Tong W. Wind Power Generation and Wind Turbine Design

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Aerodynamics and Aeroelastics of Wind Turbines 105

simulation (probably M. Hansen and T. Chaviaropoulus) were obtained. The

effort was still rather expensive: 3M cells and about 50 h CPU on a 4-processor

machine. Later Sørenesen [ 60 ] also introduced also transitional effects but with

limited success.

4.4 MEXICO

The European answer to the NREL experiment was a model experiment in con-

trolled conditions. The large-scale facility of DNW of

95 95m..×

open section

was used [ 57 ]. A complete analysis is to be worked out within the new established

IEA Annex 29 MexNext , where scientists from several countries outside Europe

will also participate. Most important is the additional measurement of the velocity

ﬁ eld by Particle Image Velocimetry (PIV).

5 Aeroelastics

5.1 Generalities

Wind is transformed into forces by striking the solid structure of the blades. These

are manufactured by regarding them as aerodynamic devices. Lift, drag and pitch-

ing moment result from the combined ﬂ ow of wind and rotating ﬂ ow. These forces

now act ona ﬂ exible structure. The interaction of aerodynamics and structural

mechanisms is called aeroelastics. As turbines become larger they necessarily

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20 25 30

Low-Speed Shaft Torque (Nm)

Wind-speed(m/s)

NREL Blind Comparison

Measurements

Performance 1

Performance 2

Performance 3

Wake 1

Wake 2

CFD 1

CFD 2

CFD 3

Aeroelastic 1

Aeroelastic 2

Aeroelastic 3

Aeroelastic 4

Figure 15 : Blind comparison of shaft rotor torque of various predictions against

measurement.

106 Wind Power Generation and Wind Turbine Design

have to become lighter, meaning that their lowest eigenfrequencies approach a

certain limit. This limit is usually given by the excitation frequency of the rotor

multiplied by the number of the blades. Therefore a model has to be constructed

which includes both aerodynamics and structural dynamics.

Different stages of sophistication have to be identiﬁ ed

I Aerodynamic

Blade Element Momentum Code (BEM) 1.

Wake Codes 2.

Full 3D-CFD including turbulence modeling 3.

II Structural Mechanics

Beam (1D) model 4.

Shell (2D) model 5.

Solid (3D) model 6.

In principle 3 · 3 = 9 possibilities for coupling the various methods can occur. At

the present time (1 with 4) coupling is one of the most commonly used in industry.

Several industrial codes are available, some of which are:

FLEX, from Stig • Øye, DTU

BLADED, by Garrad Hassan •

GAROS, by Arne Vollan, FEM •

Phatas, by ECN •

and many more.

There are several difﬁ culties in improving the accuracy of this approach. Beam-

like parts of the turbine, like the tower and blades are easy to ﬁ t into the BEM Code.

Not so easy to include are major parts of the the drive train, gear-boxes and the elec-

tromechanical parts such as generators. Also control systems which are used more

and more to decrease loads have to be included. So in the forseeable future, coupling

between more or less standardized and specialized software systems will be seen.

Examples may be MATLAB/Simulink for electrical control, ﬂ exible coupling of

multi-body systems like gear-boxes and shafts with standard FEM tools like ANSYS

or MSC NASTRAN, to name only a few. From ﬂ uid mechanics it is not easy to see

how BEM can be improved. CFD is rather time consuming and not a priori better

when BEM is improved by empirical enhancement. At the present time, coupling of

types (3 with 5) or (3 with 6) is the subject of ongoing research.

5.2 Tasks of aeroelasticity

By far the most important task of aeroelasticity is certiﬁ cation or type-approval.

Most operators of wind-farms can only ﬁ nance, operate and insure their turbine

when appropriately certiﬁ ed. Usually during this process many aeroelastic load

cases have to be simulated. They are documented within rules or guidelines.

Aerodynamics and Aeroelastics of Wind Turbines 107

Some of the tasks are to:

ensure safety against aeroelastic instabilities such as divergence/ﬂ utter, •

investigate loads from extreme events expected only a few times within the •

estimated lifetime,

accumulate the effects of loads from rapidly changing operating conditions •

during normal or electricity generation.

A turbine may be called optimized if it can resist equally against extreme winds and

fatigue loads. Because a detailed description of recent procedures is rather exhausting

to the beginner, he or she may start with a somewhat out-dated but classical text: Wind

turbine engineering design by Eggleston and Stoddard [ 76 ]. There the reader will

ﬁ nd a clear description of how the basic physics together with engineering require-

ments may be ﬁ t together in a computer code. A recent review more closely to pure

aeroelastics was given by Hansen et al. [ 25 ]. On the other hand, it is worth noting

how classical aeroelastics (usually coming from airplane design) now re-enters

into recent wind turbine design for offshore applications [ 19 ].

5.3 Instructive example: the Baltic Thunder

Presenting a whole aeroelastic case study is far beyond the scope of this short intro-

duction. Here it is tried to exemplify a description in a somewhat different way. In

2008 a Dutch organization called for a competition for a wind driven car for the

ﬁ rst time. Six teams from four countries presented their design, one of them was the

Baltic Thunder (see Fig. 16 ). Because one goal was to reduce parasitic drag as much

as possible, the weight had to be reduced as far as possible. A light but ﬂ exible struc-

ture was the result. For other reasons a vertical axis rotor was chosen (see Section

7.1) This rotor is known to be particularly prone to aeroelastic instabilities. Therefore

a Campbell diagram was produced by Vollan’s Code GAROS. Due to the soft blade

suspension a vertical bending mode of about 2.5 Hz was not to be avoided. This

gives rise to a ﬂ utter type instability at 500 RPMs . Therefore the ﬁ nal design had

carbon reinforced ﬁ ber (CRF) tubes as suspension giving much higher ﬁ rst blade

eigenfrequencies. One of the various safety proofs included safety against a 18 m/s

gust when operating in normal mode. Figure 18 shows the response of the main

rotor tower. A static (constant) force of about 700 N superimposed on the dynamic

response of the RPM excursion from about 200 to 300 RPM only. It has to be noted

that a 18 to 12 m/s increase of wind speed is equivalent to an increase of power by

factor of 3.4 if c

remains constant. In this case maximum force excursion is only up

to 1200 N so that at least the central column could be regarded as safe.

6 I mpact on commercial systems

6.1 Small wind turbines

In general it is hard to see what effect the impact of scientiﬁ c work will have on a

speciﬁ c commercial product. On the one hand, there is a huge number of engineering

108 Wind Power Generation and Wind Turbine Design

Figure 16: Photograph of the Baltic Thunder wind driven vehicle prepared

for the Racing Aeolus challenge at Den Helder, The Netherlands,

August 2008.

Figure 17: Cambell’s diagram and wind gust .

Aerodynamics and Aeroelastics of Wind Turbines 109

experts working in large companies and on the other hand real testing is possible

only for small wind turbines. An overview of small wind turbines is given ﬁ rst.

According to IEC, small WTs have a swept area smaller than 200 m

. This gives

a diameter of less than 17 m. Sometimes a subclass of WT which have swept area

even less than 40 m

are also considered. These turbines have a diameter of 7 m or

less. The main problems for these turbines are the manufacturing costs and a com-

parable aerodynamic performance to their larger relatives. Due to Reynolds num-

ber effects, the

max

c of small wind turbines is approximately 0.3 instead of 0.5 for

the best standard (2–3 MW) commercial turbines. This is mainly due to the much

lower L2D ratio at Reynolds numbers below 10

. Thus several attempts have been

made to ﬁ nd thicker (> 10%) proﬁ les giving a better performance. See Figs 19 and

20 for examples.

Further information can be found in [ 63 ].

6.2 Main-stream wind turbines

It is obvious that most efforts have been made to optimize so-called main-stream

wind turbines with several MW rated power but below 3 MW. The author [ 50 ]

was able to compare measurements of three different blade sets (see Fig. 21 ) on

the same machine. Although the tip-speed ratio was 8.5 for one blade and only 7 for

the other blades the

max

c difference varies from 0.49 to 0.46 resulting in an

improvement of 6%. As a conclusion this shows that dedicated or tailored proﬁ les

and blades can improve the performance signiﬁ cantly.

max

c currently seems to have settled down at around 0.52 for the best turbines

as to be expected from the discussion in Section 2.

New developments therefore aim to reduce loads without losing power. This can

be achieved by reducing

max

c against c

( L 2 D – max ). In contrast a safe distance

max

c also prevents early stalling. During the 1990s a lot of new aerodynamic

proﬁ les were investigated in the US (Seri), in Delft (DU) and at Risø (Risø A,B

Figure 18: RPM and force response to gust.

110 Wind Power Generation and Wind Turbine Design

-1

-0.5

0.5

1.5

-4 -2 0 2 4 6 8 10

Angle of Attack (deg)

Low Reynolds number Profile

-1

-0.5

0.5

1.5

0 0.01 0.02 0.03 0.04 0.05

Low Reynolds number Profile

L2D

Figure 20: Polar of low Reynolds number proﬁ les.

-0.3

-0.2

-0.1

0.1

0.2

0.3

0 0.2 0.4 0.6 0.8 1

y/c

x/c

Low Reynolds Number Profiles

Profile 1

Profile 2

Figure 19 : Outline of a low Reynolds number proﬁ le.

and P-series). As already and often mentioned, this has led to a

max

c close to the

theoretical maximum.

6.3 Multi MW turbines

Since around 2000 the off-shore use of wind energy has progressed, one of the ﬁ rst

being the wind farm Middlegrunden close to Copenhagen, which started operation

in 2000. It soon became clear that, due to the narrow time frame available to reach

the wind farm off-shore, they have to be much larger than usual wind turbines.

Especially in Germany the development of so-called Multi Megawatt turbines has

started, these now reaching 6 MW rated power. In this connection several questions

arise. Do the aerodynamic properties stay the same when upscaling the blades?

Aerodynamics and Aeroelastics of Wind Turbines 111

The Reynolds number of a 63-meter length (REpower 5M) blade may reach

6 million and more. A major project was started in 2002 at the UAS Kiel to mea-

sure the aerodynamic properties of a 30% thick slightly modiﬁ ed Delft proﬁ le

[ 22 , 61 , 65 ]. As an outcome avariety of aerodynamic devices were measured as well

as polars up to 10 million. This was achieved by cooling down the tunnel gas to

only 100 K (= –173° C) . Figs 22 – 24 give an impression of the results achieved so

far. An attempt to model the results numerically are reported in [ 49 ].

7 Non-standard wind turbines

7.1 Vertical axis wind turbines

Two kinds of unusual turbines are dicussed brieﬂ y below as further examples of

the application of aerodynamics to wind turbines. The ﬁ rst example is a wind

0.5

1.5

-5 0 5 10 15

lift Coefficient

le of attack (de

)

Overview Re = 3M

Clean

Triping Wird x/l = 0.3 m

Triping Wire x/l = 0.15m

Carborumdum 60

Carbo with VG

Carbo with Gurney Flap

Carobrundum 120

Carobrundum 120 Gurney

0.5

1.5

0 0.005 0.01 0.015 0.02 0.025

lift Coefficient

Dra

coefficient

Overview Re = 3M

Clean

Triping Wird x/l = 0.3 m

Triping Wire x/l = 0.15m

Carborumdum 60

Carbo with VG

Carbo with Gurney Flap

Carobrundum 120

Carobrundum 120 Gurney

Figure 22 : Polars of DU-W-300 mod at Reynolds number 3 million.

0.02

0.04

0.06

0.08

0.1

0 0.2 0.4 0.6 0.8 1

c/R

r/R

Chord Distributions 1 - 2 MW Turbines

Blade 1

Blade 2

Blade 3

Blade 4

Figure 21: c/R from four blade sets for a 1.5 MW wind turbine.

112 Wind Power Generation and Wind Turbine Design

0.2

0.4

0.6

0.8

1.2

1.4

1.6

-4 -2 0 2 4 6 8 10 12

lift Coefficient

le of attack (de

)

KKK Re 10 M

Clean Re 10,3 M

Zig-Zag Tape Re 10,2 M

Zig-Zag Tape Re 10,3 M

Carobrundum Re 10,2 M

0.2

0.4

0.6

0.8

1.2

1.4

1.6

0 0.005 0.01 0.015 0.02 0.025

lift coefficient

Dra

coefficient

KKK Re 10 M

Clean Re 10,3 M

Zig-Zag Tape Re 10,2 M

Zig-Zag Tape Re 10,3 M

Carobrundum Re 10,2 M

Figure 23 : Polars of DU-W-300 mod at Reynolds number 10 million.

0.2

0.4

0.6

0.8

1.2

1.4

1.6

-4 -2 0 2 4 6 8 10 12 14

lift Coefficient

Angle of attack (deg)

KKK Zig-Zag-Tape rougness, RE varying

Zig-Zag x/l = 0.3 Re 2,2 M

Zig-Zag x/l = 0.3 Re 7.8 M

Zig-Zag x/l = 0.3 Re 8,9 M

Zig-Zag x/l = 0.3 Re 10,4 M

Zig-zag x/l = 0.2 Re 2,3 M

Clean Re 2,2 M

0.2

0.4

0.6

0.8

1.2

1.4

1.6

0 0.005 0.01 0.015 0.02 0.025

lift Coefficient

Angel of attack (deg)

KKK Zig-Zag-Tape roughenss, RE varying

Zig-Zag x/l = 0.3 Re 2,2 M

Zig-Zag x/l = 0.3 Re 7.8 M

Zig-Zag x/l = 0.3 Re 8,9 M

Zig-Zag x/l = 0.3 Re 10,4 M

Zig-zag x/l = 0.2 Re 2,3 M

Clean Re 2,2 M

Figure 24 : Polars of DU-W-300 mod with zig-zag tape, Reynolds number varying.

turbine with a vertical axis of rotation (VAWT) and the second are diffuser aug-

mented wind turbines. A discussion of counter-rotating systems is ommitted here.

The reader may ﬁ nd information in [ 48 , 32 ].

Two types of VAWT are possible (see Fig. 25 ): those driven by drag (Savonius)

and those driven by lift (Darrieus). Aerodynamic modeling starts with the question

whether an actuator disk modeling makes any sense. The total structure is an

extended one, so at least two disks for up-wind and down-wind halves have to be

used. This double actuator disk model was formulated by Loth and Mc Coy [ 70 ].

Only circumferential averaged values are discussed. The usual momentum theory

for two independent disk was applied. As a result of these assumptions only one

optimization parameter a – the (global) velocity interference factor – remains, giv-

ing

dAD

max,

c = 0.64

. Further, the power extraction is seen to split into 80 and 20 %

shares for the ﬁ rst and second disk respectively.

Figure 26 shows the ﬁ ndings in a graph. It is stricking that the total (normal-

ized) power is >0.6 along the range 0.1 < a < 0.42 . Here a was deﬁ ned as usual

as a := v

disk

/ v

∝

. It should be noted that such high c

s have not been observed

so far. As an important design parameter the solidity s = Bc/R ( B = number of

blades; c = chord and R = rotor radius) is used. It can easily be shown that low

s corresponds to high TSR but unfortunately then there is no self-starting [ 67 ]

behavior. Only when using high s ≥ 0.4 can a self-staring turbine be

achieved.

Aerodynamics and Aeroelastics of Wind Turbines 113

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5

Double Actuator Disk

Betz-Limit

first disk

2nd disk

total cp

Figure 26 : c

(a) for a double actuator disk.

Figure 25: Vertical axis wind turbines.

Figure 27 shows a comparison between various methods of calculating c

. The

ﬁ rst method [ 18 ] uses a simple procedure for the induced axial velocity which then

is a function of circumferential angle ϕ . To simplify matters this is assumed to be

a(ϕ) = ls / 2 sin(ϕ). This method results in a

max

c which is only slightly smaller

than

Betz

c . Holme’s [ 66 ] method uses a vortex approach to describe the ﬂ ow ﬁ eld.

Here the unsteadiness was avoided by distributing the bound circulation around a

whole circle. This then gives a steady but non-symmetric model which also makes it

possible to calculate transverse forces. Figure 27 shows, however, only minor changes

to the ﬁ rst method, that of Wilson [ 18 ]. A simple blade element method was formu-

114 Wind Power Generation and Wind Turbine Design

lated by Stickland [ 74 ] in the 1970s. Here the the ﬂ ow is divided into various

stream tubes and an internal computer code interation ensures the actual balance

of axial momentum. As a result of including drag the c

(TSR) curve now becomes

much narrower and the maximum also decreases to values common for HAWTs.

In addition CFD methods can be applied to VAWT. To avoid time-consuming

unsteady computations a special technique called interface averaging between

two computational volumes with different frames of references were used. One

volume in the vicinity of the rotor experiences inertial forces due to rotation. The

delicate point now is how to pass over to the second volume where no inertial

forces are applied. In summary a much smaller

max

c may be predicted by this

method. Meanwhile [ 71 ] 3D transient CFD simulation have been carried out.

Further research is obviously necessary to reduce the large differences obtained

by the various methods. It should be noted that manufacturers of small wind tur-

bines try to use the vertical axis principle again. Unfortunately no particular sys-

tem seem tobe able to compete against HAWT. This is mainly because most

systems do not possess a dynamically stable supporting structure.

7.2 Diffuser systems

Wind-concentrating systems such as shrouds, ring-wings and diffusers have been

being investigated for a period of about 50 years. A summary has been given by

van Bussel [ 20 ], together with a 1D momentum theory and a collection of experi-

mental data. Special emphasis has been given to a discussion of the inﬂ uence of

the diffuser’s exit pressure. It should be noted that most of the designs try to use a

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5 1 1.5 2 2.5 3 3.5 4

Tip Speed Ratio

3-bladed H-Darrieus - Comparison of Methodes

Simple Actuator Disk

Linear Vortex Theory

Blade Element

CFD

Figure 27 : Comparison of different methods of describing a small VAWT.