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2009 International Conference on Energy and Environment Technology

Study on Aerodynamic Design of Horizontal Axis Wind Turbine Generator System

Li DONG, Mingfu LIAO

Insti

tute of Monitoring and Control for Rotating Machinery and Wind Turbines Northwestern Polytechnical University Xi’an, China Bernd.nwpu@gmail.com

Abstract—In this paper the choosing principles of design parameters and multi-airfoils in horizontal axis wind turbine (HAWT) generator system aerodynamic design are introduced. On the basis of the comparison analysis of wind turbine aerodynamic design method Wilson and Schmitz, a HAWT optimized design method based on Schmitz is presented. In this Schmitz optimized method different aerodynamic losses are considered and 2 real physical parameters are used instead of induced factors of Wilson method. The design results show that HAWT optimized design method based on Schmitz makes good agreement with Wilson method. After chord length distribution is corrected due to practical reasons, a twist angle correction method is also presented based on the principle of maximum wind energy capture. Applying the methods improved in this paper, a 2 MW HAWT for doubly fed induction asynchronous generator (DFIAG) is designed in terms of aerodynamic aspect, taking blade structural strength into account. Applying Schmitz extending method, the partial load characters are calculated. The results show that designed HAWT partial load characters are in agreement with the results of GH Bladed software simulation. Keywords- Schmitz, airfoil, partial load, horizontal axis wind turbine (HAWT), blade tip speed ratio (BTSR)

Yingfeng LI, Xiaoping SONG,Ke XU

Hara XEMC Windpower Co. Ltd Xiangtan, China

This paper will discuss about the issues mentioned above and a 2MW HAWT for double fed induction asynchronous generator (DFIAG) is designed in terms of aerodynamic aspect as an example. II. CHOOSING OF DESIGN PARAMETER

I.

INTRODUCTION

Wind energy utilization is a clean, raw material-costless, promising renewable energy style. A theoretical maximum for Cp exists denoted by the Betz limit Cpmax=16/25=0.593[1,2,3,4]. Modern horizontal axis wind turbines (HAWTs) work with Cp up to 0.5, close to Betz limit. One of the reasons why Cp can not reach Betz limit is that HAWT rotor aerodynamic losses exist. Therefore the aerodynamic design is important in a HAWT generator system to convert wind energy into mechanical energy. Wilson, based on Glauert method, has contributed the insight into rotor aerodynamic design which is applied widely in HAWT rotor design [2,3,4]. Induced factors, which can not be understood by engineers easily, are put forward in order to explain the principle of Wilson method. Schmitz described the aerodynamic design principle in a new way, in which real physical parameters of velocity triangle instead of abstract induced factors are applied [1]. However, blade tip losses and drag force losses are not considered in Schmitz blade design method. The rotor design parameters and airfoils choosing, blade chord and twist angle correction still need to be analyzed simultaneously, when addressing design of rotor.

978-0-7695-3819-8/09 $26.00 ? 2009 IEEE DOI 10.1109/ICEET.2009.208 841 839 836

According to the different intentions of designers, different design parameters can be chosen at the same external conditions. For the analysis of HAWT design method, a example of 2MW HAWT will be designed in this paper. As most of modern HAWT, basic design parameters are defined for the 2 MW HAWT, where blade number is 3; maximal blade tip speed is 78 m/s ,taking noise into account; rated power is 2000KW; IEC Type[5] is Class Ⅱa. For this example of 2MW HAWT, rated wind speed is defined as 13.2m/s, at which the biggest probability in the annual energy distribution occurs and the HAWT efficiency at rated wind speed, which ranges from 0.25 and 0.32 habitually according to reference [6], is defined as 0.29. Thus corresponding HAWT rotor diameter is 78.95m. Taking hub and blade tip correction into account, rotor diameter is defined as 80m, i.e. D=80m, and rotor hub diameter is 2.4m, i.e. Dhub=2.4m, and thus the maximal rotational speed of HAWT is ?max=78/R=1.95 rad/s, nmax= 18.62r/min. According to the behavior of DFIAG it is assumed that nmax/nmin is 2.2, and thus the lowest rotor rotation speed is nmin=8.5r/min, ?min=0.89 rad/s. Considering noise emission and effect for chord length, DBTSR is defined asλD=7 in this example, and thus the maximal design wind speed is VDmax=78/λD=11.14m/s and the minimum design wind speed is VDmin=?minR/ λD=5.06 m/s. Between VDmax and VDmin HAWT operates at optimum design point. TableⅠshows the parameters of the design example.

TABLE I. DESIGN PARAMETERS FOR A 2MW WIND TURBINE

EXAMPLE

Prate 2MW

Vrate 13.2m/s

λD

7

Voptmax 11.14m/s

D 80m

Dhub 2.4m

nmax 18.6

nmin 8.5

III.

AIRFOIL CHOOSING

In spanwise direction of HAWT blade, different airfoils are adopted in blade aerodynamic design, e.g. 6 airfoils are adopted in the 2MW HAWT example, as shown in Table 2. At blade tip, airfoils with high Lift-Drag-Ratio (LDR), low roughness sensitivity, low noise character should be selected to assure the most optimum aerodynamic behavior. At middle part of blade, the selected airfoils should be thicker than those at blade tip to assure strength and have good aerodynamic characters simultaneously. The circular profile and thick airfoils are selected at blade root part to connect with hub flange easily and to assure the strength of blade inner part. Simultaneously some important parameters of different airfoils selected for the blade design, e.g. the camber and corresponding position, thickness and corresponding position, attack angle at design point, Lift coefficient at design point etc, should be monotonic or close to each other to assure blade geometry continuity. In order to satisfy the strength of HAWT, relative thickness(r/R) distribution of a real HAWT blade is adopted in the 2MW HAWT example, as shown in TableⅡ[7, 8].

TABLE II. AIRFOILS AND THEIR CHARACTER AT DESIGN POINT FOR THE 2MW HAWT EXAMPLE Relative thickness (%) 100％ 29.98 25.67 21.11 17.43 14.48 Lift Coeff. － 1.207 1.2427 1.2564 1.265 1.2122 Attack angle － 7 7 7.5 7 6.5 LDR Radial position(r /R) 0 38 48 62 76 97

The driven moment of blade section, in which drag force losses and blade tip losses are not taken into account, is expressed as: ρ (2) dM = c 2tdr ?CA (α A ) sin(α ) ? CW (α A ) cos(α ) ? r ? ? 2 where apparent wind speed in the rotor plane is[1]: c = c1 cos(α1 ? α ) (3) In order to take blade tip losses into account, Prandtl’s blade tip theory[2,4] is applied in Schmitz design method in this paper. Lift force and drag force from momentum theorem in (1) are multiplied by Prandtl’s blade tip losses factor according to Prandtl’s blade tip losses theory and therefore (1) taking drag force into account (shown in Fig.1) simultaneously is changed as: ? 8π r ? (4) tCA (α A ) ? ? F sin α + tCW (α A ) ? tan (α1 ? α ) = 0 ? N ? where F is Prandtl’s blade tip losses factor[2,4]:

F= ? ? N (R ?r) ? arccos ?e 2 r sin α ? ? ? π ? ? ? ? 2

.

(5)

The driven moment of blade section taking blade tip losses and drag force losses into account is still expressed as (2) and whereas apparent wind speed in the rotor plane is changed as:

c = c1 cos(α1 ? α ) 8πr F sin α + tCW (α A ) N 8πr F sin α N

Airfoil Cylinder AH 93-W-300 AH 93-W-257 FFA-W3-211 AH 93-W-174 AH 93-W-145

.

(6)

－ 112.8 157 157 194.6 186

c2 =

c=

c1

(α cos

?α 1

)?δ

c/

2

Δc = c1 ? sin (α1 ? α ) 2

IV.

BLADE AERODYNAMIC DESIGN

β

Δc 2

V1.ax

V3.ax

V2.ax

A. Aerodynamic design method Wilson presented a blade aerodynamic design method, where induced factors [2,4], which are difficult to be understood by designers on occasion, are put forward. Schmitz presented another design method, where real physical parameters instead of induced factors are calculated through velocity triangle. Therefore Schmitz design method has real physical meaning and can be understood easily by designers. Essentially, the design results of these two methods are coincident [1]. In this paper, Schmitz design method is adopted due to its advantages. However, Schmitz design method doesn’t take blade tip losses and drag force losses into account. Thus an optimized design method based on Schmitz method is presented. The equilibrium equation from airfoil theory and momentum theorem, in which drag force losses and blade tip losses are not taken into account, is expressed as[1]:

= V1

β

Figure 1. Velocity triangle in Schmitz design method[1]

tCA (α A ) ?

8π r sin α tan (α1 ? α ) = 0 N

(1)

Therefore blade aerodynamic design can be fulfilled by Schmitz optimized design method with optimized parameters chord length t and inflow angle α, where (2) is optimized equation and (4) is constraint equation. Through Matlab program, it is convenient to solve this nonlinear optimized design. From Fig. 2 describing the comparison results between Schmitz optimized design method and Wilson method, it is clear that Schmitz optimized design method makes good agreement with Wilson method. The samll errors in blade tip and root are caused by different tip and root loss assumptions.

842 840 837

6 chord length (t/m) Schmitz Wilson

60 corrected twist angle based on corrected chord final corrected twist angle initial twist angle

50

4

40 twist angle (°)

2

30

0

20

0

5

10 15 20 25 30 distance from hub center of wind turbine (r/m)

35

40

10

60 twist angle(°) 40 20 0 -20 Schmitz Wilson

0

-10

0

5

10 15 20 25 30 distance from hub center of wind turbine(r/m)

35

40

0

5

10 15 20 25 30 distance from hub center of wind turbine (r/m)

35

40

Figure 4. The comparison of initial twist angle distribution, corrected twist angle distribution based on corrected chord and final corrected twist angle distribution for the 2MW wind turbine example

2.5

thickness (m)

Figure 2. Comparison of chord length (upper) and twist angle (nether) between Schmitz optimized method and Wilson method

2 1.5 1 0.5 0 0 5 10 15 20 25 distance from hub center of wind turbine(r/m) 30 35 40

B. Correction of blade geometry contour The results of blade aerodynamic design can not satisfy the requirements of the transport and manufacturing due to big blade chord length at root. Thus, taking the connection with rotor hub and geometry continuity into account, the blade chord length should be corrected, as shown in Fig. 3 for the 2MW HAWT. The twist angle should be also corrected corresponding with corrected chord length in order to maintain the capture of maximum wind energy at design point, i.e. (2) is also optimized equation, in which chord length t is the new corrected value and inflow angle α is unknown. Therefore the corrected inflow angle α can be acquired through the optimization of (2) and corresponding twist angle can be also acquired, as shown in Fig.4. It is clear that when the blade chord length decreases, the twist angle will increase in order to acquire maximum wind energy. The twist angle of blade root can not fulfilled due to the difficulty of manufacturing. Therefore the twist angle at root should be corrected again. The final corrected twist angle distribution along the blade is shown in Fig. 4. And, the thickness distribution is shown in Fig. 5. It is supposed that pitch axis go through the geometry centers of every blade airfoil sections. The 3D model of blade is shown in Fig.6.

6 initial chord corrected chord chord (t/m) 4

Figure 5. Thickness distribution along blade for the 2MW wind turbine example

Figure 6. Blade 3D model for the 2MW wind turbine example

V.

WIND TURBINE PARTIAL LOAD CHARACTER

2

0

0

5

10

15 20 25 distance from hub center of wind turbine (r/m)

30

35

40

Figure 3. The comparison of initial chord distribution and corrected chord distribution for the 2MW wind turbine example

The operational character of HAWT at non-design point is called HAWT partial load character. HAWT often works at partial load, especially when wind speed is beyond rated wind speed. Schmitz presented an extending method based on Schmitz design method to calculate HAWT partial load character, which takes two extreme cases into account that when blade tip speed ratio (BTSR) is much lower than DBTSR, part air will go through HAWT without doing work on HAWT, and when BTSR is much higher than DBTSR, part air in HAWT plane will round HAWT without doing work on HAWT. In order to verify the usefulness of the Schmitz extending method, HAWT partial load characters are calculated in comparison by Schmitz extending method and GH Bladed software simulation, as shown in Fig. 7-9. The results from Schmitz extending method make agreement with the results from GH Bladed software[9] simulation. The errors are small and caused by hub losses and different calculation model. Moreover, for variable speed HAWTs

843 841 838

operational zone is normally at DBTSR or below DBTSR, where the errors are very small.

0.7 Schmitz result Bladed result

0.6

0.5 Power coefficient

0.4

0.3

0.2

0.1

0

0

2

4

6 8 10 Blade tip speed ratio

12

14

16

Figure 7. Power coefficient calculation results from Schmitz extending method and GH Bladed soft ware simulation

1.4 Schmitz result Bladed result

1.2

1 Thrust coefficient

point, Lift coefficient at design point, should be monotonic or close to each other. An optimized aerodynamic design method based on Schmitz method is presented. In this optimized method different aerodynamic losses are considered and 2 real physical parameters are used instead of induced factors of Wilson method.The design results of optimized method make good agreement with Wilson method. Based on chord length correction of the designed blade, the twist angle correction method aiming to capture maximum wind energy is introduced. When the blade chord length decreases, the twist angle will increase in order to acquire maximum wind energy. Based on the methods presented in this paper, a 2 MW HAWT as a validating example in which 6 airfoils are selected is designed. The partial load characters are calculated applying Schmitz extending method. The results show that designed HAWT partial load characters are in agreement with the results of GH Bladed software simulation, which validate the correction of the methods presented in this paper. VII. NOMENCLATURE

t Cp R r dr Chord length at blade section r Power coefficient of wind turbine Wind turbine rotor radius Distance from the root to blade section The thickness of blade section Attack angle Lift coefficient at attack angle αA Drag coefficient at attack angle αA Inflow angle in rotor plane Apparent wind direction upstream Blade number Apparent wind speed in rotor plane Apparent wind speed upstream Prandtl’s blade tip losses factor Air density Deisgn blade tip speed ratio (DBTSR) Wind turbine rotor diameter Hub diameter The maximum rotation speed of wind turbine rotor The minimum rotation speed of wind turbine rotor Rated power

0.8

0.6

0.4

0.2

αA

0 0 2 4 6 8 10 Blade tip speed ratio 12 14 16

CA CW

Figure 8. Thrust coefficient calculation results from Schmitz extending method and GH Bladed soft ware simulation

0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 Schmitz result Bladed result

α α1

N c c1 F

ρ λD

D Dhub nmax nmin Vrate

Moment coefficient

REFERENCES

[1]

0 2 4 6 8 10 Blade tip speed ratio 12 14 16

[2] [3] [4] [5] [6] [7] [8] [9]

Figure 9. Moment coefficient calculation results from Schmitz extending method and GH Bladed soft ware simulation

VI.

CONCLUSIONS

In this paper, the principle of airfoil choosing for HAWT is investigated. The choosing of multi-airfoils should take geometry continuity into account. Some important parameters of different airfoils selected for blade design, e.g. the camber and corresponding position, thickness and corresponding position, attack angle at design

R. Gasch and J. Twele, Windkraftanlagen, 4th ed. Berlin: Teubner, 2005, pp. 179-281. Martin O. L. Hansen, Wind turbine aerodynamics. UK: James&James Ltd, 2000. Spera D A, Wind turbine technology . New York : ASME Press ,1994. Tony Burton, David Sharpe, Nick Jenkins and Ervin Bossanyi, Wind energy handbook. USA:John Wiley & Sons Ltd, 2005. IEC 61400-1,3rd ed., 2005. Wind energy market2007/2008, 2008. Dieter Althaus. Niedriggeschwindigkeitsprofile. Stuttgart: vieweg,1996,pp.138-230. Ruan zhikun, “Wind turbine aerodynamic calculation method taking Reynolds number into account”, Wind Power, 1990,2. GH Bladed version3.8 user manual.

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