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-
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.
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
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�/�.
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
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
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
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.
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.
References
Foucaut J.M, Carlier J, Stanislas M (2004) PIV optimization for the study of turbulent flow using
spectral analysis. Meas Sci Technol 15:1046–1058.
Foucaut J.M and Stanislas M (2002) Some considerations on the accuracy and frequency response
of some derivative filters applied to particle image velocimetry vector fields." Measurement
Science and Technology 13(7): 1058.
Gomes-Fernandes R, Ganapathisubramani B and Vassilicos J.C (2012) Particle image velocimetry
study of fractal-generated turbulence. Journal of Fluid Mechanics 711: 306-336.
Hurst D and Vassilicos J.C (2007) Scalings and decay of fractal-generated turbulence. Physics of
Fluids 19(3): 035103-035131.
Mazellier, N., & Vassilicos, J. C. (2010). Turbulence without Richardson--Kolmogorov cascade.
Physics of Fluids, 22(7), 075101-075125.
Top Related