Stereo PIV measurements of turbulence generated by a...

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-


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.


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


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�/�.


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


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


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


(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.


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.

Stereo PIV measurements of turbulence generated by a...

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