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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
Stereo PIV measurements of turbulence generated by a rectangular
fractal grid
C Cuvier1, S Zheng2 and J M Foucaut1 1: Laboratoire de Mécanique
de Lille, 59651 Villeneuve d’Ascq Cedex, France
2: Department of Aeronautics, Imperial College London, SW7 2AZ,
UK * Correspondent author: [email protected]
Keywords: Stereo PIV processing, Grid turbulence
ABSTRACT
In this paper we study the turbulent flow generated by a
rectangular fractal grid in the wind tunnel at Lille
Laboratory of Mechanics (LML). Two vertically aligned
Stereoscopic PIV systems were used to look at the
turbulence generated by a rectangular fractal grid at two
Reynolds numbers. A total of 20,000 image pairs were
acquired, and the data was processed by the modified version of
the Matpiv toolbox by LML. A self-calibration
similar to the one proposed by Wieneke (2005) was applied with
the Soloff et al. (1997) reconstruction method. The
results were compared with previous hot-wire measurements, and
the mean statistics and pdf showed good
agreement. The spectra of the inertial subrange calculated from
the SPIV result also agreed with the hot-wire data,
which validated the use of Taylor’s hypothesis under high
turbulence intensities (17%U∞ in this case). The mean
statistic profiles revealed the shear layer between the jet
created by the center of the grid and the wake from the
bars.
1. Introduction
The study of turbulence dates back to decades ago. Amongst many
turbulent flows, grid
generated turbulence is of particular interest for both
fundamental and applicational reasons.
Hurst & Vassilicos (2007) proposed new classes of fractal
grids, and the square one has been of
particular interest and studied in many following work. The
typical fractal generated turbulence
has a long production region followed by a power law decay
region, and the peak turbulence
intensity level can reach up to 12%U∞. Gomes-Fernandes et al.
(2012) studied the scaling of the
turbulence generated by such grid with a third dimension to
include the effect of drag coefficient
of each individual bars. The authors proposed that
x*����
= 0.21L�/(0.231C�t) (1)
and
u'~C�t/L (2)
where Cd is the drag coefficient of the bars and L0,t0 is the
length and width of the first iteration
of bar, respectively. The fractal generated turbulence also
showed the existence of a non-
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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
equilibrium region where some classical scaling rules do not
hold, and thence makes it
fundamentally interesting to further understand the physics.
Later on, a rectangular fractal grid
was designed to increase the transverse length scale of the
turbulent flow to simulate a local
stratum of atmospheric turbulent boundary layer. The turbulence
generated by the rectangular
fractal grid is different in several aspects of that generated
by square fractals. The purpose of the
current study is to use stereoscopic PIV to look at the center
and behind one of the largest
horizontal bars at the streamwise location where turbulence
intensity peaks, and, by comparing
the data acquired using the two methods, to further understand
the physics of the flow.
2. Experimental setup
The experiment was performed in a closed-return wind tunnel at
the Lille Laboratory of
Mechanics, and the wind tunnel test section was 20m in length
with a 2m x 1m cross section. The
facility is temperature controlled, and all data were acquired
at 17℃. A rectangular fractal grid to
fit the size of the tunnel was designed and mounted at the
entrance x=0m, and the PIV
measurement location was centered at 3.55m downstream of the
grid where the local turbulence
intensity as measured by hot-wire is 17%U∞. The design of the
fractal grid is not provided in the
present paper because it is patenting at this time.
With such a grid the turbulence intensity in the center of the
test section increases along the
streamwise direction up to a maximum and then decreases. A
preliminary campaign of
measurement by single hot wire has allowed the determination of
the maximum turbulence
location. The PIV was installed at this location. Two regions
were measured simultaneously by
SPIV: one in the wake of a bar (y = 0.17 m) and one behind the
center of the grid (y = 0.5 m).
Four 16 bit LaVision sCMOS cameras with 5.5M pixels were mounted
on the side of the wind
tunnel to build two stereoscopic PIV systems, as shown in figure
1. Two sets of Nikon micro
Nikkor lenses were used, i.e. 200mm and 105mm for field of view
of size 17 x 11cm, and 33 x
21cm, respectively. Two independent setups were used with
different size of field of view as
mentioned above, each with two Reynolds numbers (U∞=6m/s and
U∞=9m/s). To generate the
laser sheet, a dual-pulse Nd:YAG laser from B.M.Industries was
used with output power of
200mJ/pulse operated at 532nm wavelength. A set of spherical and
cylindrical lenses was used
to pass the laser sheet from the bottom of the wind tunnel, and
to orient it along the streamwise
direction at the center plane of the grid. As a result, two 2D3C
velocity fields were acquired
simultaneously for each experiment.
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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
The data was processed by the modified version of the Matpiv
toolbox by LML. A self-
calibration similar to the one proposed by Wieneke (2005) was
applied with the Soloff et al.
(1997) reconstruction method. For both fields of view, the
analysis was done with four passes
starting with 64 x 64 pixels and ending with 26 x 32 pixels
interrogation window size which was
found to be the optimal final window size. Also, before the
final pass, image deformation was
used to improve the quality of the results. The final
interrogation window size corresponds to 1.7
mm² in the physical space for the small field of view and 3.3
mm² for large one. The mesh
spacing was 0.5 mm in both directions for the small field of
view and 1 mm for the large one,
corresponding to an overlap of about 60 %. A maximum
displacement of 10 pixels was chosen in
the region of the wake interaction to ensure good results for
the turbulence intensities.
Fig. 1 Layout of the experimental setup with calibration
target.
2. Results
A total of 20,000 image pairs were acquired for each individual
data set. Figure 2 shows a
snapshot of instantaneous streamwise velocity at two locations
recorded simultaneously. It is
clear that in the wake of the bar (y ~ 0.17 m) the velocity is
lower than in the center (y = 0.5 m)
where the flow is accelerated. The streamwise mean and
turbulence intensity evolutions are
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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
compared against previous hot-wire (HW) measurements taken at
the same facility. The results
are shown in figure 3 and figure 4, respectively. The velocities
are normalized by U∞.
Fig. 2 Contour of large field instantaneous streamwise velocity
U for �� = 9�/�.
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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
Fig. 3 Mean streamwise velocity measured by hot-wire (black) and
PIV (colours) data for
�� = 6�/� and �� = 9�/� at the center (closed symbols) and in
the wake of a bar (open symbols)
for two magnifications.
In order to improve the visibility of the Figures only 3 points
of the HW which present a spacing
of 55 cm along x, and every 30 are plotted for the PIV. From
figure 3, it can be seen that the
mean profiles computed from two types of measurements collapse
well with each other for both
cases. The minor discrepancies between the two types of results
are well within the accuracy of
the measurements. The mean velocity is decreasing monotonically
along x the centerline,
whereas it increases behind the bar indicating a recovery from
the velocity deficit produced close
to the grid.. From figure 4, the turbulence intensity measured
by the two measurement methods
agree well, with discrepancies smaller than 1%U∞ The steamwise
turbulence intensity is
measured to be 17%U∞, which is higher than previously reported
values generated by the square
fractal grids (see e.g. Mazellier, N., & Vassilicos, J. C.
(2010); Gomes-Fernandes et al., 2012 ). . The
turbulence intensity along the centerline peaks at approximately
x= 350 cm, while
monotonically decreases behind the bar.
Fig. 4 streamwise turbulence intensity measured by hot-wire
(black) and PIV (colours) data for
�� = 6�/� and �� = 9�/� at the center (closed symbols) and in
the wake of a bar (open symbols)
for two magnifications.
The pdf of streamwise velocity fluctuations and the spectra are
compared against previous hot-
wire measurements. The results are shown in figure 5 and figure
6, respectively. From figure 5, it
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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
can be seen that the pdf computed from two types of measurements
collapse well with each
other for both measurement cases. The pdf at the center is
strongly skewed, showing more
positive fluctuations in this region, which can be originated
from the jet at the center of the grid.
Fig. 5 PDF of the streamwise fluctuation velocity for both PIV
(small field of view) and Hot-Wire
measurements for �� = 6�/� (left) and �� = 9�/� (right).
Fig. 6 Streamwise spectra calculated by hot-wire (black) and PIV
(red) data for �� = 6�/� (left)
and �� = 9�/� (right) at the center of wind tunnel.
The spectra calculated from the PIV data with small field of
view at the center of the tunnel are
plotted in figure 6 against the hot-wire data measured at the
same location. It is shown that, the -
5/3 slope in the inertial subrange of the spectra is well
captured by the PIV experiment. Note
that the hot-wire data was computed using the Taylor’s
hypothesis with local turbulence
intensity of 17%U∞, and the result validates the hypothesis
under relatively high turbulence
intensity at least in the present flow. It is also noticed that
the dissipative range of spectra for the
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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
9m/s case starts above k=103, which is higher compared to the
6m/s case. As a result, the
discrepancy between two spectra computed by the hot-wire and PIV
data is larger for the 6m/s
case as the resolution of PIV stays the same. The spectra will
be further analyzed based on
Foucaut & Stanislas (2002) and Foucaut et al. (2004) in
order to characterize the measurement
noise and to compute derivatives with a good accuracy to obtain
a better characterization of the
turbulence.
Figures 7 a and b give the mean velocity profiles of the
streamwise U and vertical V components,
respectively, as a function of y for the two positions in the
wind tunnel at two velocities. The U
component presents a maximum in the center and an inflection
point in the wake. The profiles of
U seems symmetrical about y = 0.5 m. The profiles of V presents
a maximum around y = 0.15m
and seems non-symmetrical. The Reynolds number effect is more
visible in the vertical direction
as it is in the same direction with the span of the wake.
(a) (b)
Fig. 7 Mean velocity profile of the streamwise (a) and vertical
(b) velocity components.
Figures 8 a, b and c gives the normalized turbulence intensity
profiles of all three components for
the two cases. The streamwise component shows a maximum of
fluctuations at y = 0.5 m and a
minimum at y = 0.12 m, which corresponds well with the local
gradient of the streamwise mean
velocity as shown in figure 7 a, suggesting a production
mechanism. The spanwise component
gives sensibly the same behavior but the profiles are more flat
in the center than for the
streamwise component. The vertical component shows a local
minimum at y = 0.5 and a
miximum around y = 0.33 m. This might suggest that the vertical
location y = 0.33 m is the
interface where the jet created at the center of the grid meets
the wake from the bar, inducing a
stronger vertical movement. Figure 8 d give the profiles of
turbulent shear stress uv normalized
by U2∞. They are anti-symmetrical with maximum magnitude at 0.33
m
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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
(a) (b)
(c) (d)
Fig. 8 Turbulence intensity profiles of the streamwise (a),
vertical (b) and spanwise velocity
component (c) and turbulent shear stress (d).
4. Conclusions
A double SPIV experiment was conducted in the LML wind tunnel in
the wake of a rectangular
fractal grid. Two regions were measured simultaneously: the
first in the wake of a bar and the
second in center where the wake of two bars interact. The
results give a very good collapse with
hot wire results in term of spectrum and PDF. SPIV gives the
three component of the velocity
which useful the statistical characterization. More it gives
spatial information which can be
studied to obtain the links between the two regions. As an
example the two-point correlations
Ruu computed in the wake with the fixed point in the center is
proposed in Figure 9. The
correlation reaches a level of 0.24 which corresponds to a high
level of coherence between the
two regions. The correlation is negative because there are
probably large structures created
between the bar and the center which gives opposite sign of the
streamwise velocity in both
regions.
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18th International Symposium on the Application of Laser and
Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 –
7, 2016
Fig. 9 Correlation Ruu in the wake region computed with the
fixed point in the center.
5. Acknowledgement
The authors acknowledge the support from Marie Curie FP7 through
the MULTISOLVE project
(grant No. 317269). This research work has been succeed thanks
to the recent LML wind tunnel
modifications supported by CISIT, la Region Hauts-de-France,
l’Union Européenne et le CNRS.
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