13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
Characterization of vortex flow transition using PIV in the Couette Taylor
system
Nizar Abcha, Noureddine Latrache, Olivier Crumeyrolle & Innocent Mutabazi
LMPG, University of Le Havre, France
nizar.abcha@univ-lehavre.fr
Abstract We have developed a Particle Image Velocimetry (PIV) adapted to the Couette-Taylor system in
order to measure the axial and radial velocity components, vorticity fields, and their spatio-temporal
dependence. The comparison between spatio-temporal diagrams obtained by flow visualization and PIV
indicates that the intensity of light reflected by Kalliroscope platelets is related to the radial velocity
component.
1. Introduction
The Couette-taylor system is composed of two coaxial differentially rotating cylinders; it represents
a good prototype for investigation of centrifugal instabilities and the transition system to turbulence
in closed flows. This flow system has been subject of intense studies since the pionneering work of
G.I. Taylor of 1923. Since then, many theoretical and experiments studies have been performed
(Chandrasekhar S (1961), Coles D (1965)). Using visualization by means of anisotropic particles
(aluminium powder (Taylor GI (1923), Coles D 1965), kalliroscope (Gorman M et al(1982),
Andereck CD et al (1986),...), it was shown that the Couette-Taylor system possesses a rich variety
of pattern depending on geometrical (aspect ratio and radius ratio) and physical (flow viscosity,
cylinder rotation speeds) parameters (Coles D (1965), Andereck CD et al (1986)). Because of the
intensive use of these particles in the investigation of flows in closed systems, theoretical and
experimental attempts have been made to relate flow properties with visualization using these
particles (Savas Ö (1985), Gauthier G et al(1998), Kalliroscope Corporation, Domnguez-Lerma et
al (1985), Matisse P et al (1984), Thoroddsen et al (1999), Prigent A (2000). Since two decades,
the visualization techniques have been complemented with of Laser Doppler Velocimetry (LDV)
(Wereley ST et al (1994), Ultrasonic Doppler Velocimetry (UDV) (Takeda et al (1993), Takeda
(1999)) and Particle Image Velocimetry (PIV) (Wereley ST et al (1998), Hwang JY et al (2004),
Wereley ST et al (2002), and Wereley ST et al (1999)). Unfortunately, no clear answer has been
provided so far to the following question: which flow information is given by the Kalliroscope
particles? In this paper, we address this question using simultaneously a comparison of space-time
diagrams obtained using both visualization technique and PIV.
2. Experimental apparatus and procedure
The experimental system consists of two vertical coaxial cylinders immersed in a large square
plexiglass box filled with water maintained at a controlled temperature. This square box allows for
minimization of distortion effects of refraction due to curvature of the outer cylinder (Fig.1) during
optical measurements. The inner cylinder has a radius a = 4 cm, the outer cylinder a radius b = 5
cm, the gap between the cylinders is d = b-a = 1 cm and the working length is L = 45.9 cm.
Therefore the radius ratio η = a/b = 0.8 and the aspect ratio is Γ = L/d = 45.9. The inner cylinder is
rotated by a motor at the angular rotation frequency Ω while the outer cylinder is fixed. The control
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
parameter is the Reynolds number Re = Ωad/ν where v is the kinematic viscosity of the working
fluid. In our experiments, we have used distilled water ( v = 0.98 × 10−2 cm2/s at the temperature T =
21.1°C).
Fig.1 : Experimental apparatus: visualization and data acquisition
For the visualization of flow structures, we have added 2% volume of Kalliroscope AQ1000, which
is a suspension of 1% to 2% of reflective flakes of a typical size of 30 µm x 6 µm x 0.07 µm (Savas
Ö (1985), Gauthier G et al(1998), Kalliroscope Corporation, Domnguez-Lerma et al (1985),
Matisse P et al (19984), Thoroddsen et al (1999), Prigent A (2000) with a relatively large reflective
optical index n = 1.85 and a density of ρ = 1,62 g/cm-3. The sedimentation of these particles remains
negligible in horizontal or vertical configurations if the experiment lasts less than 10hours. These
particles do not modify significantly the flow viscosity and no non-Newtonian effect was detected
as far as small concentrations are used. These particles align themselves along the flow and their
light reflection can provide information on the flow structure. The values of Reynolds number are
determined within a precision of 2.1%. A fluorescent tube arranged parallel to the cylinder axis was
used as a source of light for a homogeneous illumination of the region of flow visualization. A
linear charge coupled device (CCD) array with 1024 pixels oriented along the cylinders axis is used
to record the instantaneous intensity distribution, I (z) , of light reflected by Kalliroscope platelets.
The recorded length varies from 25 to 29 cm in the central part of the system, corresponding to a
spatial resolution from 40 to 30 pixels/cm. The intensity was sampled over a 256 values range,
displayed in gray levels at regular intervals along time axis in order to produce space-time diagrams
I(z,t) of the pattern. Using a He-Ne Laser beam (λ = 638 nm), with a cylindrical lens, it was
possible to visualize the cross section of the flow in the r-z plane. Then it is possible to record with
the linear CCD camera a reflected light intensity I(z) from a line in the flow cross-section, parallel
to the cylindrical axis and to plot a space-time diagram I(z,t) (Fig. 2). Using a 2-d camera, it was
also possible to record the radial distribution of the light intensity and to plot the space-time
diagram I(r,t) (Fig.3) .
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
Fig.2: Cross-section of the flow regimes visualized using Kalliroscope platelets: CF, TVF, WVF,
MWVF et TTVF
For PIV measurements, the flow was seeded with spherical glass particles of diameter 8-11 µm and
a density ρ = 1,6 g/cm-3 in concentration of about 10-4 %. The Reynolds number of these particles in
water is less than 0.1 so that the particles are assumed to follow the flow streamlines. The PIV
system consists of two Nd-Yag Laser sources, a MasterPiv processor Tecflow and a CCD camera
Kodak with 1034 x 779 pixels. The time delay between two Laser pulses varies from 0.5 to 25 ms,
depending on the Reynolds number. We have performed PIV measurements in the circular Couette
flow (CCF), in the Taylor Vortex Flow (TVF) and Wavy Vortex Flow regimes in order to calibrate
our data acquisition system and to fit data available in the literature for the two regimes (Wereley
ST et al (1998), Hwang JY et al (2004)). In the circular Couette flow, the spherical glass particles
are uniformly distributed (Fig. 3a) while in the TVF and WVF, the particles are concentrated in the
periodic vortex structures (Fig. 3b). The worst estimate of the error on the particle displacement
measurement is about ± 0.1%. The temporal resolution between two laser pulses of a few
nanoseconds over a period of 10 ms results is negligible. In the PIV technique, the flow in the test
area of the meridional plane(r,z) is visualized with a thin light sheet which illuminates the glass
particles motion of which can be recorded at short time intervals. The distance between two
consecutives images allows for determination of the flow local velocity. We have recorded 195
pairs of images of size 1034x779 pixels. Images were sampled into windows of 32x32 pxels2 with a
recovering of 50%. The velocity fields were computed using the intercorrelation function that is
implemented in the software “Corelia-V2IP”. The spatial intercorrelation of images is represented
by a “resemblance function” of a chosen image with respect to another; this intercorrelation is
calculated as follows:
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
r
r r
Σr ( I 1 ( x ) − µ1 ).I 2 ( x + s ) − µ 2 )
r
CCI 1 I 2 ( S ) = x
(1)
σ 1σ 2
where µ1 , µ 2 are the averages and σ 1 , σ 2 represent the standard deviations of the functions
I 1 , I 2 (Lecerf A (2000)). The results of these processing is illustrated by 2D velocity fields (Fig. 5),
the inflow and outflow are clearly evidenced in the case of the TVF and WVF.
Fig.3: Cross section of flow visualized with glass particles for the CF and MWVF
3. Results
The space-time diagrams I(z,t) and I(r,t) have been used to determine the spatiotemporal properties
of the flow for different values of the control parameters : wavelength and its variation, frequencies
in time dependent regimes.
Fig.4 : Space-time diagrams
for Re = 880 : a)
axial distribution I(z,t), b) radial distribution I(r,t)
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
Fig.5: Velocity field from PIV measurement: Radial and axial velocity profiles for Re = 125 (TVF),
Re = 880 (WVF)
The PIV has been used to visualize the flow streamlines in the cross section of the plane (r,z) and to
measure the radial and axial velocity components vr(r), vz(r) at a given axial position or vr(z) and
vz(z) at a given radial position (Fig.5). The radial velocity component has been fitted by a
polynomial function in order to satisfy the non-slip condition at the cylindrical wall (r = a, r = b).
We have calculated the time-average velocity components in the axial and radial directions (Fig.
5b-f). From these velocity profiles, we have deduced different quantities characterizing the flow
fluctuations in the meridional cross section for each regime: the kinetic energy, the vorticity field
and some components of the shear rate tensor. The vorticity fields and velocity components show
that in the Taylor vortex flow inflow and outflow are almost symmetric while in the wavy vortex
flow, there is a dissymmetry between outflow and inflow because of the oscillations of the
separatrices
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
Fig.6: Space-time diagrams for Re = 880: a) vr(z,t) taken at ξ = 0.5, b) vz(z,t) at ξ = 0.25 or ξ = 0.75
Fig.7: Space-time diagrams for Re = 880: a) vr(r,t) at outflow position b) vz(r,t) in
positive vortex.
the core of
The instantaneous velocity components can be superposed chronologically at regular time intervals
in order to obtain space-time diagrams (Fig.6 & 7). The resulting diagrams are colored coded as
follows: the red color correspond to positive values of the velocity and blue to the negative values.
For example in Fig. 6-a, the red color corresponds to outflow and the blue color to the inflow. In
Fig. 6-b, the red color correspond to the positive vortex core of the vortex and the blue color to the
negative vortex core. The radial velocity in the gap reaches the maximal value in the middle of the
gap and vanishes at the cylinder walls. We have compared these space-time diagrams (Fig. 6 &7)
with those obtained from visualization by Kalliroscope suspension (Fig.4). A first glance, we have
realized that the space-time diagrams obtained by Kalliroscope particles are very similar with the
space-time diagram of the radial velocity component vr(z,t) and vr(r,t). We have compared the timeaverage profile of the light intensity reflected by Kalliroscope particles and compared it with the
measured velocity profiles for the TVF and WVF. Fig. 8 illustrates the space-time diagrams for the
WVF. These plots highlights the fact that Kalliroscope particles give a signature of the radial
velocity component measured in the centre of the gap (r-a= 0.5 d). A similar comparison done with
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
the envelopes the space-time diagrams in the axial and radial directions leads to the same
conclusion.
a)
b)
Fig.8: a) Axial Profile taken at ξ = 0.5: a) light reflected intensity I/Imax, b) radial velocity
component Abs(Vr/Vrmax).
4. Discussion
The visualization technique by means of reflective particles has been a big issue in Fluid Mechanics
for a long time and has been addressed regularly in literature. Recent numerical simulations
[Gauthier et al.] have shown that the Kalliroscope or iriodin particles may be related to the radial
velocity component but no measurement were provided to sustain these arguments. The comparison
of the space-time diagrams obtained from flow visualization and PIV measurements performed for
different flow regimes has allowed us to confirm that in the case of the fixed outer cylinder the
reflective particles in the flow give information on the radial velocity component. Therefore, the
commonly admitted conjecture that the reflective particles give information on the shear rate (Savas
Ö (1985)) is in contradiction with the results of the Fig. 7. Our results give a more precise content
on the fact the small anisotropic particles align with the flow streamlines (Wereley ST et al (1998),
Hwang JY et al (2004), Wereley ST et al (2002), Wereley ST et al (1999)) by giving the precision
on the velocity component which bears these alignment. A further investigation is underway for the
case of the spiral vortex flow in the counter-rotating cylinders.
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
Acknowledgments
This work has benefited with a financial support from the CPER-Programme “Maîtrise de la
Combustion dans les moteurs”. We thank B. Lecordier and D. Allano for interesting discussions on
the PIV technique.
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