are obtained via wind tunnel


tests with a very limited range of angles of attack and Reynolds numbers. However, at some extreme conditions, such as parked conditions, yawed flows or failed control states, the blade elements may experience high angles of attack and Reynolds numbers. For this reason, aerodynamic airfoil data containing an entire range of angles of attack are often indispensable for a reliable and vigorous calculation. In order to generate additional data outside the tested range, an assumption has been widely admitted that the aerodynamic coefficients can be extrapolated only when the flow on one side of the airfoil is fully separated at high angles of attack such that the airfoil can been regarded as a curved plate. Based on this assumption, Viterna and Janetzke developed a widely used method which has been embodied into an NREL code, but the extrapolated pitching moment coefficients show less rigorous.18 Lindenburg analyzed massive test data of various airfoil geometries and derived several empirical relations which showed good agreements with experimental data19 as seen in Fig. 3. Tangler provided some beneficial guidelines for developing an empirical approach that predicts poststall aerofoil characteristics by analyzing UAE Phase VI experimental results.20 An alternative to acquire airfoil aerodynamic coefficients is numerical simulation. The most used tool for airfoil design and aerodynamic evaluation is XFOIL in which viscous-inviscid analysis methods have been integrated and always gives quite accurate results before stall. However, the viscous method is based on integral boundary layer equations which are invalid for separation flow, so the stall properties are usually unreliable. To overcome these problems, more accurate numerical methods, such as detached eddy simulation (DES),21,22 large eddy simulation (LES),23,24 have been adopted and claimed to get good results in some specific conditions.

B.

Rotational augmentation

The loads and energy output usually are underestimated using BEM and vortex wake method with static airfoil data for a rotational rotor. This augmentation of rotating blade aerodynamic properties is often referred to stall delay due to the 3D rotational effect. Figure 4 shows the lift coefficient as a function of angle of attack derived from NREL measurements at the 30% radial location for the wind speed of 25 m/s, and the static data comes from DUT wind tunnel tests at the same condition.25 It can be seen from this figure that the airfoil stalls at around 15◦ at 2D static condition and the lift coefficient Cl reaches a maximum of 1.05. However, for the rotating blade, the phenomenon of Cl stall does not happen at such angle, but is delayed to 26.4◦ and the lift coefficient is then enlarged to 2.1. The most notable features of rotational augmentation are the dramatic enhancement of lift coefficient and a delay of the occurrence of flow separation to a higher angle of attack.

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Fig. 3. Coefficients for the NACA63-215 airfoil.19

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Fig. 5. Typical dynamic stall curves of the lift coefficient.

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the study have shown that the existing models generally overestimate the loads compared to measurement data on a wind turbine blade over a range of operating conditions, none of which can fully represented the flow physics. Rotational augmentation is still a hot spot for the wind turbine aerodynamic performance prediction, and a rigorous approach is still the urgent need.

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Fig. 4. Cl at 0.3R statuary and rotating blade.25

Wind tunnel tests conducted in Refs. 26–29 have suggested that the stall delay phenomenon can be found pervasive existing at any radial locations and throughout all blade operating envelopes, particularly intense at the inboard sections of the blade. Comparative analyses of MEXICO and UAE Phase VI experimental data regarding rotational augmentation have also been performed by Schreck et al.30 The stall delay phenomena remain incompletely characterized and understood. However, it has been widely accepted that two main contributions are commonly indicated for these phenomena. One is the Coriolis force, which acts in the chordwise direction alleviating the adverse pressure gradient and hence tends to delay separation. On the other hand, the centrifugal force tends to pump airflow from blade root to tip, resulting in a thinner boundary layer. The effect of rotational augmentation must be taken into account for better predicting rotor performance. One approach is that the 3D data can be obtained directly from rotor experiments or numerical calculations.31–34 An alternative as a common method is to build a kind of stall delay model able to adjust 2D aerodynamic data to account for 3D rotational effects by a series of correction formula. For this, various stall delay models have been proposed.35–43 Comparative study on six of such models has been carried out with the use of a vortex wake code.25 The results from

C.

Dynamic stall

When a wind turbine is subjected to the time varying fluctuations in the wind or control actions inducing frequent changes of angle of attack, dynamic stall phenomena in responsible of a stall delay and hysteresis loop in aerodynamic characteristics are often observed. The dynamic stall processes with various motion patterns have been investigated in detail. Both experiments44–50 and computational fluid dynamics methods51–56 revealed that the prominent features within a full cycle of dynamic stall are incessant spreading of flow reversal on the suction side, the formation and convection of a large-scale leading edge vortex, massive flow separation, and flow reattachment. A typical dynamic stall curve of the lift coefficient for an oscillating airfoil is depicted in Fig. 5,57 where the dynamic stall features are distinctively different from the steady characteristics. Dynamic stall on wind turbine is more complicated because of its rotation and highly unsteady external operational environment, and produces large excursions of the aerodynamic loads during the vortex breakdown, resulting in fatal structural failures and violent vibrations.58,59 Therefore, the development of dynamic stall engineering models has been necessitated. Several empirical and semi-empirical dynamic stall models are available for the wind rotor aerodynamic analysis in despite of original intention for helicopter applications, which have been documented by Leishman.60 Among these models, Leishman-Beddoes dynamic stall model61 and its modified version62 are most widely used in wind industry. However, results from the applications

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of these models to wind turbines demonstrate large deviations from measured data,63,64 which at least can be attributed to two key reasons. One is the airfoils used in these models which are quite different from that specially developed for wind turbine applications. The other may be related to 2D experimental data, on the basis of which the models were developed, meaning that the rotational effects strongly affecting the development of the boundary layer are not considered. To address these issues, a lot of efforts have already been made to enhance the applicability of those models to wind turbine aerodynamics. A modified Leishman-Beddoes dynamic stall model for lower Mach numbers was proposed by Sheng et al.,65 and similar work also finished by Gupta and Leishman66 and Hansen et al..67 Larsena et al.68 introduced a new dynamic stall model taking into account attached flow and leading-edge separation. Lu and Wang69 presented a 3D dynamic stall model constructed with the emphasis of the onset, growth, and convection of the dynamic stall vortex based on a 3D wing dynamic experimental data. Despite these new progresses need to be more validated, they have provided at least some beneficial insights to dynamic modeling. Though dynamic stall has extensively been studied, the mechanism of dynamic stall has not been completely understood and characterized yet. In particular, the process that leads to the formation of the stall vortex and the mechanism that causes the vortex to detach are still controversial. Also, more generally, robust dynamic stall model is still challenging wind turbine designers and aerodynamic analysts.

V. COMPUTATIONAL FLUID DYNAMICS

Computational fluid dynamics (CFD), based on Euler or Navier-Stocks equations, has potential to provide a consistent and physically realistic simulation of the turbine flow field, and can naturally be used to solve the complex flow over the wind turbine. According to the capabilities that the length scales of turbulence are modeled, CFD can basically be divided into three catalogues for the simulations of wind turbine flowfield: Reynolds averaged Navier-Stokes (RANS), LES, and direct numerical simulation (DNS). RANS approach with empirical turbulence model has been widely applied to almost all range of flow problems experienced by wind turbines. Figure 6 shows a typical rotor wake structure calculated using RANS.70 Two equations k-omega SST turbulence model developed by Menter71 is considered to be the most outstanding representative among numerous existing turbulence models for wind turbine applications.72–75 But the results from the present investigations suggest that the empirical parameters in the turbulence model can markedly affect the simulation results. An alternative with better accuracy is LES which has been a growing interest in the area of rotor flows field simulations.76,77


X

Y

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Fig. 6. Typical rotor wake structure of NREL Phase VI blade.70

The main idea of LES is that large eddies are directly resolved and the effect of the small eddies is modeled by sub gridscale model. A subgrid-scale stress model is indispensable for the closure of LES equations. Therefore, a variety of subgrid-scale stress models have been proposed.78,79 LES has more attraction to rotor wake analysts, but is still prohibited to deal with the nearsurface regions due to its huge computational overhead. Therefore, a combined approach, detached eddy simulation (DES), in which RANS and LES are adopted in the near-surface and far-surface, respectively, has been proved to obtain good solution.80,81 DNS, which directly solves full Navier-Stokes equations and needs to catch all relevant scales of turbulence with ultrafine computational grid, is currently impossible to be applied in full wind turbine flow field. CFD methods are making inroads into the fields of industrial applications associated with both design and analysis.82 However, either of the RANS or LES, at least so far, has been applied only to very specific cases due to the massive computational costs and numerical issues.

VI. EXPERIMENTS FOR WIND TURBINE AERODYNAMICS

As in other aerodynamic areas experimental study is indispensable to wind turbine aerodynamics. Numerous experiments on wind turbines have been performed over the last three decades. The experimental study is usually carried out by two means ie., operation in field and tests in wind tunnels. Field experiments have been largely carried out over many years which have been well documented through IEA Wind Annex XIV83 and Annex XVIII.84 These files contain a large number of measurement data associated to many types of different machines. Field experiments can provide comprehensive aerodynamic and dynamic information for wind turbines operating in natural conditions. However such experiments are typically very time consuming expensive and complicated through the large volumes of data and the extensive data reduction which are required. It is there-

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Fig. 7. Tip vortex at nominal wind speed 12 m/s.86

fore often common to utilize wind tunnel testing which can be executed under controlled test conditions. A well-known experiment is the NREL unsteady aerodynamics experiment (UAE) Phase VI turbine test in the NASA Ames 24.4 m × 36.6 m wind tunnel accomplished in 2000. The test model was a two-bladed stall-regulated wind turbine with a diameter of 10.1 meters. More detailed information about the experiment has been documented by Hand.29 Another systemic wind turbine test in wind tunnel is the so-called model experiment in controlled conditions (MEXICO) subjected to the European 5th Framework Programme.85 The MEXICO turbine had a threebladed pitch-controlled upwind rotor that was 4.5 m in diameter and was tested in the NFAC 9.5 m × 9.5 m wind tunnel. It is worthy to note that a large-view flow field measurements using PIV technique with high resolution CCD cameras on a rotating small wind turbine model were conducted in a Φ3.2 m wind tunnel at the Low Speed Aerodynamics Institute of China Aerodynamics Research and Development Center (CARDC).86 The strong tip vortex was clearly captured in the experiment (Fig. 7). The results show that the tip vortex firstly moves inward for a very short time and then moves outward with the wake expansion while its vorticity decreases with time after just trailed from the trailing edge of the blade tip and then increases continuously with rapid roll-up to form a strong tip vortex.

VII. CONCLUSIVE REMARKS

Recent progresses in wind turbine aerodynamics have been selectively presented in this paper. BEM

theory, regardless of its simplification, is still a daily design tool for wind turbines. However, BEM method has many natural shortcomings, and relatively less ability to model the physics of the turbine aerodynamics in the field of high unsteady conditions, such as atmospheric turbulence, wind shear, deep stall, interactions of neighboring turbines, wake and etc. Therefore, more sophisticated vortex wake models have been developed to directly deal with vortices that dominate the wind turbine flowfield in essence and therefore may provide relatively reliable information although they require more validations. Introduction of dynamic stall model and 3D rotational effect model greatly improves the wind turbine aerodynamic load calculations. However, more accurate dynamic stall models and delay stall models are required, which can be developed only through much more experimental and computational studies. CFD methods have provided deep insight to wind turbine flowfields. However, CFD methods have not been used for design purposes with confidence. Nevertheless, with the increase in computer power and with the advances in computational techniques the CFD solver is becoming a promising and powerful tool for analysis of wind turbine aerodynamics. Wind turbine experiments are essential not only for understanding of the aerodynamic mechanism but also for code validation. By consideration of the complexity of wind turbine operation conditions, the investigation of turbine aerodynamic is still particularly challenging for wind energy exploitation. 1. H. Glauert, in: W. F. Durand ed. Aerodynamic Theory (Springer, Berlin, 1935). 2. R. Mikkelsen, J. N. Sørensen, and W. Z. Shen, Wind Energ. 4, 121 (2001). 3. M L. Buhl Jr. A New Empirical Relationship between Thrust Coefficient and Induction Factor for the Turbulent Windmill State (Boulevard, Golden, Colorado, USA, 2005). 4. M. O. L. Hansen, Aerodynamics of Wind Turbines (Earthscan Publications Ltd., 2008). 5. J. R. P. Vaza, J. T. Pinhob, and A. L. A. Mesquitaa, Renew. Energy 36, 1734 (2011). 6. T. G. Wang, L. Wang, and W. Zhong, et al., Chin. Sci. Bull. 57, 466 (2012). 7. L. Wang, T. G. Wang, and Y. Luo, Appl. Math. Mech. Eng. Ed. 32, 739 (2011). 8. L. Wang, T. G. Wang, and J. H. Wu, et al., J. NUAA 43, 672 (2011). (in Chinese) 9. M. A. Kotb, and M. M. Abdel Haq, Wind Eng. 16, 95 (1992). 10. F. N. Coton, T. G. Wang, and R. A. M Galbraith, Wind Energy 5, 199 (2002). 11. F. N. Coton, and T. G. Wang, Journal of Power and Energy 213, 33 (1999). 12. T. G. Wang, and F. N. Coton, J. Wind Een. Ind. Aerod. 89, 873 (2001). 13. B. F. Xu, and T. G. Wang, J. NUAA 43, 592 (2011). (in Chinese) 14. M Døssing, Vortex Lattice Modelling of Winglets on Wind Turbine Blades (Risø National Laboratory, Technical University of Denmark, Denmark, 2007). 15. S. Chkir, Energy Procedia 6, 777 (2011). 16. X. Shen, X. C. Zhu, and Z. H. Du, Energy 36, 1424 (2011). 17. K. Badreddinne, H. Ali, and A. David, Renew. Energy 30, 2019 (2005).

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