Geoscience Reference
In-Depth Information
corresponds to the Doppler shift related to the average
velocity of the jet at the location of the measurement
volume. The range of detected frequencies around this
maximum corresponds to the range of velocity statisti-
cally sampled by the vortices in the flow (within the range
of spatial scales selected according to the wave number
q
scat
) which scattered the acoustic wave. As a consequence,
the shape of the power spectrum directly reflects the sta-
tistical properties of the velocity field of the flow. It is
a Gaussian, centered around a frequency which corre-
sponds to the mean stream velocity of the jet flow at the
location of the measurement volume and the width of
the Gaussian corresponds to the standard deviation of the
carrier velocity field. Poulain et al. have indeed shown that
in their turbulent jet the power spectrum is well fitted by a
Gaussian:
stratified flows with geophysical motivations. One may
therefore want to use instrumented particles (called
smart
particles
) with embarked electronics able to measure scalar
or kinematic quantities in the Lagrangian frame while
continuously transmitting the information to the operator
for data storage and postprocessing.
15.4.1. Lagrangian Temperature Measurement
A smart particle has been designed to measure con-
tinuously temperature along the particle trajectory using
four thermistors, placed at the surface of the particle
directly in contact with the fluid [
Gasteuil et al.
, 2007;
Shew et al.
, 2007]. It is made of a spherical capsule of
diameter
D
= 21 mm containing temperature instrumenta-
tion, a radio frequency (RF) emitter, and a battery. It uses
a resistance controlled oscillator LMC555 timer to create
a square wave whose frequency depends on the tempera-
ture of the several thermistors. This square wave is used
directly to modulate the frequency of the radio wave gen-
erated by the RF emitter in the range 22
exp
(15.8)
δν
avg
)
2
2
δν
rms
A(ν
0
)
√
2
πδν
rms
(δν
−
PSD
scat
(δν)
=
−
and they have shown that the fitting Doppler shift fre-
quencies
δν
avg
and
δν
rms
were in excellent agreement with
hot-wire anemometry measurements of the mean and rms
velocity of the jet flow. Perhaps more interestingly, they
have shown that the quantity
q
scat
A(ν
0
)
(where
A(ν
0
)
is
the maximum of the power spectral density) gives a direct
estimate of the enstrophy spectrum of the flow at the
given wave number
q
scat
once the transfer function
H(ν
0
)
between the receiver and the emitter is applied. (An impor-
tant aspect to be considered when using this method con-
cerns the calibration of the acoustic transducers: While
this is not crucial for the Lagrangian measurement previ-
ously described, which only relies on the frequency shift
information of the scattered wave, a proper calibration
of the transfer functions of the receiver and the emitter
is required to extract the vorticity information, which is
coded in the amplitude of the power spectral density.) By
varying the working frequency
ν
0
(and hence the scatter-
ing wave number
q
scat
), it is then possible to reconstruct
the entire spectrum of enstrophy. Figure 15.16b shows
the enstrophy spectrum of the jet flow investigated by
Poulain et al. which is found to be in reasonable agreement
with the Kolmogorov phenomenology of turbulence.
26 kHz about
the carrying frequency
f
0
= 315 MHz (see Figure 15.17
−
Flip-
flop
Hall
switch
Antenna
Thermistors
RF
emitter
Oscillator
Antenna
RF
amp
RF
amp
RF
receiver
ADC
PC
Figure 15.17.
The smart particle measuring temperature uses
four thermistors, placed directly in contact with the fluid, con-
nected to a LMC555 timer to generate a square wave with
frequency in the range 22
26 kHz depending on the flow tem-
perature [
Gasteuil et al.
, 2007;
Shew et al.
, 2007]. An RF emitter
and receiver (MAX7044 and MAX1473 from Maxim Integrated
Products) are used for frequency modulation and demodulation
at 315 MHz. The emitter antenna is placed inside the capsule
with emitting circuit tuned for emission at 315 MHz using a
variable capacitor. The signal is received by a fixed antenna
amplified and demodulated before acquisition at 10 MHz with
high-speed DACQ. The slowly varying frequency of the square
wave is then continuously measured using Labview standard
library, then stored for further data analysis. A Hall switch and
flip-flop are used for turning on and off the particle approaching
a magnet close to the particle in order to save the battery when
the experiment is not running.
−
15.4. INSTRUMENTED PARTICLES
When performing Lagrangian measurement in a fluid
flow, one is usually limited in track length because of the
necessary finite size of the measurement volume. Using
particle tracking velocimetry or Doppler velocimetry, one
is also limited in the investigation of kinematic quanti-
ties (velocity, acceleration, vorticity, etc.). Tracking scalar
quantities such as salinity or temperature along parti-
cle paths may also be of prime interest, in particular for
