The average mean wind speed integrated over a disk is shown to be extremely close to the mean value of wind speed which would be measured at the center of a disk for most geometries in which a WECS (Wind Energy Conversion System) would operate. Field test results are presented which compare instantaneous records of wind speed integrated over a disk with the wind speed measured at the center of the disk. The wind field that a rotating element would experience is presented which was synthesized from the outputs of an array of anemometers

Cliff, W. C.

Verholek, M. G.

English

NASA Technical Reports Server

FLOW FIELD ANALYSIS
William C. Cliff
and
M. Gary Verholek
Battelle Pacific Northwest Laboratories
Richland, Washington 99352
ABSTRACT
The average mean wind speed integrated over a disk is shown to be extremely close
to the mean value of wind speed which would be measured at the center of a disk
for most geometries in which a WECS (Wind Energy Conversion System) would oper-
ate. Field test results are presented which compare instantaneous records of
wind speed integrated over a disk with the wind speed measured at the center of
the disk. The wind field that a rotating element would experience is presented
which has been synthesized from the outputs of an array of anemometers.
INTRODUCTION
At the present time, the Battelle PNL (Pacific Northwest Laboratories) are en-
gaged in attempting to statistically characterize the nominal and extreme wind
fields associated with flow over the disk of rotation of WECS systems. This
area is presently being addressed experimentally through a field test program
as well as by theoretical computations.
In many cases, the only measure of wind speed near a wind turbine may be a sin-
gle anemometer located at hub height. Questions, with regard to how well wind
speed measurements from this single anemometer represent the flow field over:
the disk of rotation of the wind turbine and how the measurements relate to the
wind field a _lade element would experience as it rotates, need to be resolved.
It is the intent of this paper to examine these questions theoretically and
through the use of field data collected from a set of anemometers arranged to
describe the swept area of a wind turbine. (See Figure I.)
MEAN WIND SPEED
In general, the mean wind profile in which a wind turbine operates (neutral at-
mospheric boundary layer) may be described as follows:
U_
U-z = F In z/z 0 (I)
where Uz = the mean wind speed at height z
u, = surface shear velocity = T,_ww/P
_w = surface shear stress
k =0.4
p = fluid density
z = height above grade level
z o = surface roughness length
71
https://ntrs.nasa.gov/search.jsp?R=19780011680 2020-03-20T12:55:17+00:00Z
The ratio of the mean wind speed averaged of a disk of rotation_of radius R
and hub height zh, Uzh R, to the mean wind speed at hub height, Uzh, could be ex-
pressed as:
zh + R
 zo[. ]
- I/2
Uzh,R 2zo 2-Zh2 + 2ZhZoX-Zo2X 2
- - fIR In z/z o R2 In x dx
Uzh z - R
zo
(2)
Table i gives some example results using Equation (2) to solve for the ratio cf
the mean velocity averaged over the disk of rotation to the mean velocity mea-
sured at hub height for various blade radii, hub heights and surface roughness.
To estimate the ratio of the mean velocity averaged over the disk of rotation
to the mean wind at hub height, the following formula may be used in lieu of
Equation (2).
(Zh+R) In - 1 - (Zh-R) l
Uz h - In Zh/Z o
(3)
The results obtained from Equation (2) indicate that the average wind speed from
a single anemometer at hub height will be representative of the average wind
speed over the disk of rotation in almost all cases. However, the instantaneous
wind speed measured at the hub will not represent the instantaneous average over
the disk of rotation. Averaging over the disk of rotation will act as a low
pass filter cutting off much of the high frequency content. The results of a
field test program performed at Battelle PNL show the effect of spacial averaging
over a disk. A schematic of the field test program is shown in Figure I.
The field array consists of eight anemometer sets located on the circumference of
a circle of radius 12.2 m (40 ft) and an anemometer set at the center of the cir-
cle and at a height of 24.4 m (80 ft). The instantaneous array average (simu-
lating the average over a disk of rotation) was computed by arithmetically aver-
aging the instantaneous output from the nine anemometer sets. A 15-second record
showing both the array average and hub anemometer output is shown in Figure 2.
The array average is much smoother than the single anemometer trace, as is expec-
ted. Spectral comparisons of the two traces also show the filtering effect of
averaging over an area. That is, the spectral amplitude drops off at a quicker
rate for the disk average than for the single anemometer record.
72
Using the anemometerarray depicted in Figure I, a wind record (simulating the
wind field experienced at 12.2 m from the hub by a rotating blade) was synthe-
sized by incrementally sampling the wind records from the anemometersaround the
circumference of the circle. Each O.l second, the wind record was sampled from
the next anemometeroutput.
Thus, each 0.8 second, one complete revolution around the array had occurred.
This simulates a rotation rate of 75 rpm. A 15-second synthesized wind record
is shown in Figure 3 along with the wind trace taken from the hub anemometerat
the sametime. The synthesized wind trace showsprincipally the vertical pro-
file of the wind (temperature measurementsindicated neutral conditions).
DISCUSSION
Q. If wind data are available only from a hub-height anemometer, how can the
full-disk wind flow field be estimated?
A.
Q*
A.
In general, the average value of the wind speed over the disk wind flow
field is extremely close to the average value at the hub, as shown in
Table I. However, instantaneously, the two will be different. The aver-
age over the disk could be simulated by filtering the hub anemometer out-
put with a first-order filter down 3 dB at a frequency of U-/D, where U is
the mean velocity and D is the diameter of the system. Unfortunately,
filtering processes are inherently time-averaging processes which, if
used "on line" in a decision loop, have some negative features.
How do the half-power frequency and turbulence factor change between a
single anemometer and the total average of all anemometers? How does the
energy in the O.l- to l-Hz range change by using the average of all ane-
mometers rather than a single anemometer?
In most cases, the spacial averaging over the disk of rotation does not
significantly decrease the total amount of energy in the spectrum; thus,
the half-power point would not change significantly. The changes of the
half-power frequency would have to be computed on a case-by-case basis.
Obviously, a small disk does not have as large an averaging effect as a
large disk.
The region of the spectra greatly affected by spacial averaging is the
high-frequency region. For the atmosphere, this would include the range
of O.l to l Hz, the region where most of the energy is lost. Thus, the
region from O.l to l Hz would have significantly less energy when area-
averaged over a disk commensurate with a large WECS. Again, the effect
would be a function of disk size and height above ground level.
73
Battelle welcomesall commentsand concerns which identify or assist in identi-
fying important wind characteristics associated with WECSdesign.
I. Formal requests for assistance: Dr. Charles E. Elderkin, Program Manager
(509) 946-2335
2. Informal discussion of wind characteristics for WECSdesign:
Dr. William C. Cliff (509) 942-5066
Battelle, PNL
Department of Atmospheric Sciences
Richland, WA 99352
TABLE I. - RATIO OF MEAN VELOCITY AVERAGED OVER A DISK
OF ROTATION TO MEAN VELOCITY MEASURED
AT HUB HEIGHT
Zh,R zo (meters) (a)
(meters) 0.005 0.05 0.5 5.0
70:50 0.99 0.99 0.98 0.97
50:30 0.99 0.99 0.99 0.98
15:lO 0.99 0.99 0.98 0.97
(a) The terrain features associated with various
surface roughnesses: 0.005 m = smooth
0.05 m = moderate
0.5 m = rough
5.0 m = extremely rough
(town)
74
INSTRUMENT ARRAY FOR
VERTICAL PLANE FIELD PROGRAM
GILL ANEMOMETERS NO. 1-9
TEMPERATURE PROBES NO. 10-12
T
I
120'
I
108.28"
I
80'
"I, II/ /)
_)'
r77; _ 7/"77
/
• \\
'_"2_j I I / I
11
12
.i / i I//7II27777-T7/I I/,
_----28.28'--- -_
S
\
1
\ \
\ \
\ \
\
7/
\/
¢'\\
_J
I/III/IIii7)9//7/71//11////
40'
/
71/17777
Figure I. - Field test setup for vertical plane test.
75
11
10
_8
ARRAY AVG
- i1o
,/_'r, i-
-,-.,J ,"". i HUB
--I " t "% l
',,, ,,: , \/"I
I I I I I I
2 4 6
..... W(ND SPEEDAT HUB, 24.4m(80ft)
-- WIND SPEEDAVERAGEDOVERDISK
(RADIUS = 12.2m)(4Oft)
,n,
I I
,,, ', ,,/'p,-, .._.,'_--..
2, ",,j".'.; ,., . ,. ,/ .
SELECTEDDATA ARE STORED IN9-TRACK
TAPEAND ARE AVAILABLETO OTHERTECH-
NICAL ORGANIZATIONS FOR APPROPRIATE
APPLICATIONS. TAPES OF DATA SEGMENTS
MAY BE OBTAII'EDFROM PNL FOLLOWINGA
DETERMINATION THATTHE DATA ARE
ACCEPTABLEFOR THE INTENDEDAPPLICA-
TION.
I i I I I L I. I I
8 I0 12 14
TIME,SECONDS
Figure 2, - Wind speed at hub versus wind speed averaged over disk.
11
...... WIND SPEEDAT HUB, 24.4m(80ft) --SYNTHESIZED WIND SPEED
ATA RADIUS OF12.2m(40ft)
o !i8
7
6
I I I I I I I I I I
0 2 4 6 8 I0 12 14
TIME, SECONDS
Figure 3. - Synthesized wind speed versus wind speed at hub.
76


Flow field analysis

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