A non-perturbative anemometric and flow visualization technique

TL;DR: In this article, the authors presented a new visualization technique of an hydrodynamic flow using a thermal grid, written in the liquid by means of a pulsed laser, and whose image is subsequently formed, using standard optics, by illumination by a continuous laser.

Abstract: 2014 We present a new visualization technique of an hydrodynamic flow using a thermal grid, « written » in the liquid by means of a pulsed laser, and whose image is subsequently formed, using standard optics, by illumination by a continuous laser. The experiment gives access to a new Doppler-anemometric technique which does not involve the presence of particles in the fluid and to an instantaneous image of a finite volume of the flow. J. Physique LETTRES 41 (1980) L-519 L-521 1 Classification Physics Abstracts 47.80 1 er NOVEMBRE 1980. The instantaneous visualization and velocity measurement of a finite domain of flow is of considerable interest for unsteady or turbulent velocity field u(r, t). Several methods are based on the periodic injection Fig. 1. In the Poiseuille flow cell (C) a thermal grating G is formed at initial time (t = 0) by the interference of two beams coming from a pulsed Nd YAG laser Lp. The second laser La illuminates this grid and is diffracted (orders 0, 1, 1). The Doppler shifted signals 1, 1 can be used to set an anemometric measurement by standard heterodyne technique. Another possibility is the formation of an image of the grid in the plane I conjugate of G through the lens L. If the laser La is switched on (by means of an acoustooptic modulator) for a short time period (t, t + At), the image reflects the integrated effect of the flow field between t = 0 and t. of lines of lagrangian markers (dye, solid particles, bubbles) in the fluid [1]. The lines distort as they move with the flow, due to the velocity gradients; a measurement of the integrated displacement and of u(r, t) is possible as long as the diffusion has not washed away the lines. The letter discusses a related technique in which a thermal grid is « written » in a very short time (tp 10 ns) within a liquid using the pattern formed by the interference of two beams from a pulsed laser Lp [2] (Fig. 1). In a previous paper [3] we have shown some applications of the forced Rayleigh technique [4] to hydrodynamics : if the thermal grid is « read » by a second laser La (cw HeNe 10 mW) incident at right angle with the wave vector of the index grating formed by the thermal grid, the exponential time decay of the intensity of the diffracted peaks gives access to the thermal diffusivity in the flow (Fig. 2a) as in static experiments. Moreover, the rotation and distortion of the grid caused by the velocity gradients are measured through the corresponding changes of the diffraction pattern. The average velocity u (in the grid volume) is automatically subtracted by the diffraction process; this is of particular interest for the study of the structure of turbulence which is determined in terms of the gradient components. Moreover, this experiment gives an average information over the size of the laser La. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019800041021051900 L-520 JOURNAL DE PHYSIQUE LETTRES Fig. 2. a) Classical decay of a forced Rayleigh signal : intensity of the first diffracted order (with an exponential time constant T = p2/(8 ~2 K) where p is the wavelength of the grid, K the thermal diffusivity). b) The output signal Ia of a photodetector placed in the image of the grid : a periodic modulation is superimposed to the exponential decay with a frequency 2 Av proportional to u. The present extension of the technique is quite complementary : i) it permits to observe the thermal grid not only in the Fourier space but also in real space; thus it has spatial resolution; ii) it can give a measure of u which, in the forced Rayleigh experiment, was « memorized » as a Doppler shift of the frequency of the diffracted order ± 1 as Av = plii [1] (where p = period of the thermal grid). The information in u can be extracted by mixing the diffracted beams ± 1. This is the principle of the experiment sketched in the right part of figure 1 : the two beams ± 1 are recombined to form the image of the grid in a plane I, conjugate of the index grating, through the lens L (the image is magnified by a ratio m = q’/q ’\" 10). In the focal plane of L, the screen S acts as an aperture stop in the Fourier space and suppresses the central beam. The strioscopic technique gives an image (amplitude grating) of 100 % contrast. The motion of the image at a velocity mu(r, t) follows that of the object grid. The photographs (Fig. 3) shows a sequence of two images of a flow. The grid is initially (time t = 0) perpendicular to the plates of a plane Poiseuille flow cell (the flow being uniform along the direction y of the laser La). At a subsequent time (t = 300 ~s), the parabolic velocity profile of the laminar flow is seen from the integrated motion of the grid. Fig. 3. Photographs of the grid in the image plane I at two different times : a) t = 0 : right when the grid was formed in the flow cell; b) t = 300 us : grid convected by the Poiseuille flow. We also notice the decay of intensity due to thermal diffusion between the photographs taken with equal exposure time At = 20 us. One can extend the technique to non uniform Poiseuille flows and suppress the integration along the y direction by replacing the spherical lens used to form the index grating by a cylindrical one. In particular for the visualization of small turbulent structures [5] the thickness of the vertical « ribbon » of pulsed laser light should be kept comparable to the Kolmogorov scale. The present experiment is limited by the sensitivity of the recording film [6]. In order to avoid fuzzy images, the exposure time has to be kept of the order of T/I0, where the period of displacement of the grid is T ~ 10-4 s for a grating of period p ~ 100 Ilm and u ~ 1 m/s. The limit is quite severe for turbulent flows where the attenuation of the grid intensity by turbulent diffusion can be much faster than in laminar flows. It is also possible to place a small (of extent p’/2 where p’ is the period of the image grid) photodetector in a prescribed point of the image flow field. The variaL-521 AN ANEMOMETRIC AND FLOW VISUALIZATION TECHNIQUE tion of intensity with time is given in the figure 2b. In addition to exponential diffusive decay, the periodic modulation at a frequency 2 Av (given by [1]) is a measure of the local velocity u(r) during the lifetime of the grid. This laser Doppler anemometry technique is complementary to the classical LDA one [7] : in the latter case, particles move within the flow through a fixed grid ; in the present experiment, the grid moves as a whole through the reference line of the La beam. Our experiment is not a true lagrangian one because different parts of the grid pass through the laser beam. However, it offers several advantages : i) it does not require the presence of tracer particles in the flow ; ii) it allows the simultaneous measurement of the diffusivity and of one velocity component. Such a joint information can be of interest in particular in the study of two-dimensional turbulent flow fields where it is known that the turbulent mixing can be controled by the large eddy structures [8] ; iii) measurement of the velocity in different points of the flow field can be done simultaneously or sequentially by using several small detectors in the image plane I. Let us finally note that a simpler LDA measurement can be obtained by mixing one of the diffracted beams with unshifted diffused light from the central beam. However in this case we lose the dual information on the map of velocity field obtained by means of the grid image.

Summary

Summary

• The authors present a new visualization technique of an hydrodynamic flow using a thermal grid, « written » in the liquid by means of a pulsed laser, and whose image is subsequently formed, using standard optics, by illumination by a continuous laser.
• The experiment gives access to a new Doppler-anemometric technique which does not involve the presence of particles in the fluid and to an instantaneous image of a finite volume of the flow.

Full text

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A non-perturbative anemometric and ow visualization
technique
M. Fermigier, P. Jener, J.C. Charmet, E. Guyon
To cite this version:
M. Fermigier, P. Jener, J.C. Charmet, E. Guyon. A non-perturbative anemometric and ow
visualization technique. Journal de Physique Lettres, Edp sciences, 1980, 41 (21), pp.519-521.
�10.1051/jphyslet:019800041021051900�. �jpa-00231836�

L-519
A
non-perturbative
anemometric
and
flow
visualization
technique
(~)
M.
Fermigier
(*),
P.
Jenffer
(**),
J.
C.
Charmet
and
E.
Guyon
(**)
Laboratoire
d’Hydrodynamique
et
de
Mécanique
Physique,
E.S.P.C.I.,
10,
rue
Vauquelin,
75231
Paris
Cedex
05,
France
(Re~u
le
10 juillet
1980,
accepte
le
16
septembre
1980)
Résumé.
2014
Nous
présentons
une
nouvelle
technique
de
visualisation
d’un
écoulement
hydrodynamique
utilisant
une
grille
thermique,
«
écrite
»
dans
le
liquide
au
moyen
d’un
laser
pulsé,
dont
l’image
est
ensuite
formée,
avec
une
optique
classique,
par
éclairement
avec
un
laser
continu.
L’expérience
donne
accès
à
une
nouvelle
technique
d’anémométrie
Doppler
qui
ne
nécessite
pas
la
présence
de
particules
dans
le
fluide,
et
à
une
image
instantanée
d’un
volume
fini
de
l’écoulement.
Abstract.
2014
We
present
a
new
visualization
technique
of
an
hydrodynamic
flow
using
a
thermal
grid,
«
written
»
in
the
liquid
by
means
of
a
pulsed
laser,
and
whose
image
is
subsequently
formed,
using
standard
optics,
by
illu-
mination
by
a
continuous
laser.
The
experiment
gives
access
to
a
new
Doppler-anemometric
technique
which
does
not
involve
the
presence
of
particles
in
the
fluid
and
to
an
instantaneous
image
of
a
finite
volume
of
the
flow.
J.
Physique
-
LETTRES
41
(1980)
L-519 -
L-521
1
Classification
Physics
Abstracts
47.80
1 er
NOVEMBRE
1980.
The
instantaneous
visualization
and
velocity
measu-
rement
of
a
finite
domain
of
flow
is
of
considerable
interest
for
unsteady
or
turbulent
velocity
field
u(r,
t).
Several
methods
are
based
on
the
periodic
injection
Fig.
1.
- In
the
Poiseuille
flow
cell
(C)
a
thermal
grating
G
is
formed
at
initial
time
(t
=
0)
by
the
interference
of
two
beams
coming
from
a
pulsed
Nd
YAG
laser
Lp.
The
second
laser
La
illuminates
this
grid
and
is
diffracted
(orders
0, 1, -
1).
The
Doppler
shifted
signals
1,
-
1
can
be
used
to
set
an
anemometric
measure-
ment
by
standard
heterodyne
technique.
Another
possibility
is
the
formation
of
an
image
of
the
grid
in
the
plane
I
conjugate
of
G
through
the
lens
L.
If
the
laser
La
is
switched
on
(by
means
of
an
acoustooptic
modulator)
for
a
short
time
period
(t, t
+
At),
the
image
reflects
the
integrated
effect
of
the
flow
field
between
t
=
0
and
t.
of
lines
of
lagrangian
markers
(dye,
solid
particles,
bubbles)
in
the
fluid
[1].
The
lines
distort
as
they
move
with
the
flow,
due
to
the
velocity
gradients;
a
measu-
rement
of
the
integrated
displacement
and
of
u(r,
t)
is
possible
as
long
as
the
diffusion
has
not
washed
away
the
lines.
The
letter
discusses
a
related
technique
-
in
which
a
thermal
grid
is
«
written »
in
a
very
short
time
(tp -
10
ns)
within
a
liquid
using
the
pattern
formed
by
the
interference
of
two
beams
from
a
pulsed
laser
Lp
[2]
(Fig.
1).
In
a
previous
paper
[3]
we
have
shown
some
appli-
cations
of
the
forced
Rayleigh
technique
[4]
to
hydro-
dynamics :
if
the
thermal
grid
is
«
read »
by
a
second
laser
La
(cw
HeNe
10
mW)
incident
at
right
angle
with
the
wave
vector
of
the
index
grating
formed
by
the
thermal
grid,
the
exponential
time
decay
of
the
inten-
sity
of
the
diffracted
peaks
gives
access
to
the
thermal
diffusivity
in
the
flow
(Fig.
2a)
as
in
static
experiments.
Moreover,
the
rotation
and
distortion
of
the
grid
caused
by
the
velocity
gradients
are
measured
through
the
corresponding
changes
of
the
diffraction
pattern.
The
average
velocity
u
(in
the
grid
volume)
is
auto-
matically
subtracted
by
the
diffraction
process;
this
is
of
particular
interest
for
the
study
of
the
structure
of
turbulence
which
is
determined
in
terms
of
the
gradient
components.
Moreover,
this
experiment
gives
an
average
information
over
the
size
of
the
laser
La.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019800041021051900

L-520
JOURNAL
DE
PHYSIQUE -
LETTRES
Fig.
2.
-
a)
Classical
decay
of
a
forced
Rayleigh
signal :
intensity
of
the
first
diffracted
order
(with
an
exponential
time
constant
T
=
p2/(8
~2
K)
where
p
is
the
wavelength
of
the
grid,
K
the
thermal
diffusivity).
b)
The
output
signal
Ia
of
a
photodetector
placed
in
the
image
of
the
grid :
a
periodic
modulation
is
superimposed
to
the
exponential
decay
with
a
frequency
2
Av
proportional
to
u.
The
present
extension
of
the
technique
is
quite
complementary :
i)
it
permits
to
observe
the
thermal
grid
not
only
in
the
Fourier
space
but
also
in
real
space;
thus
it
has
spatial
resolution;
ii)
it
can
give
a
measure
of u
which,
in
the
forced
Rayleigh
experiment,
was
«
memorized
»
as
a
Doppler
shift
of
the
frequency
of
the
diffracted
order
±
1
as
Av
=
plii
[1]
(where
p
=
period
of
the
thermal
grid).
The
information
in
u
can
be
extracted
by
mixing
the
diffracted
beams
±
1.
This
is
the
principle
of
the
experiment
sketched
in
the
right
part
of
figure
1 :
the
two
beams
±
1
are
recombined
to
form
the
image
of
the
grid
in
a
plane
I,
conjugate
of
the
index
grating,
through
the
lens
L
(the
image
is
magnified
by
a
ratio
m
=
q’/q ’"
10).
In
the
focal
plane
of
L,
the
screen
S
acts
as
an
aperture
stop
in
the
Fourier
space
and
suppresses
the
central
beam.
The
strioscopic
technique
gives
an
image
(amplitude
grating)
of
100 %
contrast.
The
motion
of
the
image
at
a
velocity
mu(r,
t)
follows
that
of
the
object
grid.
The
photographs
(Fig.
3)
shows
a
sequence
of
two
images
of
a
flow.
The
grid
is
initially
(time t
=
0)
perpendicular
to
the
plates
of
a
plane
Poiseuille
flow
cell
(the
flow
being
uniform
along
the
direction y
of
the
laser
La).
At
a
subsequent
time
(t
=
300
~s),
the
para-
bolic
velocity
profile
of
the
laminar
flow
is
seen
from
the
integrated
motion
of
the
grid.
Fig.
3.
-
Photographs
of
the
grid
in
the
image
plane
I
at
two
different
times :
a)
t =
0 :
right
when
the
grid
was
formed
in
the
flow
cell;
b)
t =
300
us :
grid
convected
by
the
Poiseuille
flow.
We
also
notice
the
decay
of
intensity
due
to
thermal
diffusion
bet-
ween
the
photographs
taken
with
equal
exposure
time
At
=
20
us.
One
can
extend
the
technique
to
non
uniform
Poi-
seuille
flows
and
suppress
the
integration
along
the
y
direction
by
replacing
the
spherical
lens
used
to
form
the
index
grating
by
a
cylindrical
one.
In
parti-
cular
for
the
visualization
of
small
turbulent
structures
[5]
the
thickness
of
the
vertical
«
ribbon »
of
pulsed
laser
light
should
be
kept
comparable
to
the
Kolmo-
gorov
scale.
The
present
experiment
is
limited
by
the
sensitivity
of
the
recording
film
[6].
In
order
to
avoid
fuzzy
images,
the
exposure
time
has
to
be
kept
of
the
order
of
T/I0,
where
the
period
of
displacement
of
the
grid
is
T ~
10-4
s
for
a
grating
of
period
p ~
100
Ilm
and
u ~
1
m/s.
The
limit
is
quite
severe
for
turbulent
flows
where
the
attenuation
of
the
grid
intensity
by
turbulent
diffusion
can
be
much
faster
than
in
laminar
flows.
It
is
also
possible
to
place
a
small
(of
extent
p’/2
where p’
is
the
period
of
the
image
grid)
photodetector
in
a
prescribed
point
of
the
image
flow
field.
The
varia-

L-521
AN
ANEMOMETRIC
AND
FLOW
VISUALIZATION
TECHNIQUE
tion
of
intensity
with
time
is
given
in
the
figure
2b.
In
addition
to
exponential
diffusive
decay,
the
periodic
modulation
at
a
frequency
2
Av
(given
by
[1])
is
a
mea-
sure
of
the
local
velocity
u(r)
during
the
lifetime
of
the
grid.
This
laser
Doppler
anemometry
technique
is
complementary
to
the
classical
LDA
one
[7] :
in
the
latter
case,
particles
move
within
the
flow
through
a
fixed
grid ;
in
the
present
experiment,
the
grid
moves
as
a
whole
through
the
reference
line
of
the
La
beam.
Our
experiment
is
not
a
true
lagrangian
one
because
different
parts
of
the
grid
pass
through
the
laser
beam.
However,
it
offers
several
advantages :
i)
it
does
not
require
the
presence
of
tracer
particles
in
the
flow ;
ii)
it
allows
the
simultaneous
measurement
of
the
diffusivity
and
of
one
velocity
component.
Such
a
joint
information
can
be
of
interest
in
particular
in
the
study
of
two-dimensional
turbulent
flow
fields
where
it
is
known
that
the
turbulent
mixing
can
be
controled
by
the
large
eddy
structures
[8] ;
iii)
measurement
of
the
velocity
in
different
points
of
the
flow
field
can
be
done
simultaneously
or
sequentially
by
using
several
small
detectors
in
the
image
plane
I.
Let
us
finally
note
that
a
simpler
LDA
measurement
can
be
obtained
by
mixing
one
of
the
diffracted
beams
with
unshifted
diffused
light
from
the
central
beam.
However
in
this
case
we
lose
the
dual
information
on
the
map
of
velocity
field
obtained
by
means
of
the
grid
image.
References
[1]
KLINE,
S.
J.,
Flow
visualization
(Film)
in
Illustrated
experiments
in
fluid
mechanics,
National
Committee
for
Fluid
Mecha-
nics
Films;
MERZKIRCH,
W.,
Flow
Visualization,
Chap.
2
(Academic
Press)
1974.
[2]
Nd YAG
laser
(Quantel YG
48)
frequency
doubled
(03BB = 0.53
03BCm)
with
20
mJ
pulses
and
0.5
Hz
repetition
rate.
[3]
FERMIGIER,
M.,
GUYON,
E.,
JENFFER,
P.,
PETIT,
L.,
Appl.
Phys.
Lett.
36
(1980)
361.
[4]
EICHLER,
H.
J.,
Festkörperprobleme,
XXVIII,
J.
Treusch
ed.,
(Vieweg,
Braunschweig)
1978,
p.
241.
[5]
Consideration
of
spatial
distribution
of
vorticity
at
different
scales
is
presently
considered
as
one
of
the
key
factors
in
the
understanding
of
the
so-called
«
homogeneous
turbu-
lence
».
[6]
Kodak
Recording
2475 ;
it
can
be
processed
with
a
sensitivity
of
4000
ASA
corresponding
to
an
optical
density
of
0.1
with
an
energy
density
of
10-4
erg/cm2.
[7]
DURST,
F.,
MELLING,
A.,
WHITELAW,
J.
H.,
Principles
and
practice
of
laser
Doppler
anemometry
(Academic
Press)
1976.
[8]
BREIDENTHAL,
R.,
AIAA
J.
17
(1979)
310.