gt2013-94158 - uni siegen · gt2013-94158 small horizontal axis wind turbine: analytical blade...

1 Copyright © 2013 by ASME

Proceedings of the ASME Turbo Expo 2013 GT2013

June 3-7, 2013, San Antonio, Texas, USA

GT2013-94158

SMALL HORIZONTAL AXIS WIND TURBINE: ANALYTICAL BLADE DESIGN AND COMPARISON WITH RANS-PREDICTION AND FIRST EXPERIMENTAL DATA

Tom Gerhard, Michael Sturm, Thomas H. Carolus University of Siegen

Department of Fluid- and Thermodynamics,

57068 Siegen, Germany

ABSTRACT State-of-the-art wind turbine performance prediction is

mainly based on semi-analytical models, incorporating blade element momentum (BEM) analysis and empirical models. Full numerical simulation methods can yield the performance of a wind turbine without empirical assumptions. Inherent difficulties are the large computational domain required to capture all effects of the unbounded ambient flow field and the fact that the boundary layer on the blade may be transitional.

A modified turbine design method in terms of the velocity triangles, Euler’s turbine equation and BEM is developed. Lift and drag coefficients are obtained from XFOIL, an open source 2D design and analysis tool for subcritical airfoils. A 3 m diameter horizontal axis wind turbine rotor was designed and manufactured. The flow field is predicted by means of a Reynolds-averaged Navier-Stokes simulation. Two turbulence models were utilized: (i) a standard k-ω-SST model, (ii) a laminar/turbulent transition model. The manufactured turbine is placed on the rooftop of the University of Siegen. Three wind anemometers and wind direction sensors are arranged around the turbine. The torque is derived from electric power and the rotational speed via a calibrated grid-connected generator.

The agreement between the analytically and CFD-predicted kinematic quantities up- and downstream of the rotor disc is quite satisfactory. However, the blade section drag to lift ratio and hence the power coefficient vary with the turbulence model chosen. Moreover, the experimentally determined power coefficient is considerably lower as predicted by all methods. However, this conclusion is somewhat preliminary since the existing experimental data set needs to be extended.

NOMENCLATURE A area (m2) CP power coefficient (-)

D diameter (m) Fax axial force (N) Fu tangential force (N) N number of data points (-) P power (W) Re Reynolds number (-) T torque (Nm) U generator electriv voltage (V) a axial induction factor (-) a' tangential induction factor (-) c velocity (m/s) cF friction coefficient (-) cp pressure coefficient (-) fS sampling frequency (Hz) l chord length (m) m mass flow rate (kg/s) n angular velocity (min-1) p static pressure (Pa) r radius (m) t circumferential blade spacing (m) u circumferential velocity (m/s) w flow velocity in the rotating frame of reference (m/s) y+ dimensionless wall distance (-) z number of blades (-) angle of attack (°) flow angle (°) γ intermittency factor (-) drag to lift ratio (-) efficiency (-) tip speed ratio (-) ν kinematic viscosity (m2/s) ρ fluid density (kg/m3) σ solidity (-) τ shear stress (N/m2)


Subscripts 0 position far upstream 1 position before rotor 2 position after rotor 3 position far downstream ∞ position in rotor plane BE blade element F friction L lift P power ave average drag profile drag eff effective el electric hub hub position m meridional (axial) max maximum r radial position tip tip position tot total u circumferential wind freestream conditions far upstream

INTRODUCTION The paper deals with the performance analysis of a small

horizontal axis wind turbine. State-of-the-art performance prediction tools are mainly based on semi-analytical models, incorporating some form of blade element momentum (BEM) analysis, extended airfoil polar curves and other empirical assumptions for off-design operation (see e.g. Hansen in Brouchaert [1] or Hansen [2]).

In principle, CFD methods can yield the fundamental performance of a wind turbine without empirical assumptions. Moreover, they include the interaction of the spanwise blade sections and other 3D effects. 3D CFD simulations of different wind turbines, e.g. conducted by Laursen et al. [3] or Mahu et al. [4], yield a fairly well suited performance prediction. However, they showed that using transition turbulence models seem to result in an overprediction of integral values like the generated torque at the hub. Advanced methods, e.g. Large-Eddy Simulations (LES), have the potential to be linked to structural or aeroacoustic computational tools, e.g. to investigate the aerodynamic and aeroacoustic effects of different tip shapes as shown by Fleig et al. [5]. Inherent difficulties, however, are (i) the large computational domain required to capture all effects of the unbounded ambient flow field on the rotor and (ii) the fact that the near-blade flow field is transitional from laminar to turbulent. Nevertheless, the flow field data provided by the numerical simulation allow a detailed insight on flow mechanisms in the vicinity of the turbine blade and a comparison with assumptions made in the analytical design (see e.g. Hartwanger and Horvat [6] or Bazilevs et al. [7]).

Hence, a first objective of this study is the prediction of the flow field in the vicinity of a small wind turbine rotor and the associated overall power yield by means of a steady, incompressible, three-dimensional, Reynolds-averaged Navier-Stokes (RANS) simulation. A strong focus is on the effect of the turbulence model selected within the RANS simulation, here (i) a standard turbulence model without transition and (ii) a laminar/turbulent transition model are used.

The second objective is the experimental validation of the predicted turbine power output. In general one can place a test turbine in a wind tunnel or a free field environment. The first option requires either model scale turbines or a huge wind tunnel. Yang et al. [8] presented a study to characterize the evolution of the wake vortices and flow structures downstream of the rotor by a high-resolution Particle Image Velocimetry (PIV). The 1:350 scaled down 90 m diameter wind turbine was placed in an atmospheric boundary layer wind tunnel. Despite enormous efforts, the small model dimensions eventually led to Reynolds numbers significantly lower than for full scale. For the investigation of mitigation methodologies of adverse pressure gradients on turbine blades at higher Reynolds numbers, Schreck and Robinson [9] placed a wind turbine with 10.1 m diameter in a wind tunnel with a cross sectional area of 24.4 x 36.6 m2. A free field environment allows the collection of realistic data, but requires statistical data processing because of the inherent temporal unsteadiness and spatial inhomogeneity of the wind field. Free field investigations of small wind turbines were carried out e.g. by Vick and Clark [10]; they focused on sound emissions of different blade shapes. A good overview of the different ways to evaluate the near and far wake region of wind turbines is given by Vermeer et al. [11]. In that paper it is also mentioned that the consideration of the laminar–turbulent transition is challenging, but probably of utmost importance. Vermeer et al. refer to a study of Johansen and Sørensen [12] which showed that the assumption of a fully turbulent flow can lead to a significant underprediction of the airfoil lift coefficient as compared to experiments.

In this study we place the small wind turbine investigated in the free field and confine ourselves to design operating conditions.

As almost any common performance prediction tool needs the detailed geometry of the wind turbine as an input, a more indirect objective of this study is the development and application of an analytical wind turbine design method (see e.g. Kulunk and Yilmaz [13]). In many BEM-based design tools the blade is considered as a number of wing sections subjected to an approaching flow under a given angle of attack (see e.g. Spera [14], Gasch and Twele [15], Burton et al. [16], Manwell et al. [17]). By contrast, designers of other low solidity axial turbomachinery (such as low pressure fans) often consider a cascade of isolated wings (see e.g. Carolus and Starzmann [18]). Associated with this idea are velocity triangles at the rotor entrance and exit plane with the relevant flow velocity being the vector mean of the relative flow


velocities. Here, the meridional component of the absolute velocity is linked to the volume flow rate through the rotor and the tangential component of the exit flow to the work done by the rotor (via Euler’s equation of turbomachinery). The benefit of the latter formulation is that flow field data can readily be compared with circumferentially averaged near-rotor velocity data from computational fluid dynamics (CFD). This allows a better identification of deficits in the aerodynamic design methodology and an improved understanding of loss mechanisms.

1. ANALYTICAL BLADE DESIGN METHOD Due to the widening of the boundary stream tube of a wind

turbine (Fig. 1), the free stream wind speed far upstream of the rotor c0 is eventually retarded to c3 far downstream. At any coaxial strip at a given radius containing a number of blade elements (BEs) one can draw the velocity triangles at the rotor entrance and exit plane, Fig. 2. Ideally, the absolute flow enters the rotor perpendicular with the velocity c1 = cm1, i.e. without swirl, and leaves it with c2 at the same radius, i.e. without a potential chordwise shift of streamlines due to centrifugal effects. Since the axial extension of the rotor is small, we assume the meridional (i.e axial through flow) velocity at rotor entrance and exit plane being equal, cm1 = cm2. As common, an axial induction factor a is defined such that

1 2 0 3 01 and 1 2m m m mc c c a c c a c . (1)

Moreover, c2 has the tangential component cu2 (i.e. the swirl) which is the key quantity for work extracted from the flow by the blades. A tangential induction factor a’ is defined such that

2 2 uc a' u . (2)

Fig. 1: WIND TURBINE ROTOR IN BOUNDARY STREAM

TUBE The mass flow through the bladed annulus is

02 1 2 mm c r r ( a )c r r . (3)

From axial momentum conservation on the complete coaxial strip in the stream tube one obtains the axial force on the strip

0 3 2 1 ax mF c c m p p A (4)

with p1 and p2 as the static pressure up- and downstream of the bladed annulus. Employing Eulers’s equation of turbomachinery in the form

2 22 1 1 22p p w w , (5)

Fig. 2: WIND TURBINE ROTOR: ENTRANCE AND EXIT PLANE VELOCITY TRIANGLE AND VECTOR MEAN

RELATIVE FLOW VELOCITY w∞

with w1 and w2 being the flow velocities in the relative frame of reference (see Fig. 2), one obtains δFax in terms of kinematic variables a and a' as

2 1 4 axF u a' a' r r . (6)

Eliminating Fax from eqs. (4) and (6) and introducing the tip-speed ratio and the local-speed ratio


0 0

ar

tip

u u r,

c c r (7)

we end up with a first equation for the unknown variables a and a' as a function of the local-speed ratio

2

11 1

2 4

r

r

a aa' f

. (8)

Again, according to Eulers’s equation of turbomachinery, the power due to all blade elements in the coaxial strip is

22 01 4 BE uP uc m u a' a c r r . (9)

The power provided by the wind

30 2

2windP c r r (10)

serves to define a strip power coefficient in the common way

24 1 BEP,BE r r

wind

PC a' a f

P

. (11)

This is a second equation for the unknown variables a and a’. The strategy now is: For a set of local-speed ratios r find a and a' from eqs. (8) and (11) which yield the maximum value of CP,BE. A closed solution is difficult, but a simple iteration is rather straight forward. Eventually, we arrive at the known Glauert/Schmitz graph as published e.g. by Gasch and Twele [15], see also Fig. 9. Now the solidity for the blade cascade has to be determined for a given lift to drag ratio of a selected airfoil. Referring to the angular momentum conservation the circumferential force on a blade element becomes

2u u mF c c t r . (12)

By introducing the vector mean velocity w∞ (Fig. 2)

2 20 1 1 1 1rw c a a' a (13)

and the flow angle β∞

1 1

1 r

aarctan

a'

(14)

in terms of the induction factors a and a', the circumferential force can be expressed using the lift coefficient cL and the lift to drag ratio ε

2

2u L

wF sin c l r

. (15)

Now, the desired solidity of the blade cascade can be calculated by eliminating δFu from eqs. (12) and (15)

2

2

4

1 11 1 1

1 1

r

L r r

a'l

t a' a'c a

a a

(16)

with the circumferential blade spacing t. The overall design power coefficient of the wind turbine is

obtained by summing up all elementary strip power coefficients

all strips

P tip drag P,BC C (17)

weighted with the airfoil drag efficiency

drag

sin 11 cot 1

sin 1

r

a'

a

(18)

and an efficiency according to Betz and Prandtl (see Gasch and Twele [15]) associated with the tip losses

2

2tip

41 0 92

9D. z

. (19)

As a summary the input parameters for the rotor design are

hub diameter Dhub

tip diameter Dtip

freestream velocity c0

tip-speed ratio λ

local angle of attack α

number of blades z

and the desired airfoil shape

with the blade coordinates being the key result. The design method has been encoded in MATLAB‘ as our in-house design tool 'dWind'. Fully integrated in the design process is the software XFOIL (Drela [19]) which yields the blade element airfoil lift and drag coefficients as a function of the chosen airfoil, angle of attack and local Reynolds number. A linear-vorticity second order accurate panel method is used for inviscid analysis. This panel method is coupled with an integral boundary layer method and an approximate en-type transition amplification formulation (Mueller [20]). Here we select the default value nCrit = 9 as for an airfoil in a standard wind tunnel.

2. DESIGNED ROTOR Utilizing 'dWind' a 3 m diameter three-bladed wind

turbine for a design tip-speed ratio of λ = 7.5 and a hub-to-tip ratio of 0.07 has been designed, Fig. 3. The blade is segmented into 15 sections. The design wind speed is c0 = 6 m/s, corresponding to a design tip Reynolds number Retip =


2.15·105. Here, the local radial Reynolds number Rer is based on the radial chord length lr and the relative flow velocity w1 (instead of w∞)

1 rr

w lRe

. (20)

The blades are fixed pitch and made up of Somers (Somers [21]) airfoil sections (Tab. 1) with an design angle of attack = 5°.

Tab. 1: AIRFOIL SECTIONS OF THE INVESTIGATED WIND TURBINE BLADE

Blade station Airfoil section r/rtip < 0.4 S835 0.4 < r/rtip < 0.75 S833 r/rtip > 0.75 S834 As seen in Fig. 5 the manufactured blades have clipped

blade sections for 0.07 < r/rtip < 0.27 because of structural constraints. Furthermore, for a reduction of vertices shedding off from the tip, the tip shape was modified by rounding the leading edge corner at the blade tip (Gyatt and Lissaman [22]), see Fig. 5. Both geometrical modifications were taken into account in the numerical RANS simulation. Hence some caution is necessary when comparing numerical and experimental data with the more idealized results from ‘dWind’.

Fig. 3: ROTOR AND BLADE OF THE 3 m WIND TURBINE

AS OBTAINED BY THE DESIGN SOFTWARE 'dWind'

3. PROCEDURE FOR NUMERICAL PERFOMANCE PREDICITION

3.1 Numerical setup

The numerical domain extends four times the rotor radius in upstream and radial direction as seen from the rotor plane and 12 times the radius downstream of the rotor plane, Fig. 4. The turbine symmetry enables the simulation of only one-third of the annulus to save computational costs. Consequently, periodic boundary conditions were imposed in the circumferential direction. A velocity inlet was imposed at the upstream boundary with a consistent turbulence intensity of 5%. The outlet boundary condition consists of an area averaged static pressure.

The steady, incompressible, three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations are solved in a rotating reference frame with the commercial 3D Navier-Stokes code ANSYS FLUENT. For turbulence modeling we used the standard fully turbulent k-ω-SST turbulence model (Menter [23]) and additionally an implemented laminar/turbulent transition model. For the latter, ANSYS FLUENT uses an approach which connects the k-ω-SST transport equations with an empirical correlation approach based on the work by Langtry [24]. Two additional transport equations are implemented, one for the intermittency factor γ and one for the transition onset criterion in terms of the momentum thickness Reynolds number. An empirical correlation describes the difference between a critical Reynolds number, where the intermittency starts to increase and the model is activated, and the transition Reynolds number (ANSYS Inc. [25]). The model constants used by ANSYS FLUENT are predominantly taken from Menter et al. [26].

Fig. 4. COMPUTATIONAL DOMAIN While the block-structured numerical grid for the k-ω-SST

case consists of 10 million nodes, the transition SST model requires a finer wall resolution which led to a total grid size of more than 16.5 million nodes. Along the blade span 550 nodes have been used which corresponds to a spatial resolution of less than 3 mm. In chordwise direction 72 non-uniformly spaced nodes were used. For the k-ω-SST simulations, the maximum value of the dimensionless wall distance y+

max for the first node adjacent to the blade surface was y+

max < 30, whereas the area averaged value y+

ave at the blade was about 7. The

increased wall resolution for the transition SST simulations led to y+

max values of less than 5 and a blade average below 1.5. Furthermore common grid quality criteria were considered; for instance, the grid angles were all above 25°. However, the aspect ratios for the transitional case were, with maximum


values of about 170, quite high. For both cases a convergence criteria of 1·10-6 was reached and integral sizes were constant over numerous iterations.

3.2 Numerical data analysis The overall performance of the turbine is calculated by the

torque at hub provided by the post-processor ANSYS CFD-POSTTM. The velocity components required for the calculation of the induction factors are evaluated at the spanwise position r/rtip = 0.27 in a reference plane one chord length downstream of the trailing edge. This axial position of the reference plane was chosen as a good compromise between the very near wake region with the velocities not levelled out at all and the far wake where the stream tube has widened too much. The radial distribution of the relevant flow variables was evaluated by circumferential averaging.

4. EXPERIMENTAL PERFORMANCE ANALYSIS

4.1 Experimental setup The designed blades are installed on a full scale small

horizontal axis wind turbine that was built as a test facility on the rooftop of the University of Siegen, Fig. 5. The hub height is 5 m above roof.

Fig. 5: FULL SCALE WIND TURBINE OF THE UNIVERSITY OF SIEGEN

The turbine is pivoted passively by a wind vane. A 2.5 kW

generator converts the mechanical power into electrical which is fed in the public grid via a rectifier and inverter. To foster cut-on at low wind speeds the controller starts to load the rotor with the full torque with a 15 seconds delay time. During that time no electric power is produced and the system is idling. A braking resistance sets in when the generator exceeds a critical voltage due to high rotational speeds. The characteristic curve of the generator, i.e. the electrical power vs. electric voltage is programmable via a software interface. The rotational speed, which in turn is proportional to the electric voltage, is measured directly on the shaft of the generator. Three wind

anemometers and wind direction sensors are arranged around the turbine in a distance of 2.5 rotor diameter according to the German standard for the measurement of power performance of electricity producing wind turbines, DIN EN 61400-12-1 [27], see Fig. 6. For the determination of the ambient density the temperature is measured.

The data acquisition (Fig. 7) is running continuously 24 hours per day. The parameters recorded are

date and time,

three wind speeds, three wind directions,

generator electric current,

generator electric voltage,

rotational speed of rotor

temperature.

A relatively high temporal resolution of the data is required for the statistical post-processing. Therefore a sampling frequency of fS = 1000 Hz and an averaging time of 0.1 s have been chosen. A data record consists of N = 864.000 values per parameter and day.

Fig. 6: ARRANGEMENT OF THE ANEMOMETERS AND

WIND DIRECTION SENSORS AROUND THE WIND TURBINE (VIEW FROM TOP)

4.2 Experimental data processing The data processing is also shown in Fig. 7. The torque T

from the generator as seen by the wind turbine rotor is derived from the electric power Pel and the rotational speed n. Prior to the wind turbine tests, the isolated generator was calibrated on a standardized test rig. From that the true mechanical shaft power of the wind turbine is obtained. According to DIN EN 61400-12-1 [27], an effective wind speed ceff is calculated from the mean value of those anemometers that are not operating in the slipstream of the turbine defined by the 74° cone indicated


in Fig. 6. The orientation of the turbine is assumed to agree with the mean wind direction. This effective wind speed and the rotational speed of the rotor are used for the subsequent calculations of the instantaneous tip-speed ratio. The data is then sorted into bins of λ = ±0.25. At this stage the data may still contain values where the turbine is not operating properly e.g. during cut-on. Hence, data are eliminated that are not within the loading characteristic curve of the generator. In the next step the overall performance parameters are calculated by taking the mean value from each bin. Eventually, in order to exclude any Reynolds number effect, only data are used where the design wind speed c0 = 6 m/s is met by ceff within ± 1%. For the design tip speed ratio λ = 7.5 this corresponds to n = 280.86 rpm ± 1%. In addition, a threshold for the electrical power of Pel = 50 W is used. Averaging of the thus remaining Cp values yields a single nominal value which is believed to be suitable for an adequate comparison with analytical and numerical results.

Fig. 7. DATA EVALUATION PROCESS

The distance between the wind measurement stations and the rotor hub (7.5 m) may cause de-synchronization of wind speed signals and turbine power. Assuming a frozen turbulence structure convecting with ceff towards the turbine, the time shift of the measured wind speed and the electrical power can be estimated. It was found to have no significant affect on the turbine integral performance parameters.

5. RESULTS Fig. 8 shows a comparison of the pressure coefficient cp

and the friction coefficient cF at two spanwise blade positions as predicted by RANS and XFOIL (as integrated in ‘dWind’). Pressure and friction coefficient are calculated with the dynamic pressure pdyn,1 at the rotor entrance plane. cp is defined as

0 0

21

12

p

dyn,

p p p pc

p w (21)

and cF as

1

Fdyn,

cp

(22)

with the wall shear stress τ. The pressure distribution from both RANS methods fit

quite well to the XFOIL predictions. The transitional SST-model predicts a slightly higher pressure level than the k-ω-SST model over the entire blade surface. In the blade tip region (above r/rtip = 0.85) both numerical models tend to predict a significant lower pressure compared to XFOIL. Note that the numerical calculation always contains tip effects which at r/rtip

= 0.97 are not negligible (see Fig. 8a), totally unknown to the XFOIL calculation.

0 0.25 0.5 0.75 1

-2

-1

0

1

a)

x/c [-]

r/rtip = 0.97

c p [-]

0 0.25 0.5 0.75 1

-2

-1

0

1

a)

x/c [-]

r/rtip = 0.97

c p [-]

0 0.25 0.5 0.75 1-5

0

5

10

15

20x 10

-3

c F [-]

x/c [-]

r/rtip = 0.97

b)

0 0.25 0.5 0.75 1-5

0

5

10

15

20x 10

-3

c F [-]

x/c [-]

r/rtip = 0.97

b)

Fig. 8: a) PRESSURE COEFFICIENT AND b) FRICTION

Data acquisition (fS: 1000 Hz)

Raw data (864.000 data points per day for each parameter)

Averaging time: 0.1 s

Calculate T (Pel, n)

Determine ceff (DIN 61400-12-1 [27])

Divide data into λ - bins

Select data at proper operating points

Select data at design point (n ± 1%, ceff ± 1%)

Averaging of all Cp-values → nominal CP at λ = 7.5


COEFFICIENT ON SUCTION SIDE AT r/rtip=0.97; SOLID LINE: k-ω-SST MODEL; DASHED LINE: TRANSITION SST MODEL; DOTTED LINE: XFOIL RESULTS ; THE ARROW

INDICATES TRANSITION The transitional process, which is taken into account by

XFOIL and therefore by our design code 'dWind', is characterized by the bends in the XFOIL pressure distribution. As expected, the k-ω-SST model does not show a comparable shape. However, even the transition SST model does not reveal the XFOIL predicted transition process. The wall shear stress coefficient shows the transitional process more clearly. Here the XFOIL predictions and the transition SST model correspond quite well, especially in the outer parts of the blade (Fig. 8 b)). Both numerical models yield near wall streamlines as well as wall shear distributions on the blade surfaces (not depicted here) that indicate widely attached flow.

Comparing the velocity flow field data in terms of the

induction factors, one has to keep in mind that the results are only comparable for spanwise positions r/rtip > 0.27 because of the root modification of the real blade. Nevertheless, the impact of these modifications seems to be apparent even above r/rtip = 0.27. The authors assume that the local increase of CP,BE up to r/rtip = 0.45 is due to these modifications. However, the impact is not quantified exactly. In the mid span region the agreement between the analytical and numerical data is quite satisfactory. While the k-ω-SST model predicts a slightly lower axial induction factor a, the transition SST model predicts a higher a with increasing radius compared to 'dWind'. In the tip region cm2 shows a sharp increase which leads to a decreased a and thus a decrease of CP,BE. This trend is consistent with the mentioned smaller surface pressure on the outer parts of the blade. The authors assume that this drop is due to tip effects which are taken into account by 'dWind' only by the global tip loss efficiency ηtip.

0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

r/rtip [-]

a [-

], a

' [-]

, C

P,B

E [

-]

CP,BE

a

a'

'dWind'

k--SSTtransition SST

0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

r/rtip [-]

a [-

], a

' [-]

, C

P,B

E [

-]

CP,BE

a

a'

Fig. 9: DESIGN AND NUMERICALLY OBTAINED

INDUCTION FACTORS AND LOCAL POWER COEFFICIENT The measured performance data of the turbine are

illustrated in Fig. 10 and Fig. 11. Fig. 10 shows the histogram after sorting the data in bins of the tip speed ratio λ. It is obvious that the turbine operates predominantly at a tip speed ratio of 7.5.

5 6 7 8 9 10 110

5

10

15

20

25

30

rel.

fre

quen

cy [

%]

[-] Fig. 10: HISTOGRAM OF THE λ BINS

Fig. 11 depicts the electrical power Pel as a function of the

generator voltage U, which in turn is proportional to the rotational speed of the turbine. The grey points represent all 0.1 s time averages, while the black points indicate data where the rotor speed and the effective wind speed are within ± 1% of the turbine's design values. Nevertheless, the scatter of Pel is rather large, probably due to highly unsteady wind speed and direction and hence dynamic effects. This must not be confused with the classical measurement uncertainty which is estimated as n = ± 1%, c = ± 1%, Pel = ± 1%, Pm = ± 3%. Following the law of propagation of uncertainty, this leads to a CP of approximately ± 5%. The set generator characteristic is the solid green line. The resulting value of Cp is 0.34. Note, that a dataset of more than 14 million measured values were available. 3.728 data points were inside the 1% range of the design point criteria, see Fig. 7.

A comparison of all performance parameters is shown in

Tab. 2. The agreement between the analytical and numerical results is quite satisfying, in particular with a view on the mentioned modifications in the blade hub and tip region. The already observed increase of the overall performance in case of a consideration of the transitional process e.g. reported by Johansen and Sørensen [12] or Laursen et al. [3], can be confirmed. Although the operating range matches the design tip speed ratio (λ = 7.5), the performance coefficient is considerably lower as compared to the analytically and numerically predicted values.


150 200 250 300 350 4000

400

800

1200

1600

U [V]

P el [

W]

Fig. 11: gray: RAW DATA POINTS, black: SELECTED DATA

AT DESIGN POINT (n ± 1%, ceff ± 1%), green line: GENERATOR CHARACTERISTIC CURVE

Tab. 2: PERFORMANCE PARAMETERS AT DESIGN POINT (λ = 7.5) (EXPERIMENTAL NUMBERS ARE NOMINAL)

CFD

'dWind' k-ω-SST Trans SST

Experimental

CP [-] 0.44 0.41 0.49 0.34 ± 5% Fax [N] 132 133 146 - T [Nm] 14.7 13.6 16.1 10.7 ± 2% Pm [W] 432 402 474 315 ± 3%

SUMMARY AND CONCLUSION Based on a modified blade element momentum theory a

modified analytical design method for horizontal axis wind turbine blades is developed. The airfoil performance predictor XFOIL has been fully integrated. With that a 3 m diameter turbine with three blades is designed. The code yields the geometry of the blades and the anticipated power coefficient at design operating conditions. The manufactured wind turbine is integrated in fully instrumented free field test rig providing wind speed and direction and turbine performance parameters such as rotational speed and power output. A statistical analysis method was applied to remove non-relevant data from long period data records.

The flow around the turbine was simulated with a RANS-method. Special attention was given on the effect of the turbulence model (either the standard k-ω-SST model or a transition SST model for turbulence transitional processes).

The agreement between the analytically and CFD predicted kinematic quantities up- and downstream of the rotor disc is quite satisfactory. However, the choice of the turbulence model affects the RANS-predicted power coefficient. The k-ω-SST model does not account for any transition; it assumes purely turbulent flow which is not adequate for the flow along this wind turbine blade. This explains the 'better' performance employing the transition SST model, which has also been reported by e.g. Laursen et al. [3].

As in any free field test it is a challenge to operate the turbine at the desired design tip speed ratio and a design Reynolds number. In the experiments reported this could be achieved well by carefully setting the generator characteristics in combination with a statistical data processing. Nevertheless, the experimentally determined power coefficient is considerably lower than anticipated. For a conclusive interpretation it would be beneficial to determine the entire performance characteristic curve of the turbine. Since design tip speed ratio more or less coalesces with the maximum power coefficient one could then identify the true design tip speed of the manufactured turbine which may deviate due to manufacturing inaccuracies. Complete performance characteristics can be obtained by varying the load on the turbine through a systematic adjustment of the characteristic curve of the generator. In the numerical set up, the boundary conditions would need a systematic variation.

In future measurement campaigns a sensor for the instantaneous azimuthal position of the turbine will be functional and allow excluding data obtained with oblique wind incidence. Given the fact that the turbine shaft power is related to the free stream velocity to the third power, this can be the so far neglected source of error. Possible changes of the generator calibration curve should be taken into account by regular checks. Furthermore, losses in some part of the electric system, not taken into account here, should be quantified and included.

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