Feb 22, 1989 - mum at z/Ro = 0 and y/Ro = +1 but it is missing because of lack of measurements. Note that z/Ro = 0 implies the wind turbine's hub height and ...
Solar & Wind Technoloyy Vol. 7, No. 2/3, pp. 177-184, 1990 Printed in Great Britain.
0741-983X/90 $3.00+.00 Pergamon Press pie
WAKE MEASUREMENTS BEHIND A H O R I Z O N T A L - A X I S 50 kW W I N D T U R B I N E H . D . KAMBEZIDIS Institute of Meteorology and Physics of the Atmospheric Environment, National Observatory of Athens, P.O. Box 20048, 118 10 Athens, Greece and D . N . ASIMAKOPOULOS a n d C. G . HELMIS Laboratory of Meteorology, Department of Applied Physics, University of Athens, 33 Ippokratous Str., 106 80 Athens, Greece (Received 22 February 1989 ; accepted 26 April 1989) Abstract--This paper presents some results on the wake of a full-scale 50 kW wind turbine located in N/isudden peninsula, Gotland Island, Sweden. It is found that the wind velocity deficit, A~, and turbulence intensity, au/~, take greater values at the centre of the wake than its boundaries. Also the temperature structure parameter, C 2, takes higher values at the centre of the wake than its edges. A 2-D au/~ plot shows two maxima (the third is missing because of lack of measurements) and a minimum at the expected positions in the wake. The u-component power spectra levels seem to be higher at the high frequencies around the central parts of the wake while at its boundaries they are higher at the lower frequency portion of the spectrum. All results agree with theory and other experimental findings.
INTRODUCTION Theoretical and experimental research on the wake of wind turbines is relatively recent. The first approach to the problem of W E C S interference may be that of Templin [1] who theoretically modelled the interferences of an "infinite" wind park. Later Lissaman [2] constructed a simplified 2-D model of a wind turbine wake based on air momentum conservation within it and the interaction between atmospheric and mechanical turbulence. At the time of Lissaman's report no experimental data from wind turbine wakes were available. At the end of the 1970s, however, the first wind tunnel simulation studies appeared in Holland (TNO, Apeldoorn), Sweden (The Aeoronautical Institution of Sweden, Stockholm) and soon after in U.K. (CERL, Leatherhead). Vermeulen [3] summarized all available laboratory data to that moment and suggested some modifications to the original Lissaman's W I N D S model renamed afterwards to M I L L Y . The most important modification was the introduction of the term of mechanical turbulence generated by the blades and the tower. Lately a 3-D wake model appeared [4] based on Lissaman's [2] and Taylor's [5] models. Lissaman [6] has also presented a new version of his W I N D S for hilly terrain named AVENU. F r o m 1980 onwards data from wind tunnels started
to appear; nevertheless, measurements on full-scale wind turbines are still rare. Vermeulen et al. [7] found from an experiment with a vertical-axis 5 m diameter machine that at 25 m downstream, the kinetic energy is 75% of its undisturbed value; they claim that the intense turbulence near the ground is responsible for this phenomenon. Taylor [8] gives some results on the meandering effect of a horizontal-axis 17 m rotor diameter machine. Swift-Hook et al. [9] present some results from the N I B E project in D e n m a r k where the measurements of two horizontal-axis 40 m wind turbines were taken by anemometers installed on four towers situated around each machine every time. Baker and Walker [10] present experimental results on the wake of a horizontal-axis 91 m 2.5 M W wind generator in U.S.A. They find that at a distance 9D downstream, the wind velocity deficit is 15-18% of its undisturbed value under stable conditions, while the deficit decreases to 10% or less under unstable atmospheric conditions. The utilizability of this data is still in question because of the irregularity of the terrain at the W E C S site. Haines et al. [11] published some results on the wind velocity deficit downstream for two wind turbines with 20 m rotor diameters. Recently H6gstr6m et al. [12] presented experimental results on a full-scale 77 m 2.2 M W horizontal-axis wind turbine in Sweden. Apart from the wind velocity deft177
178
H. D. KAMBEZIDISet
cit and turbulence intensity measurements at a distance 2D downstream, they also give results about C 2 levels, u-component power spectra levels and temperature fluctuations in the wake. This paper deals with some wake effects of a full-scale 50 kW 15 m horizontal-axis wind turbine in Nfisudden peninsula, Gotland Island, Sweden. EXPERIMENTAL DETAILS A map of the experimental site is shown in Fig. 1. The position of the 50 kW V E S T A S horizontal-axis wind turbine as well as the 145 m instrumented meteorological tower arc also shown. As seen from the figure, the terrain is extremely fiat with a slope of 5%o downwards! The ground is partly cultivated and partly swampy with scattered bushes of 1-2 m height. At remote places there are some dense pine trees which produce no effect on the turbine's wake. The wind turbine has three blades with a rotor diameter of 15.4 m, a hub height of 23.5 m above the ground and rated power output of 50 kW in the wind speed range ! 3-30 m s ~; the cut-in wind speed is 3 m s 1. The manufacturer gives a mean power coefficient cp ~ 0.4. The experiments about this wind turbine were part of the N I B W A K ' 8 4 (Nfisudden Internal Boundary and Wake) project concerning mainly measurements of the wake characteristics of a 2.2 M W wind turbine
al.
situated 300 m away from the 50 kW one in Nfisudden. For the present work two research groups participated : the Meteorological Institute, Uppsala University, which operated the meteorological tower and the Department of Applied Physics, University of Athens, which performed the probing of the wake with a set of three acoustic sounders ; the sodars were constructed by the University of Athens group and were used because of their flexibility. Comparisons between the acoustic sounders and the meteorological tower showed a _+0.1~).2 m s 1 compatibility as far as the mean wind speed is concerned and +0.1 in the case of longitudinal turbulence intensity. A triple monostatic "umbrella" type configuration of the sodars was used in the experiments (see Fig. 2). In this configuration all three sodars were placed at equal distances downstream of the wind turbine in a nonvertical direction. In this mode the operation of an acoustic sounder is capable of giving the horizontal wind component at various heights above ground the direction of which in the case of a wake coincides with its mean axis. Thus the "umbrella" configuration was able to give a cross-section of the wake characteristics at a certain distance downstream having, of course, been corrected for the tilt of the antennas and the small deviations of the wind direction which were observed during the experiments. Table 1 gives the details of the experiments with the sodars and the 50 kW wind turbine. All five experiments were of a duration of I hour approximately and took place under unstable atmospheric conditions. As seen from the table the mean wind speed at 26 m varied in the range 5.3-8.2 m s I thus giving a tipspeed-ratio, 2 V r / l ~ , V r "~ 26 m s-~ being the tip speed, in the range 4.9-7.6. Figure 3 shows the location of the sodars during the experiments and the prevailing wind directions. All sodar outputs rep=
WIND
.'-
!,,, ,j/ iikkT!'!i0. Fig. 1. Map of Nisudden peninsula showing location of the 50 kW (WI), 2.2 MW (W2) and 145 m meteorological tower
(T).
Fig. 2. The 3-monostatic "umbrella" configuration of the sodars.
179
Wake measurements behind a horizontal-axis wind turbine Table 1. Some basic information about the wake experiments. The wind speed ~i® refers to conditions out of the wake at 26 m height on 145 m tower. The meteorological conditions were deduced from potential temperature profiles at the tower. LST stands for Local Summer Time Experiment
Date
Time LST
Sodar configuration
Meteor/cal conditions
li~ (In s 1)
3-monostatic "umbrella" type 1347 1430 3-monostatic "umbrella" type 1452 1550 3-monostatic "umbrella" type
unstable
8.2
unstable
8.0
unstable
6,8
1226-1254
unstable
5.3
unstable
5.7
17.8.84 la
1245-1345
lb lc 18.8.84 2a 2b
3-monostatic "umbrella" type 1258 1328 3-monostatic "umbrella" type
resent wake conditions except sodar II of exp. 2 which was out of the wake at the time. Sodar I in the same experiment was placed vertically. The sodars were tilted away from the turbine to deduct additional data and avoid selection of acoustic noise which is created
primarily by the blades and secondarily by the shear of the wind. A more detailed description of a sodar as well as its capabilities is given by Brown and Hall [13], Cole et al. [4] and Asimakopoulos et al. [15, 16]. The pulse repetition frequency (prf) of the sodars during the experiments was 1 Hz and their echoes were recorded on magnetic tapes for off-line processing. A filtering effect during the data analysis process rejected all echoes with signal-to-noise ratio below a predetermined value. Special software was made for the analysis of the data while all programmes ran on the University of Athens main frame computer system.
BASIC THEORETICAL ASPECTS This section quotes briefly all necessary theoretical points used in this study. The wind velocity deficit in the far-wake region, where all sodars laid, is given by [17]: (Aff/fto~)r = (A5/5o~)o[1--(r/R)"s]:
caL
(1)
at a distance r from the centre line where the wake radius is R ; ti~ is the mean upwind air velocity. Equation (1) contains the distance x / D from the wind turbine; according to Vermeulen [17] in the presence of a lower boundary to the turbine (i.e. the ground) :
( Aa/a~)o o~ (x/ D )- '.
Fig. 3. Location of the three sodars during the experiments with the 50 kW wind turbine. Mean wind directions have also been drawn.
F r o m eq. (1) it is found that Aft is greater at hub height (r = 0) and smaller at the edges of the wake (r = R) which consequently implies that ff becomes minimum at hub height and maximum at the tips of the blades. It is also found (e.g. Abramovich [18] that :
180
H. D. KAMBEZIDISet al. (2)
(ffu/U)rOQ(a)r
which gives maximum values of a.l~ at the tips of the blades and m i n i m u m at hub height. For isotropic atmospheric conditions and flat terrain, Cv2 is given by [19] :
C-~ = 4/3kz/3('F/g)Q4/3z
4/3
(3)
with T = c o n s t , Q0 = const and k = 0.4, eq. (3) can be written as : (4)
CT2 = AZ 4/3
where A = 4/3k2/3(T/y)Q4/3 = const. For isotropic atmospheric conditions, homogeneous terrain and assuming inertial subrange, Kaimal et al. [20] found :
(1) Wind speedprofiles, Figures 4 and 5 show the mean wind velocities at various positions of crosswind in the wake for experiments la and 2a respectively. In Fig. 5 only two sodar profiles are shown because the third was placed vertically and was not therefore able to give ti profiles. Also shown are the wind profiles from the tower for reference. In the case of experiment la (Fig. 4) the greatest wind velocity deficit is exhibited by sodar III and the least by sodar II. This is so because sodar III, as seen in Fig. 3, is on the central line of the wake while I and II are at a distance from, but still in, the wake. For two distances r I and r2 from the centre line with r~ > r2 it is found from eq. (1) that (Aff/ti~)rl < (Ati/lL~)r2. Similar results were obtained 140,
F.(K,) = 0.25C~KC ~..3
(5)
9
13 Sodor I
t30
\
• Soclar TT 0 S o d o r T~
t2O
• 145m
tower
ItO
and
lOCI
8o
9O
CZv = 13.6f S . ( f ) ( f / t i ) a/3.
(6)
By applying Taylor's hypothesis (e.g. Lumley and Panofsky [21]):
~/ I"~
60 50 40
Fu(gl)Ki = S u ( f ) f
30
and taking into account (5) and (6) it is found :
2O I0
Su(f) = 0 . 0 7 4 C ~ 2 / 3 f
5/3
(7)
I
6.0
6.5
7D
7,5
Wind speed
which shows that: Su(f) oc f - 5/3
(8)
8.5
9.0
J
9.5
(ms -I)
Fig. 4. Wind speed profiles of the sodars and the tower for experiment la.
i.e. in a log-log presentation the power spectral estimates must follow the - 5/3 law.
/
'4°1 130
• Sodar
12C
0 Sodorm"
• t 4 5 m tower
tiC
RESULTS In this section, results of wind speed, longitudinal turbulence intensity and temperature structure parameter profiles as well as the u-component spectra levels of the 50 kW turbine wake are presented at a distance 2D downstream. Because of the similar atmospheric conditions (see Table 1) a selection of representative profiles is given. This selection concerns experiments la and 2a for the three first parameters and lc for the spectra. In the case of wind speed and turbulence intensity the corresponding profiles from the tower have also been drawn for reference to undisturbed conditions.
8.0
lOC 90 80
r:
70 60 50 40 30 2O I0
o
2.5
I
3.0
I
3,5
I
4.0
Wind speed
4.5
5.0
5.5
I
6.0
( m s -p)
Fig. 5. As in Fig. 4 but for experiment 2a.
I 65
181
Wake measurements behind a horizontal-axis wind turbine during experiment 2a where sodar II is considered to monitor outside the wake and therefore its estimates are compared well with the tower profile (see Fig. 5). These results are in agreement with previously published work [3, 17, 22, 23] in wind tunnel simulations and [9, 10, 12] at in situ measurements. (2) Longitudinal turbulence intensity, au/a Figures 6 and 7 show a,/g profiles in the wake which correspond to Figs 3 and 4, respectively. They indicate that significantly higher turbulence intensity values can be obtained at the edges of the wake and lower ones at hub height. Also tru/ti levels are higher near the centre line and lower away from it. The first point
130
• Sodar cr
120
0 Sodar m • 145m t o w e r
lie 1
80 L_
~
i
60
"£. 'iF 0.04
,
0.06
,
0.08
,
0.1
Longitudinal
,
0.12
,-,-, 0.16
0.14
turbulence
0.18
intensity
,
is justified by eq. (2) ; wherever ti is maximum (at the tips of the blades) tr,/ft shows also a maximum, and wherever m i n i m u m (at hub height) a,/ff is also minimum. The second point is verified by the supposition of the mechanical turbulence generated by the shear in the wake. This type of turbulence was introduced by Vermeulen [3] and plays an important role even at the beginning of the far-wake region as has also been pointed out by Abramovich [18]. H r g s t r r m et al. [12] found similar conclusions for a big wind turbine. Figure 8 shows a 2-D picture of tr,/ti in the wake of the turbine at a distance 2D downstream. The x axis coinciding with the centre line of the wake comes out of the picture at location m. The data from all five experiments have been used for the calculation of a mean value of a,/g at the position of each sodar and for various heights in the wake. The result is what is expected from eq. (2). Two maxima ( M = 0.26) and one m i n i m u m (m = 0.17) are indicated. The locations of the maxima are at z/Ro=___l and y / R o = - - I approximately, i.e. where the tips of the blades are. The location of the m i n i m u m is found at z/Ro = 0 and y/Ro = O. Another maximum corresponding to the third blade should be found to the right of the minim u m at z/Ro = 0 and y/Ro = + 1 but it is missing because of lack of measurements. Note that z/Ro = 0 implies the wind turbine's hub height and y/Ro = 0 the location of a,t~ minimum, m.
-I 5
, ,
-I 0
-0.5
0
0 2 0.22 0.23 (%)
Fig. 6. Longitudinal turbulence intensity profiles of the sodars and the tower for experiment la.
140 o 130
120
k \
• Sodar U 0 Sodar TIT • 145m t o w e r
IIC
0.5
Z/RQ 0
100 90 -0.5
-I 0
-2.0
'iF
O.C~ 0.08 0.1
0.12 0.14 0.16 0.18
Longitudinal
turbulence
0.2
I I
y/Ro
0.22 0 . 2 4 0 2 6 0.27
intensity (%)
Fig. 7. As in Fig. 6 but for experiment 2a.
Fig. 8. A cross-section of the longitudinal turbulence intensity pattern at a distance 2D downstream. M = 0.26 and m = 0.17.
182
H. D. KAMBEZIDISet al.
No perfect axial symmetry of the wake in terms of its y axis is seen; this is depicted clearly in Fig. 8. Similar behaviour is also reported by H6gstr6m et al. [12] on the 2.2 MW wind turbine. One reason attributing to this phenomenon is possibly the rotation of the wake about its x-axis which has also been observed by Alfredson and Dahlberg [24] in wind tunnel experiments. The rotation is caused by a torque which is transferred to the wake from the air stream. The vorticity (rotation) of the 50 kW turbine was not measured but it is believed that it must be smaller than Alfredson and Dahlberg's model ; this is so because of the bigger size of the wake of the turbine and the smaller flexibility than those of the model. Nevertheless, Taylor [8] and Baker and Walker [10] find normal ~o/~ patterns with a maximum around the main wake axis at different distances downstream, i.e. 1D and 2.5D in Taylor's case and 3D, 5D and 7D in Baker and Walker's. The cause for this discrepancy between our and H6gstr6m et al.'s results on the one hand and Taylor's and Baker and Walker's on the other is not yet apparent ; construction details related to the characteristics of the blades and/or operational conditions of the turbines are possibly responsible for this. (3) Temperature structure parameter, C~ The same logic with cr,/g seems to be followed by Cvz. Figure 9 shows Cv2 for experiment l a. Near the centre line of the wake, C~ levels are higher than at its edges. It is apparent that the shear in the wake deduces higher cr,/~ values at the centre line of the wake, as
already explained, and this in turn gives rise to higher temperature fluctuations in the central region of the wake which is depicted by higher CT2 levels. Similar findings were reported by H6gstr6m et al. [12] for the 2.2 MW wind turbine in Nfisudden. As seen from Fig. 9 Cv2 follows - 4 / 3 law with height well during experiment la; this may be attributed to the local isotropic conditions existing in the wake, in accordance with eq. (4). (4) u-component power spectra, Su Figure 10 shows u-component power spectra levels at three heights within the wake from sodar III during experiment lc. The - 5/3 law line has also been drawn for reference to local isotropic conditions according to eq. (8). Though the inertial subrange is not exhibited clearly because of the low prf of the sodars, it is intuitive that the - 5/3 law is followed ; local isotropic conditions therefore existed in the wake during the experiment lc too. If the whole spectrum is split arbitrarily into a high frequency portion and a low frequency one at the point of 0.01 Hz, it is seen that spectra levels at hub height ( ~ 25 m) are a bit higher than those at 15 or 35 m corresponding to the tips of the blades. In the lower portion of the spectrum the opposite occurs; spectra levels at 25 m exhibit relatively lower values than at the other two heights. This is in agreement with H6gstr6m's findings [12] for the 2.2 MW wind turbine and is attributed to the mechanical turbulence produced by the turbine itself being greater at the central region of the wake. According to the above a wind turbine may be thought as a high-pass filter for the atmospheric eddies and
IE+2
IE+2
-
g'~•
-5/3
T
IE+I
v IE+O
IE+I
Q•
•
-6 g ~Oo Soclar T • Sodar 11" o Sodar rrr
iE.c ~-2
o 15rn • 25rn o 35rn
3
I
I
IE-I Temperature
IE-I
IE~-O structure
J
4E+O
p o r o r n e t e r (°C2m-2/3)
Fig. 9. Temperature structure parameter profiles from the sounders for experiment la.
IE-2
rE-4
q
IE-3
I
IE-2
[
IE-I
I
IE+O
Frequency(Hz)
Fig. 10. Power spectral densities at various heights in the wake from sodar III for experiment lc.
Wake measurements behind a horizontal-axis wind turbine therefore small-sized eddies are likely to exist in the wake. In this way the wind turbine m a y be considered as a black box which accelerates the physical evolution o f the a t m o s p h e r i c eddies. CONCLUSIONS In this study it was s h o w n t h a t the acoustic sounder is a versatile a n d powerful tool t h a t gives accurate m e a s u r e m e n t s of the wake characteristics even for medium-sized wind turbines. F r o m the analysis o f the experimental d a t a the following results were deduced. The wind speed a n d turbulence intensity profiles follow the expected theoretical behaviour at any single location in the wake a n d agree with experimental results o f o t h e r workers' wind tunnel or full-scale measurements, t h a t is, m i n i m u m values at h u b height a n d m a x i m u m at the ends o f the blades. A t various locations the s o d a r being closer to the centre line o f the wake gave greater wind velocity deficits a n d turbulence intensities t h a n the o t h e r sodars situated at further distances from the m a i n axis. T h e t e m p e r a t u r e structure profiles showed higher C~ values at the central parts o f the wake r a t h e r t h a n its boundaries. O n some occasions C~ followed the - 4 / 3 law with height implying the existence of local isotropic conditions in the wake. There was f o u n d a close relationship in the variation between a J 5 a n d CT2 profiles with location within the wake. This was attributed to a m e c h a n i s m which produces higher t e m p e r a t u r e fluctuations in the x z plane in the wake where au/5 levels are also bigger. A 2-D picture o f ~ru/5 at a distance o f 2D d o w n s t r e a m showed n o complete axial symmetry a b o u t the y-axis of the wake in agreement with H 6 g s t r 6 m et al. [12] ; it also showed two m a x i m a at locations z / R o = +_ 1 a n d y / R o = - 1 a n d a m i n i m u m at location z / R o = 0 a n d y / R o = 0 as should be expected. Besides this normal result Taylor [8] a n d Baker a n d W a l k e r [10] f o u n d one m a x i m u m only a r o u n d the x-axis o f the wake. This discrepancy between o u r a n d their results is n o t yet apparent. It seems t h a t a e r o d y n a m i c details o f the blades a n d / o r o p e r a t i o n a l conditions of the t u r b i n e are responsible for this. F r o m u - c o m p o n e n t p o w e r spectra levels the following conclusions were d r a w n : (i) the spectra levels are greater at the high frequency p o r t i o n o f the spect r u m t h a n the low one at the same height a b o v e g r o u n d if the sampling p o i n t is closer to the x z plane ; this implies i n t r o d u c t i o n o f high frequency turbulence by the t u r b i n e itself; a n d (ii) spectra levels are higher at h u b height a n d in the high frequency end of the spectrum t h a n at o t h e r heights in the wake where
183
spectra levels are f o u n d to be higher in the low frequency p o r t i o n o f the spectrum. The latter is also caused by the mechanical turbulence o f the turbine. O n several occasions the u spectra followed the - 5/3 law implying local isotropic conditions in the wake. A wind turbine m a y be t h o u g h t as a high-pass filter for the a t m o s p h e r i c eddies according to the above. Acknowledgements--The authors express their gratitude to
Prof. U. H6gstr6m who organized the expedition and to the personnel of the Meteorological Institute, Uppsala University, for providing the meteorological tower data. Also to the National Energy Administration of Sweden for sponsoring the NIBWAK project and the Greek Secretariate of Science, Research and Technology (G.S.S.R.T.) for its financial assistance in the development of the acoustic sounders.
NOMENCLATURE C2 Cv2 D Ati = 5 ~ f
temperature structure parameter, °C 2 m 2/3 velocity structure parameter, m 4/3 S-2 rotor diameter, m 5 wind speed deficit in the wake, m s frequency, Hz Fu one-dimensional spectral density in the wavenumber domain, m s 2 g gravity acceleration, m s-2 k von K~.rmfi.n constant = 0.4, dimensionless K1 wave number in the mean wind direction, m 2 tip-speed-ratio (dimensionless) Qo = w'T' surface heat flux (m K s- i) r distance of a point in the wake from centre line, m R radius of wake, m R0 rotor radius, m Su u-component spectral density, m 2 s 2 Hz tru/g longitudinal turbulence intensity in the wake (dimensionless ; expressed as a number smaller than unity or bigger than unity if multiplied by 100) mean potential temperature at height z, K T' fluctuation of potential temperature from its mean value, K w' fluctuation of w wind component from its mean value, m s- 1 ~ mean wind speed upstream, m sz height above ground, m
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Proc. Delphi Workshop on Wind-Energy Applications, Delphi, Greece, pp. 15-25.20-22 May 1985. G. J. Taylor, 3rd Symp. Wind-Energy Systems, Copenhagen (1980). P. B. S. Lissaman, D. R. Foster, B. D. Hibbs, D. T. Lindberg, C. K. Thompson and J. H. Rumbaugh, Technical description of AVENUE: A comprehensive computer software system for wind farm design. Proc. Int. Conf. on Windfarms, Leeuwarden, The Netherlands, 1316 October, 1987. P. E. J. Vermeulen, P. Builties, J. Dekker and G. L. Bueren, An experimental study of the wake behind a full-scale vertical-axis wind turbine. TNO Report 7906118, Apeldoorn, Holland (1979). G. J. Taylor, Wake and performance measurements on the Lawson Tancred 17 m horizontal-axis windmill. Proc. IEEE 130, A (1980). D. T. Swift-Hook, J. Hojstrup, D. N. McIntosh, D. J. Milborrow and G. J. Taylor, Nibe wake measurements project in Denmark, EWEA Conf., Hamburg (1984). R. W. Baker and S. N. Walker, Wake measurements behind a large horizontal-axis wind turbine generator. Solar Energy 33, 5 12 (1984). R. S. Haines, D. J. Milborrow, D. I. Page, A. D. Scott, W. G. Stevenson and G. J. Taylor, Wake interactions between the Holden HWP-3000 and the WEG MS-I wind turbine generators on Orkney, U.K. European Wind Energy Ass. Conf. and Exhibition, Rome, pp. 453 455 (1986). U. H6gstr6m, D. N. Asimakopoulos, H. D. Kambezidis, C. G. Helmis and A. Smedman, A field study of the wake behind a 2 MW wind turbine. Atmos. Environ. 22, 803 820 (1988). E. H. Brown and F. F. Hall, Advances in atmospheric acoustics. Rev. Geophys. Space Phys. 16, 47 110 (1978).
14. R. S. Cole, D. N. Asimakopoulos, T. J. Moulsley, S. J. Coughey and B. A. Crease, Some aspects of the construction and use of atmospheric acoustic sounders. Inst. Elec. Radio Engrs 50, 585 597 (1980). 15. D. N. Asimakopoulos, T. J. Moulsley, C. G. Helmis, D. P. Lalas and J. Gaynor, Quantitative low-level acoustic sounding and comparison with direct measurements. Bound. Layer Met. 27, 1-26 (1983). 16. D. N. Asimakopoulos, C. G. Helmis and G. J. Stephanou, Atmospheric acoustic mini-sounder. J. Atmos. Ocean Technol. 4, 345 347 (1987). 17. P. E. J. Vermeulen, Report on mixing of simulated wind turbine wakes in turbulent shear flow. TNO Report 7909974, Apeldoorn, Holland (1979). 18. G. N. Abramovich, The Theory of Turbulent Jets. MIT Press (1963). 19. J. C. Wyngaard, Y. lzumi and S. A. Collins, Behaviour of the refractive-index-structure parameter near the ground. J. Ac. Soc. Am. 61, 16461650 (1971). 20. J. C. Kaimal, J. C. Wyngaard, Y. Izumi and O. R. Cote, Spectral characteristics of surface layer turbulence. Quart. J. Roy. Met. Soc. 98, 563 589 (1972). 21. J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence. J. Wiley, New York (1964). 22. P. E. J. Vermeulen, A wind-tunnel study of the wake of a horizontal-axis wind turbine. TNO Report 78-09674, Apeldoorn, Holland (1978). 23. P. E. J. Vermeulen, Studies of the wake structure of model wind turbine generators. TNO Report 79-012904, Apeldoorn, Holland (1979). 24. P. H. Alfredson and J. A. Dahlberg, Measurements of wake interaction effects on the power output from small wind turbine models. The Aeron. Int. of Sweden, Technical Note FFA HU-2181 (1981).
