Environmental Engineering Reference
In-Depth Information
without any
ground reflection
,
and the plate is assumed to be of constant thickness, planar
(
i.e.
untwisted), and metallic in order to produce maximum scattering.
When the direct signal is a
plane electromagnetic wave
with its electric field vector in
the
x-y
plane, the horizontal component of the idealized scattered signal at the receiver is
lw
exp[-
j
2p z/l] | sin(f
R
)| ×
E
R
,
P
=
j
|
E
WT
,
D
|
l
z
p
l
l
×
sinc
[
p
sin(W
t
) +
q
cos(W
t
)]
×
p
w
l
[
p
cos(W
t
) +
q
sin(W
t
)]
(9-17a)
×
sinc
p
= sin(q
T
) cos(f
T
) + sin(q
R
cos(f
R
)
(9-17b)
q
= cos(q
T
) + cos(q
R
)
(9-17c)
where
E
R, P
=
scattered signal field at the receiver, from a rotating plate at the wind
turbine representing one rotor blade (mV/m)
|
E
WT, D
| = amplitude of the direct signal field at the wind turbine (mV/m)
l
,
w =
length and width of the plate, respectively (m)
l
= wave length of the direct signal (m)
z
= distance from the receiver to the wind turbine (m)
sinc
{
}
= |sin{ } /{ } | (1/rad)
r
T
,
q
T
, f
T
= spherical coordinates of the distant transmitter;
r
T
®¥ (m, rad, rad)
z, q
R
, f
R
= spherical coordinates of the receiver (m, rad, rad)
As a result of the assumption of a plane wave, the direct (or
incident
)
signal at the receiver
has the same amplitude as that of the signal incident at the plate. Actually, these two quan-
tities may differ, as indicated in Figure 9-6. To maximize the signal scattered by the plate,
we first assume that W
t =
q
R
= q
T
= p
/
2
.
This gives an idealized amplitude of
lw
lz
sin (f
R
)
sinc
p
l p
l
|
E
R
,
P
|
=
|
E
WT
,
D
|
(9-18a)
p
= cos(f
T
) + cos(f
R
)
(9-18b)
In modelling a wind turbine rotor,
l
is much larger than
w
,
and the time dependence
of the modulation shape function is primarily determined by the first
sinc
factor in Equation
(9-17a). This sinc function is a maximum (unity) when
p =
0, which is the case for
specular
or
backward scattering
(f
R
=
p - f
T
)
and
forward scattering
(f
R
=
p + f
T
). For
these two directions the idealized scattered signal is independent of time. In directions near
these, however, the modulation function is a time-varying sinusoid with frequency twice the
rotation frequency. In receiving directions that are well away from it p ± f
T
,
measurements
show that the waveform consists of sine-like pulses with a width proportional to
l
repeating
at twice the rotation frequency [LaHaie and Sengupta 1970]. The fact that there is no
time-varying modulation in the directions of maximum scattering is a consequence of
modeling the turbine blade as a flat plate rotating in its own plane, which is not quite true
Search WWH ::
Custom Search