O.OBm. 0.42 m. 8 (r/R) = (6° + S,;p) - 6.67 r/R, for 0.3 .s r/R .s 0.9. 0.06 m, no twist. The rotor axis with its bearings is placed in extension tube leaving 0.75 m free ...
MEASUREMENTS ON THE PROPERTIES OF THE TIP VORTEX OF A ROTOR MODEL
L.J. Vermeer
Delft University of Technology; THE NETHERLANDS
INTRODUCTION
Specifications of the model Radius: Number of blades: Aerofoil section: Root cutout: Chord: Blade length: Blade twist:
The performance of a wind turbine depends on many factors, such as aerofoil characteristics, blade geometry, terrain complexity and wind conditions. In the present research, attention is paid only to the rotor and its aerodynamics, thus leaving out influences which can't be tested on a rotor model in a wind tunnel. Only the main driving force of a wind turbine is left over to examine : the lift on the blade. The trailing vorticity from the lift force over the blade is left behind in the flow and creates the rotor wake, which in turn determines the inflow conditions in the rotor plane: lift force and wake structure have a mutual dependency.
Replaceable tip:
0.6m 2 NACA0012 0.18 m (30%)
O.OBm 0.42 m 8 (r/R) = (6 ° + S,;p) - 6.67 r/ R, for 0.3 .s r/R .s 0.9 0.06 m, no twist
The rotor axis with its bearings is placed in extension tube leaving 0.75 m free space behind the rotor plane.
Power and load prediction codes exist in a wide variety. Ranging from very global with presumed linearity of blade chord and twist to very detailed with a dense grid of vortex filaments. With the degree of detail and freedom, the computational time rises steeply. In the middle of the road lies the prescribed wake approach, which takes into account the trailing vortex sheet from the blade and the free vortex from the tip, but only in pre-described positions. The position of the vortex sheet and the tip vortex spiral determine the output of this approach. To supply the users of this method with some empirical data, a first series of wind tunnel experiments on a rotor model have been performed, in which several properties of the free tip vortex are determined.
Specifications of the test rig Hub height: Pitch angle: Axial force meter: Torque meter: Azimuth counter: Motor/generator:
2.33 m (=tunnel axis height) adjustable within 0.1 o by hand 50 N, between hub and first bearing, signal transmission by sliprings 10 Nm 1 and 720 pulses/revolution 1.5 kW, speed of revolutions adjustable from 0 to 16Hz
Instrumentation
The undisturbed tunnel wind velocity is measured with a Pilot tube connected to a Betz manometer. The Pilot tube is placed at a position representing the average velocity over the outlet area.
EQUIPMENT
Wind tunnel
The velocities in the wake are measured with constant temperature hot wire equipment. The cross wire probe has been calibrated before every measurement session, because of overnight temperature changes in the laboratory. The probe orientation is set with the plane of the wires parallel to the rotor plane.
The measurements have been performed in the open jet wind tunnel of. the Institute for Wind Energy. The specifications of this tunnel are described in earlier publications, e.g. Vermeer
(1).
The probe position is set by a traversing system. In radial direction, this can be done by computer, with an absolute error of 0.2 mm. In axial direction, the adjustment is done by hand; the absolute error is 2 mm (the exact position of the rotor plane is difficult to detect!), but with an incremental error of only 0.2
Model
The model has been specially designed for aerodynamic measurements in the wind tunnel, see figure 1. In the research, the emphasis is put on the rotor, which must therefor be well-defined and suitable to produce data for verification of numerical simulation programs. The aerofoil of the blades is not a common HAWT blade section, but it was chosen because of the availability of wind tunnel data over a wide Reynolds number range. The blades are manufactured on a i numerical milling machine to obtain the highest feasible form accuracy.
mm. A PC-based data acquisition system, with a dedicated measuring program, is used to measure and store all signals and related time and angle information. The max1mum sample frequency of the data acquisition card is 100 kHz, enough for 720 samples/ rev for 8 signals at 16 Hz rotor frequency.
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MEASUREMENTS
From the azimuthal position at which the tip vortex is detected and the rotational speed of the rotor, the elapsed time between rotor plane and hot wire can be reduced . Together with the axial position of the probe, a z-t plot for the tip vortex can be made. The slope of this curve is the axial transportation velocity of the tip vortex, see figure 4. Since this curve is straight over the who le measured range, the transportation ve locity of the tip vortex is constant.
Configurations and conditions
For the detailed velocity measuremer,ts, five different configurations have been considered: at tip-speed ratio A= 8: tip pitch angle Slip= 4, 2 and oo; at A= 6: Slip= 2 and oo. These configuration were chosen to match the conditions in previous measurement sessions , see Vermeer (1), so the total data set is coherent.
This transportation velocity can be compared with the azimuthal averaged velocity, which changes very gradually over the wake boundary, see figure 5. lt is often suggested that the tip vortex can be considered a roller bearing, travelling at the average speed of the flo w velocity inside and outside the wake. Now, both flow velocity and vortex speed are plotted in one graph, but the average flow ve locity at the radial position of the tip vortex and the vortex speed itself differ too much to hold this assumption.
During all the measurements the speed of revolutions was kept constant at f = 11.65 Hz, the tunne l velocity was adjusted, to approximately 5.5 and 7.3 m/s, to match the tip speed ratio of respectively A= 8 and 6. In this way the Reynolds number at the ti p is kept constant (Re = 240.000) for comparison. The zero azimuth angle of the rotor is chosen with blade 1 in vertical down position. The traversing system is set up to traverse horizontally at azimuth angle 90° . In this way, the vertical front wire is more sensitive for axial and radial components of the ve locity, the horizontal hind wire for axial and tangential components.
At a fixed axial position z!R=1 .0, the wake expansion is related to the total axial load on the rotor. Two references are consu lted for comparison with theoretical models: Wil son (2) and 0ye (3). Wilson developed a analytical approximation for the flow field of a rotor with a cylindrical vortex sheet wake from the actuator-disk theory. Th e exact function for the velocity along the axis is taken to be valid for the whole flow field . Initially, no expansion of the wake is taken into account, this is later introduced by applying the continuity equation. This approach might be too much simplified to make a valid comparison. 0ye considered an idealized turbine with an infinite number of blades, modelled as lifting lines with constant strength. The root vortices unite into one vortex, the tip vortices form a vortex
Data acquisition
In each of the five configurations, radial traverses with the hot wire probe have been made at 12 axial positions: z/R = 0.05, 0.1, 0.15, 0.2, 0.25, 0.35, 0.45, 0.55, 0.7, 0.85, 1.0 and 1.25. At each axial position, first the radial position at which the tip vortex core passes exactly through the hot wire was determined, by means of the specific hot wi re signal. From this radial position, two in ward (5 and 10 mm) and two outward (5 and 10 mm) positions were also set.
tube with expanding radius downstream. The vorticity on this tube is modelled by discrete vortex rings , wh ich radii are equal to their local wake radius. So, in this latter model the vortex rings are physically related to the measured occurrences of the vortices and therefor form an appropriate comparison with the measJrements. For this reason, the agreement is also better than for the very simplified model of Wilson, see figure 6. Yet, the whole concept of the wake as an expanding tube might be ready for revision. The wake radius seems clearly defined by the radial position of the tip vortex at the position of the tip vortex, but in between the successive revolutions of the vortex spiral, !herS) is no measure for the wake radius . The wake radius between the tip vortex occurrences supposedly is a kind of a compound sinusoidal form, depending on vortex strength, position in the wake and even rotor geometry. An indication for this can be found in Hasegawa and van Bussel (4), where results of detailed calculations show that the axial, circumferential and radial induced velocity distribution are not circle symmetric.
For each station in the traverses, velocity samples were taken of both wires every 4 o azimuth angle of the blades over 14 successive revolutions. For practical reasons the sampling rate is chosen lower than the maximum possible rate . In figure 2, a typical plot is given of the ve locity distribution over 1 revolution,
For each station in the traverses, velocity samples were taken of both wires every 4 o azimuth angle of the blades over 14 successive revolutions. For practical reasons the sampling rate is chosen lower than the maximum possible rate. In figure 2, a typical plot is given of the velocity distribution over 1 revolution, averaged per azimuth angle over the 14 revolutions, for the middle and two outer radial positions, showing the different influence of the passage of the tip vortex on the velocity at each of the positions. Because this model has been in use over some years now, the global properties of the rotor, Cp-A and C0 ax-A, are known for a range of configurations and conditions.
CONCLUSIONS
Practicable data relating the tip vortex from a rotor model operating in a wind tunnel can be obtained using hot wire anemometry. This data can be used to improve the modelling of output and load prediction codes, based on the prescribed wake approach. This calls for further investigations on this subject, with a wider range of parameters and, if possible, on different models.
RESULTS
From the recorded radial position of the tip vortex, the wake expansion versus axial position can be plotted as a function of ~he experiment parameters S,;p and A, see figure 3. In this plot, 1! can be seen that when the tip vortex "leaves" the tip, there is a slight, but distinct contraction of the radius at which the vortex travels.
The "roller bearing" assumption, which states that the tip vortex travels at the average flow velocity inside and outside the wake, does not seem to hold with the results from the present measurements.
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The theoretical representation of the wake expansion needs more than simple models. lt might even be needed to revise the concept of the wake as an expanding tube and introduce a more complex form.
ACKNOWLEDGEMENTS
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I would like to thank mr. Simon Toe! for his assistance and persistence during the measurements.
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REFERENCES
1. Vermeer, N-J., 1992, "Local circulation on rotating wind turbine blades from velocity measurements in the wake of a model rotor", Proc. of the Fourteenth BWEA ConferenceWind Energy Conversion 1992, Editor B.R. Clayton, London, Mechanical Engineering Publications, 117- 121.
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2. Wilson, R.E., 1986, "Wind turbine flow field model", Journal of Solar Energy Engineering, 108, 344-345.
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3. 0ye, S., 1989, "A simple vortex model", International Energy Agency, Proc. of the third symposium on the aerodynamics of wind turbines, Editor K.F. McAnulty, Harwell.
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135 180 225 270 315 360
Rotor azimuth angle(') 4. Hasegawa, Y., Bussel, G.J.W. van, "Modification of airfoil characteristics by the three dimensional potential flow of horizontal axis windturi:Jine rotors", Proc. of the Fourteenth BWEA Conference- Wind Energy Conversion 1992, Editor B.R. Clayton, London, Mechanical Engineering Publications, 67-72.
Figure 2.
Azimuthal velocity distribution at z/R
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The rotor model in the wind tu nnel.
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