17th Australasian Fluid Mechanics ConferenceAuckland, New Zealand5-9 December 2010

A Wind-Tunnel Investigation of the Wake Behind a Wind-Turbine in a TurbulentBoundary-Layer Flow

S. Cochard1 and D. Lander1

1Faculty of Engineering & ITThe University of Sydney, New South Wales 2006, Australia

Abstract

Wind-tunnel experiments were performed to study the lowerhalf of the near wake of a 86-cm diameter 4-bladed wind tur-bine model placed in a fully developed boundary layer. Stereo-PIV (Particle Image Velocimetry) was used to measure the threecomponents of the velocity on a vertical plane behind the tur-bine. In parallel to the stereo-PIV system, a Constant Tempera-ture Anemometer (CTA) system was used to record time seriesof the componentu of the velocity parallel to centreline of thewind-tunnel at different locations. This paper presents a com-parison of the mean velocity and its standard deviation of thelowest half of the boundary layer with and without the turbine.The mean velocity shows a large reduction of the componentu in the lowest part of the wake in response to the non-uniformincoming boundary layer, while the deficit is close to zero attheheight of the hub. The deficit of the standard deviation of thevelocity increases at mid-turbine radius while staying constanteverywhere else.

Introduction

Today the best wind-turbines have an efficiency of 45% [6]while the maximum theoretical efficiency, given by the Betznumber, is 59.3% [2]. Reasons for not achieving this theoret-ical value can be found in the turbulent, fully 3-dimensional,and due to the nature of the boundary layer, unsteady and non-symmetric flow which take places in the wake of the turbine [7],[3].

To improve our understanding of the turbulent field around andbehind wind turbines in different boundary layers, we proposeto map the velocity field of the turbine wake using a stereo-PIVsystem. This paper presents our setup as well as our first stereo-PIV results for one boundary layer at one location. The intentof testing the wind-turbine in different boundary layers isnotto mimic a particular set of atmospheric boundary layers con-ditions but to understand how the asymmetry of the incomingflow affect its wake. The same can be said for the wind-turbine;for an adequate assessment of a model in a wind tunnel environ-ment, it must possess a geometrical as well as a kinematic anddynamic similarity to the eventual full scale design, whichisimpossible to achieve in a low speed wind tunnel. Therefore thewind turbine used is not a model of an existing full-scale pro-totype but one specially design to give maximum performancewithin the range of wind-speeds produced by our wind-tunnel.

The model tested in the boundary layer wind tunnel of theSchool of Civil Engineering at the University of Sydney wasa 86-cm diameter 4-bladed wind turbine. The tunnel wasequipped with a Stereo-PIV and a CTA (or hot-wire) system tomeasure the velocity of the lowest half of the near wake. Work-ing with a CTA and a PIV has the advantage of combining thetemporal resolution of the CTA and the spatial resolution ofthePIV.

Experiments

Wind-Tunnel

The open circuit boundary layer wind tunnel has a test section of2.0 x 2.4 m and a fetch of 20 metres. The fetch can be equippedwith variable levels of roughness to produce different boundarylayer profiles with specific turbulence characteristics. The max-imum wind speed in the boundary layer section is of the orderof 16 m/s.

An arbitrary co-ordinate system was used throughout the test;the x-axis being the turbine axis, they-axis is the height andthez-axis is the width, while the origin is at the blade centre ofrotation (figures 1 and 2).

Blade(350mm)

Hub(106mm)

Blade(350mm)

0.5 rt

625mm

rt(403mm)

rt(403mm)

625mm

PIV Window

0.5 rt

y

z

Figure 1: Front view of the wind turbine in the wind tunnel

Hotwire

measurements

200mm

0.5 rt

350mm

500mm

400mm

PIV window

200mm

30mm

y

x

Hotwire

measurements

Flow Direction

Figure 2: Side view of the wind turbine in the wind tunnel

The position and size of the wind turbine as well as the posi-tion of the hot-wires and the PIV acquisition window are givenin figures 1 and 2. The hot-wires were fixed on a vertical mastpositioned atz = 625 mm, midway between the wind turbinehub and the tunnel wall during a PIV recording. Five hot-wires recorded the velocity 200 mm upstream of the actuatorat heights: 0· rt (hub),±0.5 · rt and±1.0 · rt , wherert is theradius of the turbine. The lowest point of the actuator disk istherefore at a distance 0.5· rt from the tunnel floor. It should benoted that the turbine rotates anti-clockwise.

Figure 3: Rear picture of the wind turbine within the boundarylayer wind tunnel. The CTA is on the left of the turbine.

Wind-Turbine

The wind-turbine was specifically designed as a research modeland was not intended to mimic a full scale prototype. The modelwas composed of 6 separate components:

• the blades had a length of 350 mm and a chord of 48 mmwith a NACA 0020 profile. They were cut in high densityfoam and could be twisted up to 60◦.

• the docks, which connected the blades to the hub, were40-mm-diameter cylinders. The docks could easily be re-moved from the hub to set the pitch angle of both the baseand the tip of the blades and, by doing so, defining thetwist. During this test, the pitch angle was set to 45◦ at thehub and 90◦ at the tip of the blades.

• the hub (106 mm in diameter) was directly connected tothe torque and position sensor. Two different hubs werebuilt, with 3 and 4 connection docks to test turbines with1, 2, 3 or 4 blades. In this paper only the 4 blades config-uration is presented.

• the rotary torque and angular position sensor measuredthe angular velocity and torque at the shaft of the wind-turbine. The torque and angular sensor was positioned be-tween two 30 mm bearings.

• the brass fly wheel increased the inertia of the model andthereby provided greater stability to the angular velocity.

• the friction break applied a torque directly to the fly wheel.

The torque and angular position sensor measured the angularvelocity and torque imposed on the shaft of the turbine so thepower output could be computed. The power of the wind-turbine could therefore be measured rapidly for different break-ing forces and angular velocities. Only the results for the de-signed point of operation, giving the maximum power, are pre-sented in this paper.

The position sensor was also used to trigger the PIV system.As Microsoft Windows is not a real-time operating system, thelaser was triggered directly by the acquisition card at an internalfrequency of 20 MHz. A set of PIV images could therefore becaptured within 50 micro-degrees of the blade’s angular posi-tion. Each image was taken with an increment of 3◦ from thepreceding image to cover all the range of angles from 0 to 90◦

to equally weight the angular position of each blade. Duringthis test 180 images were taken and averaged.

CTA

The CTA was composed of a controller, 5 hot-wire velocityprobes, 1 temperature probe and 1 reference probe. The 5 hot-wires were calibrated against the reference probe (54T29 fromDantec) for which the voltage-velocity relationship was wellknown. The temperature probe was used during both the cali-bration process and during normal tests to correct the computedvelocity as a function of the temperature variations.

The CTA was used to:

• measure the temporal incoming boundary layer conditionsat 5 heights ahead of the turbine (see figure 2) during a PIVtest.

• measure the velocity deficit∆u at 12 discrete points be-hind the wind turbine in the same plane as the PIV (seefigures 1 and 2).

Stereo-PIV

PIV is a non-penetrative technique of extracting the two com-ponents of the velocity from a desired planar flow region (seeFigure 4) [4]. A laser pulse lights a plane section of the flowand highlights particle tracers while a camera records their po-sition. A second laser pulse illuminates, a short time later(∆t= 100 µs), the same section of the flow. Two components ofthe velocity fields can be retrieved from the position differenceof the particles in the plane of the laser sheet. To measure thethree components of the velocity, two cameras take images ofthe laser sheet from different angles. The two images combinedtogether give the three components of the velocity [5].

Particle images

Correlation

Image frame from pulse 1

Image frame 2

I1

I2

∆x

X

Z

Target area

Y

Cylindrical lens

Flow with seeding particles

Imaging optics

CCD

dA

Interrogation area

∆t

Double- pulse laser

∆t

Figure 4: Principle of a PIV system (adapted from Dantec PIVposter)

Our stereo-PIV system was composed of a double head 400 mJ-per-pulse laser and 2 x 11 MPx cameras. This setup enabled usto measure the velocity field in a plane of 0.4 x 0.5 m. The ac-quisition frequency of the PIV system was 0.5 Hz as the pictureswere recorded directly on the hard disc.

Olive oil particles, with a mean diameter of 6µm, were used toseed the flow [1].

Wake characteristic

The velocityuhub measured by the CTA at hub height, withand without the turbine, were, respectively, 8.91±1.46 m/s and

9.01±1.38 m/s. The torque measured on the turbine axis was0.36± 0.1 Nm and the hub rotational velocity was 10.0± 0.7rps, resulting in an average power output and a tip speed ratio,of 22 W and 2.8 respectively

The mean velocity field, recorded by the PIV system, is pre-sented for the boundary layer with and without the turbine infigures 5 and 6 respectively.

x [mm]

y[m

m]

uwt [m/s]

400 500 600 700 800−350

−300

−250

−200

−150

−100

−50

0

4

4.5

5

5.5

6

6.5

7

7.5

8

Figure 5: Mean velocity field ¯uwt of the wind turbine wake

x [mm]

y[m

m]

ubl [m/s]

400 500 600 700 800−350

−300

−250

−200

−150

−100

−50

0

4

4.5

5

5.5

6

6.5

7

7.5

8

Figure 6: Mean velocity field ¯ubl of the boundary layer withoutthe wind turbine

The mean velocity deficit∆u= uwt− ubl highlights the presenceof the turbine wake by removing the average velocity field of theboundary layer ¯ubl from the turbine wake ¯uwt. Figure 7 shows aincrease of the absolute velocity deficit|∆u| from the hub level(y= 0) where the deficit is almost zero to the lowest part of thewindow where the deficit is larger than -2 m/s. The velocitydeficit ∆u remains constant along thex-axis .

The u-velocity component was also measured, using the CTA,in the same plane as the PIV window (z= 0.5· rt ), for 3 heights;y = 0 mm (hub), -200 mm and -400 mm as well as for 4 dis-tances behind the turbine; x = 300 mm, 500 mm, 700 mm and900 mm with and without the wind turbine. The mean velocitydeficit is presented in figure 8 in a similar manner to figure 7to facilitate comparison. The velocity deficit field∆u measuredby the CTA shows an increase of the deficit from the hub heightto the lower part of the actuator disk similarly to the velocitydeficit field measured by the PIV. The absolute value of the ve-locity deficit given by the CTA should be read with care as hotwires record principally the perpendicular component of the ve-locity, in our caseu andv as the wires were positioned horizon-tally.

x [mm]

y[m

m]

∆u [m/s]

400 500 600 700 800−350

−300

−250

−200

−150

−100

−50

0

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

Figure 7: Mean velocity deficit∆u measured by the PIV system

x [mm]

y[m

m]

∆u [m/s]

300 500 700 900

0

−200

−400

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

Figure 8: Mean velocity deficit∆u measured by the CTA system

The mean deficit velocity fields∆v and∆w are shown, respec-tively, in figure 9 and figure 10. As expected, the clockwisewake rotation is visible as∆v decreases iny. Similarly ∆w de-creases withy. The magnitude of∆v and of∆w are in the orderof 1 m/s in the PIV window. The velocity deficit component∆vdecreases with increasing value ofx while ∆w stays constant.It should be noted that the deficits∆v and∆w are equal to themean velocities ¯vwt andwwt as vbl = wbl = 0 and are not pre-sented here. The deficits∆v and∆w are nevertheless presentedhere, instead of the mean velocities ¯vwt andwwt, to ensure thatany misalignment of the laser plane is corrected.

x [mm]

y[m

m]

∆v [m/s]

400 500 600 700 800−350

−300

−250

−200

−150

−100

−50

0

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Figure 9: Mean velocity deficit∆v measured by the PIV system

Figures 11, 12 and 13 present the deficit in velocity standarddeviation, respectively, in thex, y andz-direction. The deficit in

x [mm]

y[m

m]

∆w [m/s]

400 500 600 700 800−350

−300

−250

−200

−150

−100

−50

0

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Figure 10: Mean velocity deficit∆w measured by the PIV sys-tem

velocity standard deviation∆σu increases fromy = −150 mmto−250mm while the remainder of the field is almost constant.In contrast, both the deficits in velocity standard deviation ∆σvand∆σw increase with the presence of the turbine, especially inthe lowest part of the recorded wake.

x [mm]

y[m

m]

∆σu [m/s]

400 500 600 700 800−350

−300

−250

−200

−150

−100

−50

0

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Figure 11: Deficit in velocity standard deviation∆σu

Discussion

This paper presents the first stereo-PIV results obtained withour setup and demonstrates the feasibility to measure the 3-components of the velocity in the near wake of a wind turbine inthe Boundary Layer Wind Tunnel of the University of Sydney.

The results for lowest part of the near wake shows, as expected,a rotation of the wake in the opposite direction to that of theblades and a decrease of the velocity componentu. The velocitydeficit ∆u decreases from the hub level to the lowest part ofthe wake while the standard deviation of the velocity deficitσuincreases from the hub to mid-blade and then decreases to thetip of the blade.

Future work

As the feasibility to measure the velocity in the near wake ofawind turbine has been demonstrated, the next step is to measurethe full wake, from the hub to 8 diameters downstream of theturbine, at differentz-positions, for the lowest and upper part ofthe wake, for different wind speed and boundary layer profiles,and for different wind turbines.

x [mm]

y[m

m]

∆σv [m/s]

400 500 600 700 800−350

−300

−250

−200

−150

−100

−50

0

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Figure 12: Deficit in velocity standard deviation∆σv

x [mm]

y[m

m]

∆σw [m/s]

400 500 600 700 800−350

−300

−250

−200

−150

−100

−50

0

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Figure 13: Deficit in velocity standard deviation∆σw

References

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[6] Robinson, M., The darrieus wind turbine for electricalpower generation,Aeronaut. J., 85, 1981, 244–255.

[7] Vermeer, L., Sorensenb, J. and Crespo, A., Wind turbinewake aerodynamics,Progress in Aerospace Sciences, 39,2003, 467–510.