Geoscience Reference
In-Depth Information
much larger t
han
the inverse of the Kolmogorov time
→
u
→
scale 1
/τ
η
=
/ν
with a spatial resolution comparable
with the Kolmogorov scale
η
=
ν
3
/
1
/
4
in order to
access the very small scales of the particle motion. For
typical water flows at the laboratory scale, one there-
fore needs to track particles with sizes in the range
10
θ
D
100
μ
m with a sampling frequency larger than sev-
eral kilohertz, which is a severe limitation in terms of
camera specifications and cost of the experiment. To
increase the temporal resolution at a modest cost, one
possibility is to rely on scattering techniques using a
reference wave (either using ultrasound or laser light)
that will be scattered by the moving particles. This is
the basis of the so-called laser Doppler velocimetry (an
Eulerian measurement technique) and of extended laser
Doppler velocimetry, which is its extension to Lagrangian
measurements.
−
40 MHz
AOM
Principle of Laser Doppler Velocimetry
The principle of
laser Doppler velocimetry is quite simple: It uses two
coherent laser beams (with wavelength
λ
0
) intersecting
with an angle
θ
to create an interference pattern con-
sisting of fringes perpendicular to the plane of the laser
beams, separated by a distance
a
=
λ
0
/(
2 sin
(θ/
2
))
. When
a particle crosses the fringes, it scatters light with an inten-
sity
I(t)
modulated with a frequency
f
p
=
u
Laser
AOM
40,1 MHz
Figure 15.5.
Optical arrangement of extended laser Doppler
velocimetry detailed by
Volk et al.
[2008, 2011]. Two laser
beams (with wavelength
λ
0
) forming an angle
θ
inter-
sect to create an interference pattern with fringe spacing
a
=
λ
0
/
[
/a
,where
⊥
u
⊥
is the component of velocity perpendicular to the
fringes (Figure 15.5). If the measurement volume (region
where the beams intersect) extends over a large region of
space, a continuous detection of the instantaneous fre-
quency
f
p
(t)
gives access to the evolution of the particle's
velocity as a function of time. Such an extended laser
Doppler velocimetry was developed by
Volk et al.
[2008,
2011] to perform velocity tracking of small particles in
high-Reynolds-number flows.
. Each beam is shifted in frequency with an
acousto-optic modulator and expended using a telescope. The
measurement volume is imaged onto a photodetector. A par-
ticle crossing the fringes scatters light modulated at frequency
f
p
(t)
=
δf
+
u
2sin
(θ/
2
)
]
(t)/a
with
δf
the frequency shift between the
⊥
beams and
u
(t)
the component of velocity perpendicular to
⊥
the fringes.
Optical Arrangement
In order to obtain interference
fringes in a large region of space, only one laser beam
is used: It is separated by a beam splitter into two
coherent beams separately expanded using two pairs of
lenses as telescopes. The sign of the velocity can be
extracted if one creates a set of
traveling
interference
fringes. This is achieved by shifting one of the optical
beams at a frequency
δf
so that the actual modulation
of the scattered signal is at frequency
f
p
(t)
=
δf
+
u
of the flow motion. Using a 1 W continuous argon laser
with wavelength 514 nm and a small angle between the
beams, one can obtain a fringe spacing
a
=41
μ
m. This
is much larger than in classical LDV applications and
allows to use as tracers small polystyrene fluorescent (with
size 30
μ
m) or larger nonfluorescent particles, which are
almost neutrally buoyant in water. For the fluorescent par-
ticles case, scattered light is weaker and the measurement
volume has to be imaged on a low-noise photomultiplier
with high gain. For particles larger than 100
μ
m, the scat-
tered signal is stronger and the detection can be made
using amplified photodiodes and using less than 0.5 W of
laser power. As opposed to fluorescent particles, the opti-
cal contrast of the scattered signal strongly depends on
the photodetector location and particle size; the detector
is located in the plane of the beams and at 45
◦
from the
beams.
(t)/a
.
Shifting is done by propagating the two laser beams
through acousto-optic modulators (AOMs) with fre-
quency shifts
f
1
=40 MHz and
f
2
= 40.1 MHz so that
the fringes are actually moving at constant velocity
v
f
=
a(f
2
−
⊥
f
1
)
=
a
·
δf
.
Particle Detection
In practice, the intensity needed for
the measurement depends on the particles used as tracers
