18th Australasian Fluid Mechanics ConferenceLaunceston, Australia3-7 December 2012

Volumetric Measurements by Tomographic PIV of an Open Channel Flow Behind a TurbulentGrid

T. Earl1, R. Ben Salah2, L. Thomas2, B. Tremblais3, S. Cochard1, L. David2

1School of Civil EngineeringUniversity of Sydney, NSW 2006, Australia

2Institut PprimeUniversite de Poitiers, 86968 Futuroscope, France

3Department XLIM-SICUniversite de Poitiers, 86968 Futuroscope, France

Abstract

This paper investigates the energy dissipation rate behindtwocombinations of trash racks (or meshes) in an open channelflow from tomo-PIV measurements. Five trash rack assembliesdivided the flume into four identical pools. Each trash rack as-sembly is composed of a fine wire mesh and two regular squaregrids, characterised by their mesh sizeM. The Reynolds num-bers with respect toM were 4300 and 9600 corresponding to amean velocityU through each pool between 0.35 and 0.315 m/s.This aim of this paper is to investigate the turbulent energydis-sipation behind two configurations of regular grids in an openchannel.

Introduction

The measurement of turbulence in a flow generated behinda regular grid has been extensively investigated, with originslinked to the conception of the hot-wire anemometer and usedin Taylor’s Statistical Theory of Turbulence (1935). The regu-lar grid was designed to generate homogeneous isotropic turbu-lence (HIT). A number of different time-resolved, point mea-surement techniques are used to measure small scale character-istics of turbulence and the mean turbulent energy dissipationrate 〈ε〉, such as hot wire anemometry (HWA), laser Dopplervelocimetry (LDV) and other novel probes [1]. However, thesetechniques are limited in that they cannot resolve large vortexstructures.

With the advent of particle image velocimetry (PIV), planar,spatially resolved measurements of turbulence have been made[4, 7]. From these results, it has been possible to measure theanisotropy of these turbulent flows by measuring two compo-nents of velocity. Stereo PIV can recover the 3 velocity com-ponents but not the full velocity gradient tensor. Only the ve-locity gradients that lie in the measurement plane can be com-puted, as the measurement takes place in a ‘thin’ planar lightsheet. Therefore, these techniques make the assumption aboutthe isotropy of the flow if one were to calculate the instanta-neous velocity tensors to obtain energy dissipation.

With techniques such as tomo-PIV [5], it is possible to obtainvolumetric velocity fields, i.e. all 9 components of the velocitygradient tensors. Tomo-PIV is technique that allows the deter-mination of three component, three dimensional (3C-3D) veloc-ity fields [5, 2, 8]. The concept is to record, with typically fourcameras, two sets of simultaneous images of particles that areseeded in the flow and illuminated by a thick laser sheet overa small time step. Those images are then used to reconstructthe light density distribution of each volume. Velocity vectorfields are then obtained by performing a correlation betweenthetwo volumes, which deduces the most probable displacements

of groups of particles. Akin to 2D PIV techniques, there arespatial limitations due to the interrogation window size ofPIVmeasurements [6, 7]. Recently Worthet al. [12] and Buchmannet al. [3] used tomographic PIV to measure turbulence, the laterpaper dealing specifically with grid generated turbulence in wa-ter.

This paper details the experimental facility and initial resultsobtained from measurements behind two configurations of reg-ular grids in an open channel. The aim is to investigate the flowstructures and turbulence dissipation of the flow.

Experimental Details

Experiments were conducted in an open channel (figure 1) atInstitut Pprime at the Universite de Poitiers, France. Thein-clined channel was rectangular in cross section with dimension500 × 304 mm2 (height× width, W) and had 30 mm thickperspex walls and base to allow full optical access. The chan-nel was divided into 4 identical pools that were separated bytrash rack assemblies, described further inTrash Rack and GridDetails. The inclination of the channel for the two trash rackassembly types presented was 5%. The weir gate height wasadjusted so that there was a regular head loss,∆H, across eachtrash rack with a constant flow rate ofQ= 34 L/s.

Pool 4 Pool 3 Pool 2 Pool 1

Reservoir

5 500 L

5000 mm

Reservoir

2 500 L

Trash rack assemblies

750 mm 750 mm 750 mm750 mm

Weir

34 L/s

Inclined channel

Figure 1: Schematic of experimental set-up.

Trash Rack and Grid Details

Each pool was separated by a trash rack assembly that was ap-proximately vertical in orientation. The trash racks were com-prised of, from upstream to downstream, a fine wire mesh andthen a pair of regular grids that were fabricated from 2 mm thickstainless steel plates. The grid pairs used were G1-G2 and G3-G4, with square opening geometries as shown in figure 2. Therewas a stream-wise spacing between the components of the trashrack that was nominally 90 mm. The solidity ratiosσ, definedby σ=(D/M)(2−D/M) are also defined in figure 2, whereD isthe thickness of each bar andM is the centre-to-centre bar spac-ing of the grid. The grid geometries furthermost downstream,

that is G2 and G4, are used for the dimensionless analysis in thispaper as the resulting turbulence downstream is characterisedby these grids.

M

M

GRADES (mm)

M D

Mesh

G1

G2

G3

G4

2.4

12

14

30

35

0.4

2

4

5

10

D

D

0.31

0.31

0.49

0.31

0.49

σ

Figure 2: Grid geometries.

Flow properties

The water temperature was 15.4±0.5◦ C, with associated kine-matic viscosityν ≈ 1.15× 10−6 m2/s . The mean velocity ofthe flow through each pool,U = Q/(hcW), wherehc is the flowdepth at the centre of the pool, was approximately 0.35 m/sand 0.315 m/s for the G1-G2 and G3-G4 configurations respec-tively. Likewise, the respective Reynolds numbers with respectto grid geometry were 4300 and 9600. The hydraulic radius,Rh = hcW/(2hc+W) for this channel was in the order of 0.1 mfor both combinations.

Tomo-PIV Details

Tomo-PIV measurements were taken in pool 3 to ensure a de-veloped flow (figure 3). The tomo-PIV system was comprisedof four 1600× 1200 px2 8 bit cameras positioned symmetri-cally in an inverted pyramid configuration, with nominal decli-nation and inward angles of approximately 20◦ (see figure 3).All cameras were fitted with 50 mm lenses, 532 nm pass opticalfilters and lens mounted Scheimpflug adapters, adjusted so thatthe camera focal planes were coincident with the laser sheet.Additionally, the apertures were set at atf# = 22 during acqui-sition for superior depth of focus. Neutrally buoyant, sphericalpolyamide particles of mean diameterd50 ≈ 56 µm were usedto seed the flow.

Z

X Y

Camera 1Camera 2

Camera 3 Camera 4

304 mmDirection

of flow

Trash Rack Assembly

ROI

5%

Y

XZ

275 mm

550 mm

ROI

Direction

of flow

ΔH

84

70 mm

100 mm

(a)

(b)

ΔH

20° 20°

20° 20°

20°

Trash Rack Assembly

Figure 3: Schematic of Pool 3 showing measurement volume orregion of interest (ROI) in (a) plan and (b) elevation. The originand axis orientation along with inverted pyramid configurationof the cameras are shown.

A thick laser sheet was used to illuminate the measurement vol-ume, realised with a Twins CFR ND:YAG laser with 120 mJper pulse. The measurement volume was 100× 70 × 15 mm3

(X × Y × Z) and was positioned centrally and aligned withthe flow direction in pool 3. This positioning corresponds toadimensionless region 16≤ x/M ≤ 23 for the G1-G2 configu-ration and 6.4 ≤ x/M ≤ 9.3 and for the G3-G4 configurationdownstream.

The time between corresponding images,∆t, was 2 ms, cho-sen to achieve mean particle displacements of 10 px for eachcamera. These image pairs (which make a velocity field) wereacquired at 5 Hz. The total data set consists of 5000 images percamera, corresponding to 2500 velocity fields for each grid con-figuration. The initial results presented in this article correspondto approximately 250 velocity fields for each configuration.

The tomo-PIV software used was developed using the SLIP li-brary [10] and developed at the Universite de Poitiers. Recon-struction was performed with MinLOS–MART (minimum line-of-sight, multiplicative algebraic reconstruction technique) [9].The volume size was 1380× 920× 211 voxels3 with each cu-bic voxel having sides of 0.076 mm, approximately 15% largerthan the pixel size. Processing was undertaken on an Intel Corei7 2.93 GHz machine, and each 2 GB volume took in the orderof 40 minutes to reconstruct.

Treatment of data

The tomo-PIV process is sensitive to a number of parameters,so image processing and calibration methods must be carefullyconsidered. Image processing to remove background noise wasconducted with a sliding 16×16 px2 mean window to ensurea homogeneous particle per pixel ofppp≈ 0.022 for all cam-eras at both time-steps. A gaussian filtering kernel was thenap-plied to smooth particle images, the kernel size chosen to matchthe average particle diameter. Small bubble entrainment inthewater due to the free surface and subsequent turbulent mixingthrough the trash rack assembly was evident, and as these cre-ated ‘particles’ larger than the mean, detracted from the qualityof image reconstruction. A pinhole model was used to calibratethe cameras. A calibration plate was traversed at 3±0.005 mmspacing through the illuminated volume. Due to the large de-viations in the lines-of-sight of each camera through the thickperspex walls, the camera calibration was improved with a selfcalibration technique analogous to Wieneke [11].

Preliminary results are obtained with a single pass cross-correlation program. A 64×64×64 voxel3 correlation volumewith 50% overlap was used to find the most probable displace-ment of particles across the two reconstructed volumes. Thisresulted in 6000 vectors per acquisition at a spatial resolutionof 4.9×4.9×4.9 mm3. A 5×5×5 filter kernel was used thatreplaced spurious vectors with the median vector in the filteringkernel. As tomographic reconstruction has been shown to beparticularly susceptible to noise [12], a bilateral filter was usedto filter the velocity fields, which was preferred over a gaussianfilter as it preserves edges.

Results

The data sets have been set to dimensionless volumes down-stream by dividing through by the respectiveM for each con-figuration. This is shown to be appropriate after comparing theenergy dissipation rate〈ε〉 as a function ofX for both cases (fig-ure 8), where〈. . .〉 denotes ensemble averaging.

The tomo-PIV captured the global flow characteristics. Figure 4shows contour plots in theXY-plane ofu for the G3-G4 con-figuration that were averaged over 250 velocity fields over the

laser sheet thickness∆Z. The measured averageu velocity of0.324 m/s correlates well withU estimated from the flow rate.Similarly, the time averaged results for the G1-G2 plots yield asimilar figure, albeit with a measured averageu of 0.354 m/s,which also corresponds well with the expectedU . The contoursindicate that the flow is decelerating in the stream-wise direc-tion; this is explained by the expansion of the volume of flow.There is a declination of the channel base in the stream wise di-rection however there is a comparatively level free surface. Thecontour plot also indicates that more velocity fields are requiredto form the mean field, owing to the high level of variability.

X/M

Y/M

77.588.59

1.5

2

2.5

U [m/s]

0.330

0.328

0.326

0.324

0.322

0.320

0.318

0.316

Figure 4: Mean velocity vector field showing contours ofu (m/s) and velocity vectorsu andv indicating flow from rightto left (in positiveX-direction, for configuration G3-G4.

The instantaneous vorticity fieldsω were analysed to comparethe level of vorticity present in each configuration. The tomo-PIV allows for full recovery of the velocity gradient tensors andhence vorticity. From figure 5, vorticity iso-surfces showingωz are plotted: The presence and power of vortex structures isgreater in the G3-G4 case. It is noted that G3-G4 has larger gridsizes in the trash rack and in a dimensionless sense, it is nearerto the back of the trash rack. In the following section it is shownthat these results give good qualitative agreement to the decaydissipated energy of the system, as with the decay in energy itis expected that the level of vorticity decays also.

Local Dissipation Rate

The trace of the local dissipation tensor, with componentsεi j

εi j = 2ν∑k

∂ui

∂Xk

∂u j

∂Xk(1)

is used to calculate the local dissipation rate〈ε〉 in the flow.

The average dissipation of the flow does not evolve over time,asobserved in figure 6. It was found that the dissipation is approx-imately 3.4 times greater in the G3-G4 configuration than in theG1-G2 configuration. The turbulent kinetic energy is greater inthe G3-G4 configuration and is dissipated in the basin (figure5).

The time averages were considered to determine whether thestatistics are well converged. The convergence of the mean dis-sipation rate is presented in figure 7. It is observed that conver-gence is achieved after 200 velocity fields.

Finally, the evolution in the spatial direction of the flow, the dis-sipation of space-time average, is presented in figure 8. In thisfigure, the data are averaged over time and in the planes perpen-dicular to the flow. It can be seen that the magnitude of dissipa-tion decreases exponentially, with a coefficient of attenuation of0.106. Initial studies into the eigenvalues of the energy tensordissipation were undertaken (not presented here) to investigate

X/M

1617

1819

2021

2223

Y/M

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Z/M

0

X/M

6.57

7.58

8.59

Y/M

1

1.5

2

2.5

Z/M

0

a)

b)

Figure 5:ωz iso-contours at 0.008 m−2 (red) and−0.008 m−2

(blue) for configuration (a) G1-G2 and (b) G3-G4 with velocityvectors.

0 50 100 150 200 2500

20

40

60

80

100

N

ε/2ν

[s2]

G3−G4 G1−G2

Figure 6: Evolution of the temporal average of the dissipationin G1-G2 and G3-G4, where N indicates the number of velocityfields considered.

the contribution of each velocity component. It was found thatthey evolve in parallel but at different magnitudes (when con-sidering the spatial direction of the flow, following figure 8),indicating anisotropy of the dissipation. These results are still

0 50 100 150 200 25010

20

30

40

50

60

N

ε/2ν

[s2]

G3−G4 G1−G2

Figure 7: Evolution of the mean dissipation over time for G1-G2 and G3-G4, where N indicates the number of velocity fieldsconsidered.

being analysed as this paper goes to press, but the initial find-ings show the benefits of recovering all velocity gradient tensorswhen studying turbulence, using a technique such as tomo-PIV.

5 10 15 20 2510

20

30

40

50

60

70

80

X/M

ε/2ν

[s2]

G3−G4 G1−G2

Figure 8: Energy dissipation in the direction of flow for bothG1-G2 and G3-G4 configurations with power law fit.

Conclusions

Tomo-PIV was used to measure the flow in a pool of an inclinedopen channel behind a trash rack. Two assembly configurationsof grids were compared: analysis of the vorticity and energydissipation show qualitative and quantitative agreement of thedecay of turbulent kinetic energy following a power law. Theenergy dissipation was found to decay exponentially in the di-rection of flow. By normalising with mesh size, the same powerlaw could be used to describe the decay. Initial analyses of theeigenvalues of the energy dissipation tensors show anisotropyof the decay, a finding made possible by the recovery of the fullvelocity gradient tensors through tomo-PIV.

Future Work

Two trash rack configurations that form part of the experimentaldata set were not included herein. More data are being analysedto ensure the quality of the statistical analysis. Furthermore,analysis of the relevant length scales is required to describe theevolution of dissipation. The spatial resolution and theireffecton the derivative variances in conjunction with differences be-tween the mean and total energy dissipation rate are being in-vestigated.

Acknowledgements

The authors would like to express gratitude for the continuedsupport of an Australian Postgraduate Award (APA) and JoanMcConnell scholarship. The experiments were conducted atthe Universite de Poitiers, France, and were funded by l’ANRVIVE3D and FEDER.

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