12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

THREE-DIMENSIONAL TURBULENT JET STUDY USING VOLUMETRIC PARTICLE
TRACKING VELOCIMETRY
Nimesh Virani
Department of Mechanical, Automotive andMaterials Engineering
University of Windsor
401 Sunset Avenue, Windsor, Ontario, N9B 3P4,
Canadaviranin@uwindsor.ca

Vesselina Roussinova
Department of Mechanical, Automotive andMaterials Engineering
University of Windsor
401 Sunset Avenue, Windsor, Ontario, N9B 3P4,
Canadavtr@uwindsor.ca

Ram Balachandar
Department of Civil and Environmental Engineering
University of Windsor
401 Sunset Avenue, Windsor, Ontario, N9B 3P4, Canada
rambala@uwindsor.ca

ABSTRACTThis paper presents the three-dimensional (3D) evaluation ofa turbulent free jet using volumetric particle tracking
velocimetry (3D-PTV). The volumetric measurements (V3VTM)
results are complemented with laser Doppler velocimetry (LDV)
measurements. Mean velocity and turbulence quantities
calculated from both techniques are compared, and similarities,
as well as differences in results, are discussed. Special attention
is paid to achieving higher spatial resolution in the depth-wise
direction for the volumetric measurements. A final resolution of
0.036d is achieved, (where d is the jet exit diameter) in the depthwise direction. Measurement uncertainty estimates arecalculated for the V3V measurements based on a systematic
approach to quantify the uncertainty based on the volumetriccalibration and reconstruction error. The turbulent jet has a
Reynolds number of 38,500 based on the nozzle exit diameter(d) of 7 mm and exit velocity, Uj, of 5.5 m/s. Due to V3V’s
capability of providing access to all nine components of thevelocity gradient tensor, the study of jet’s behaviour in the
spanwise plane is feasible. Global jet entrainment at different
axial positions is calculated for the spanwise plane and comparedwith the results in literature.

Violato and Scarano (2011, 2013) attempted to understand the
3D behaviour of flow transition and jet core breakdown incircular jets, which plays a considerable role in the generation of
acoustic noise.
The measurement performance of Tomo-PIV relies on ahigh concentration of successfully reconstructed particles in themeasurement volume. Higher seeding particles in the flow canboost the number of reconstructed particles after the processing
stage, albeit, it results in the ambiguity of the reconstruction
process and ghost particles (Elsinga et al., 2011; Discetti and
Coletti, 2018). To overcome this limitation, Boomsma andTroolin (2018) implemented a novel technique for particle
reconstruction with improved accuracy and reconstruction
density called Dense Particle Identification and Reconstruction(DPIR). It can manage particle image density of 0.05 ppp with areconstruction rate of 91 % real particles. Owing to DPIR’s
superior performance in the reconstruction of particles andvolumetric PTV’s capability of achieving fine measurement
resolution, we have performed volumetric PTV with the DPIR
algorithm.
The objective of this study is twofold. Performing
volumetric measurements provides us with an opportunity to
study the jet in the relatively less explored spanwise plane, andwe have also complemented the analysis with the wellestablished LDV technique. LDV dataset facilitates thevalidation of the more recently introduced volumetric technique.
Additionally, LDV measurements are time-resolved, and they
can capture contributions from small-scale flow structures,
hence, using it as a reference confirms V3V’s ability to capturesmall-scale turbulence.
Experiments were performed in the jet experimental facility
at the University of Windsor. The jet is generated from a pipe,with a diameter d = 7 mm and 70 mm long. It is released into aquiescent water channel filled with water and with a crosssection of 43d wide and 43d deep. In the streamwise direction,
the channel is 200d long. The jet opening is at the centre of thechannel in the spanwise and depth-wise directions. The water
channel is made from a transparent plexiglass material, whichenabled optical access for velocity measurement. For this study,
x, y, and z coordinates refer to streamwise, transverse andspanwise directions, respectively. The instantaneous velocity

INTRODUCTION
The evaluation of large-scale coherent structures in the nearfield of a turbulent jet requires the complete velocity field (i.e.
three velocity components) in the 3D domain (Liepmann and
Gharib, 1992; Discetti and Coletti, 2018). Such full volumetric(3D-3C, i.e., three-dimensional and three-components)
measurements become possible with the advent of new hardwarein photogrammetry and advanced processing algorithms.
Several studies explored the near field dynamics of the coherent
structures and their effects on the self-similar zone of a turbulent
axisymmetric jet, starting from the seminal work of Crow andChampagne (1971) and George (1988) among others. Recently,
the tomographic particle image velocimetry (Tomo-PIV)
technique was used by Breda and Buxton (2019) to obtain 3D
velocity measurements. The study investigated the effect ofcoherent structures in the near field of a turbulent jet and theireffect on the rate of entrainment. Similar, investigations by1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
a)
0.20

1.0

0.8

0.15

U 0.6
Uc

0.10

u'

2

Uc

0.4
0.05
0.2

0.0
-1.0

V3V
LDV

-0.5

0.0

0.5

0.00
1.0

y d

b)
0.14

0.010

0.12
0.005

0.10

v'

2

Uc

u' v'

0.08
0.000
0.06
0.04

U2c

-0.0050.02

Figure 1. Experimental setup and V3V measurement systemarrangement

0.00
-1.0

-0.5

0.0

0.5

-0.0101.0

y d

and corresponding velocity fluctuations are denoted by u, v, w,
and u’, v’, and w’, respectively. The associated mean velocities
are defined by U, V, and W. The jet is fed by an overhead watertank which is maintained at a constant level by a continuous
water supply from a reservoir using a pump. The jet facility andthe experimental setup are shown in Fig. 1.
The commercial V3V system (TSI, Inc.) consists of three
PowerView cameras mounted on a custom-designed triangularshaped stand. A dual pulsed Nd: YAG laser (200 mJ/pulse) anda LaserPulse synchronizer form the essential components of thesystem. The flow is illuminated by a laser cone generated from25 mm and 50 mm cylindrical lenses staggered at the laser
opening. The flow is seeded with 60 μm polyamide particles. All
three cameras have a CCD array with 8 million pixels and 3320
× 2496 resolution, and they are equipped with 50 mm lenses withthe aperture setting of f#8. The camera mounting frame islevelled and adjusted to ensure that it is parallel with the channel
walls using an alignment laser. Laser pulses are straddled at 100
μs and the measurement was performed at 5 Hz. A total of 1500
images were captured and analyzed with a final measurement
volume of 18d × 13d × 5d in the x, y, and z directions.
Instantaneous vectors are derived from particle images
captured using TSI INSIGHTV3V-4G software. A DPIR
algorithm based on the work of Boomsma and Troolin (2018) isused in a multi-pass mode for identifying, reconstructing andtracking particles. It starts with the identification of 2D particle
locations on camera sensors (in both frames) for all threeapertures, which leads to the determination of 3D particle
locations in a real-world coordinate system by triangulating eachparticle using its image from all camera sensors. Once the 3D
location is known, particles are tracked between two frames andthree velocity components are calculated. Finally, the randomly

Figure 2. Comparison between LDV and V3V results in theradial direction at a streamwise location of x = 3d

distributed vectors from all 1500 images are ensembled andstatistics are calculated on a regular grid using an in-house
MATLAB code. Detailed uncertainty analysis was conducted toquantify the uncertainty levels in all three components ofvelocity. The w-velocity has a maximum uncertainty of 7% andthe other two have less than 3%.
V3V results are complimented with point-wise velocity
measurement using a two-velocity component LDV system(Dantec Dynamics Inc.). Two orthogonal velocity components u
and v are acquired simultaneously by operating the LDV system
in coincidence mode. Laser wavelengths of 532 nm and 561 nm
are used for measuring streamwise and transverse velocity
components, respectively. To avoid directional ambiguity, afrequency shift is applied by operating a Bragg cell at 80 MHz.
The resultant measurement probe volume is 0.194×0.194×3.2
mm3 with a fringe spacing of 4.55 μm. For signal processing, a
BSA F600 processor is used, and data acquisition is controlled
by BSA flow software v6.72. Maximum uncertainty for the LDV
measurement is less than 3% for turbulence quantities and lessthan 1% for mean velocities based on a confidence interval of95%.

RESULTSFor volumetric PTV, mean and turbulence quantities arecalculated on a regular grid (equally spaced) by spatial binningand ensemble averaging over 1500 data sets. Here, each snapshot

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
Validation
V3V and LDV measurements are compared near the jet exit
at a streamwise location of x = 3d. In Fig. 2(a) streamwise mean
velocity (on the left axis) and rms of turbulence fluctuations (onthe right axis) are compared with the corresponding LDV
measurements at the same location. Both quantities arenormalized by the local centreline velocity, Uc. Peak turbulence
level and mean velocity profile in the potential core and shear
layer regions show excellent agreement between the twotechniques. In Fig. 2(b), radial profiles of rms of turbulencefluctuations in the transverse direction (y) and Reynolds shear
stress are provided. For both Reynolds normal and shear stresses,
peak values occur at y/d = 0.5, which represents the strong shear
in the near field mixing layer of the jet. The linear region of theshear stress profiles near the centre of the jet (at approximately 0.14< y/d <0.14), coincides with the linear distribution of shear
stress observed for the pipe jet, as reported by (Xu and Antonia,
2002). The near-field radial profiles provide insights into thecondition of the jet at the exit of the pipe. Overall, thiscomparison reiterates that the V3V technique can capture theturbulent statistics faithfully.
The mean streamwise centreline velocity decay is shown in
Fig. 3(a) for the data recorded by both techniques. The selfpreserving round jet decay rate, K, can be calculated by

a)
3.5

V3V
LDV

3.0
2.5

Uj
2.0
Uc
1.5
1.0
0

2

4

6

8

10 12
x d

14

16

18

20

b)
0.30

0.30
V3V
LDV

0.25

0.25

0.20

0.20

u' 0.15

0.15

2

Uc
0.10

0.10

0.05

0.05

0.00
0

2

4

6

8

v'

2

Uj 1 x x0= ( − )Uc 𝐾 d dUc(1)

In Eq. (1), x0 is the virtual origin of the jet. Fitting Eq. (1) to thevelocity decay rate data between x = 10d and x = 20d provides
the decay rate for LDV and V3V data as 5.97 and 6.12,
respectively. These values are similar to what was reported byBoersma et al. (1998) and in reasonable agreement with eachother. Apart from the decay rate, the length of the potential coreof jet can be estimated by centerline velocity decay data. In thepotential core, jet velocity remains almost the same as jet exit
velocity, Uj. By fitting a straight line to the velocity decay
profile, we found the length of the potential core as x ≈ 5d.
In Fig. 3(b) rms values of axial and transverse velocity
fluctuations normalized by the local centerline velocity areplotted along the centerline of the jet. In the entire potential coreregion, turbulence levels are constant, and both values linearly
increase after the end of the potential core region until x ≈ 10d.
After 10d, it starts to achieve a plateau region where it remains
almost constant at about 25% and 20% levels for streamwise andtransverse velocities, respectively. Fig. 3(b) highlights theanisotropic behaviour of turbulence along the centerline of thejet. Where jet anisotropy can be estimated by the ratio between
rms values of u-component and v-component of velocity. The
maximum anisotropy is found at the immediate region after theend of the potential core, where u’ is 35% to 40% more than thev’ and/or w’, for both cases. Thorough validation of V3V datawith LDV in the radial direction as well as along the centerlineof the jet using mean quantities and second-order turbulent
moments, confirms the suitability of volumetric measurements
for further investigation.

0.00
10 12 14 16 18 20

x d

Figure 3. LDV and V3V data along the centerline of the jet

is uncorrelated to each other and vectors for each snapshot arestochastically distributed owing to the Lagrangian approach
used for the current case (Godbersen and Schröder, 2020).
Unlike PIV, where bin size is restricted by the predefinedcorrelation windows, for the PTV, the bin size is only restrictedby the number of available snapshots for ensembling. The
process starts by combining randomly spaced 3D vectors in
different bins based on their locations. Outlier vectors are firstremoved by applying a threshold of minimum and maximum
absolute velocities for all velocity components. After thatstandard deviation for each bin is calculated using all available
vectors in each bin. Any vectors exceeding the local mean value±3σ for u, and v and ±2σ for w velocity components are removed.
Here, σ is the local standard deviation of vectors. Corrected
vectors are used for calculating statistics in each bin. Based on
the available snapshots and the requirement for maintaining alower uncertainty level, a final bin size of 2×1×1 mm3 isachieved with an overlapping of 75 %, which resulted in the final
resolution of 0.5×0.25×0.25 mm3 for the uniform grid. This
resolution is equivalent to having 28 measurement points acrossthe diameter of the jet in the radial direction. For consistency,
LDV measurement is also performed with the same spatial
resolution.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
3.5

that decomposes the flow field based on energy-containing
largescale (coherent) structures. It provides a complete
orthogonal set of spatial eigenfunctions, which are also known
as modes, and ranks the modes based on their energy level. The
eigenvalues, λi, related to these modes, represent the amount ofkinetic energy of the flow field. This essentially means that the
low-order modes represent the large-scale structures and higherorder modes correspond to small-scale structures. Here, POD isapplied on a spanwise 2D plane (yz) located at the axial locationof x = 3d. All 1500 snapshots are used for this analysis as they
are uncorrelated.
The POD is performed on the fluctuating velocity u’ = [u’,’v , w’] of the instantaneous velocity field u = [u, v, w] which canbe written as a snapshot matrix U ∈ 𝑅𝑁𝑡×𝑝. Here, 𝑁𝑡 represents
the number of snapshots and p is the number of grid points on
the 2D plane considered here. Following Essel et al. (2020) andCortina-Fernández et al. (2021) singular value decomposition(SVD) technique is applied to obtain the decomposition basis inspace, φ, and time, ψ and it decomposes the matrix U as follows

V3V
Crow & Champagne 1971
Zaman 1996

3.0

Q 2.5
Q0
2.0

1.5

1.0

0

2

4

6

8

10

x d

Figure 4. Global entrainment ratio of the jet

Global Jet Entrainment
A full volumetric 3D dataset of jet provides access to the
spanwise plane of the jet at different axial locations. This allows
studying one of the most interesting properties of the jet,entrainment. Jet entrainment can be calculated using the mean
flow data. Usually, it is evaluated based on the streamwise
volumetric flow rate Q, which is normalized by its initial value
at the nozzle exit, Q0 (Grinstein, 2001). Here, the volume flux isdefined by an area integral over the streamwise mean velocity
component following (Wygnanski and Fiedler, 1969; Crow andChampagne, 1971; Liepmann and Gharib, 1992).

U=ψ∑φ

where ψ is 𝑁𝑡 × 𝑁𝑡 orthogonal matrix, φ is p × p orthogonal
matrix and ∑ is a non-negative diagonal matrix with the same
dimensions as U . The matrix ∑ contains eigenvalues which
represent the energy associated with each mode and is arranged
in descending order. Further details about POD method
implementation can be found in Sen et al. (2007) and Meyer etal. (2007).
Here, spatial modes φ for all three velocity components (𝜑u ,𝜑v , 𝜑w ) are reconstructed using the low-order modes forunderstanding the dynamics of energetic structures. Theseenergetic large-scale structures and their effect on jet
entrainment were also studied by El Hassan and Meslem (2010)
for orifice jets. POD is a tool which facilitates the separation ofthese structures from the overall flow and hence it is applied in
the present study for a circular pipe jet case. The first 10 modes
are reconstructed and some of the selected ones are used in Fig.
5 to discuss the flow field. The vectors are plotted using the inplane components (𝜑v , 𝜑w ) and iso-contours represent the outof-plane (𝜑u ) component. In this way contribution from all threevelocity components is included. The contours in Fig. 5 reveal
high (𝜑u > 0) and low (𝜑u < 0) momentum regions (Essel et al.,2020) and it is normalized by the maximum value of 𝜑u among
all the modes presented here. The red circle indicates theapproximate edge of the jet for all the modes. The jet edge isidentified by a line on which, mean streamwise velocity of thejet becomes 10% of the local centerline velocity at x = 3d.
The first mode has kidney-shaped distinct high and low
momentum regions. This confirms the presence of large-scale
structures and their role in the entrainment of the jet, which ishighlighted by drawing the in-plane streamtraces. Streamtraces
demonstrate the entrainment mechanism by two distinct regionsof the jet, one is a circular region approximately at the edge ofthe jet and another is at the center of the jet where all
streamtraces converge. The second mode contains the ring shapestructure with low momentum and the related entrainment
process is revealed by the in-plane vectors. The jet edge circle
covers the entire zone where entrainment occurs.
In Fig. 5, odd and even number modes are divided between
the left and right columns. For brevity, some of the modes are

2π ∞Q = ∫ ∫ Ur drdθ
0

(3)

(2)

0

Here, r is the radial distance. The initial volumetric flux rate is
calculated as Q0 = 𝜋d2 U0 /4 . The volume flux rate can becalculated at any x location if the radial integration Ur
converges. The radial integration can be converged by including
enough area in the spanwise plane so that the entire surrounding
fluid region affected by the jet is included.
The ratio Q/Q0 is plotted against the axial distance x/d in Fig.
4. Entrainment calculation is only presented up to x/d = 10
because of the limit on measurement data available in the depthwise (z) direction. Entrainment calculated from present datashows a good agreement with Crow and Champagne (1971) in
the near field until the end of the potential core. Further
downstream Q/Q0 starts deviating from the previous data. Thisdifference can be attributed to the unconverged radial direction
integral and/or differences in the initial conditions andexperimental facility between Crow and Champagne (1971) andthe current case. For comparison rectangular nozzle jet data from
Zaman (1996) is also provided in Fig. 4.

Proper Orthogonal Decomposition
To understand the dynamics of large-scale structures andhow they are organized in the cross-stream plane, the snapshot
implementation of the proper orthogonal decomposition (POD)
method is carried out (Sirovich, 1987). POD is a powerful tool4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 5. Iso-contours of 𝜑u of POD modes 1, 2, 3, 4, 6, and 7 with superimposed vectors generated by 𝜑v and 𝜑w for the spanwise planeat x = 3d. The red circle shows the approximate edge of jet at the given axial location based on 10% of streamwise mean velocity. Here,ENT and EJE represent entrainment and ejection, respectively.

skipped and only the one which shows distinct spatial structures
are presented. As the mode number increases, the organizationof structures change for both odd and even number modes, albeit
in a unique way. However, one thing remains common for all themodes is that entrainment and ejection both occur within the area
covered by the jet edge. Previous researchers Liepmann and
Gharib (1992) and Romano (2002) discussed the role of ejectionof secondary transverse fluid and their relation to KelvinHelmholtz shear layer primary instabilities in axisymmetric jets.
This ejection of fluid can be related to a secondary counter-rotating mushroom shape structure found in the spanwise plane.
Traces of similar kinds of structures can be observed in higherorder modes (3, 4 and 7) in Fig. 5. These structures are very
similar to the counter-rotating vortices reported by Capone et al.
(2013) in the cross-stream plane at x = 2.5d. Although, theyreported these vortices using velocity vectors from flow
snapshots captured with a high-speed acquisition method, theirresemblance to the present structures is remarkable.

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
Elsinga, G. E., Westerweel, J., Scarano, F., and Novara, M.,
2011, "On the Velocity of Ghost Particles and the Bias Errors in
Tomographic-PIV", Experiments in Fluids, Vol. 50, pp. 825–
838.
Essel, E. E., Roussinova, V., and Balachandar, R., 2020,"Free Surface Effects on Spanwise Turbulent Structure in the
Far-field of Submerged Jets", Physics of Fluids, Vol. 32, pp.
035108.
George, W. K., 1988, "Self-preservation, and Its Relation toInitial Conditions, and Coherent Structures", Advances in
Turbulence, WK George & R Arndt, pp. 39–73.
Godbersen, P., and Schröder, A., 2020, "Functional Binning:
Improving Convergence of Eulerian Statistics from LagrangianParticle Tracking", Measurement Science and Technology, Vol.
31, pp. 095304.
Grinstein, F. F., 2001, "Vortex Dynamics and Entrainment
in Rectangular Free Jets", Journal of Fluid Mechanics, Vol. 437,
pp. 69–101.
Liepmann, D., and Gharib, M., 1992, "The Role ofStreamwise Vorticity in the Near-field Entrainment of RoundJets", Journal of Fluid Mechanics, Vol. 245, pp. 643.
Meyer, K. E., Pedersen, J. M., and Özcan O., 2007, "A
Turbulent Jet in Crossflow Analysed with Proper Orthogonal
Decomposition", Journal of Fluid Mechanics, Vol. 583, pp.
199–227.
Romano, G., 2002, "The Effect of Boundary Conditions by
the Side of the Nozzle of a Low Reynolds Number Jet",
Experiments in Fluids, Vol. 33, pp. 323–333.
Sen, M., Bhaganagar, K., and Juttijudata, V., 2007,"Application of Proper Orthogonal Decomposition (POD) to
Investigate a Turbulent Boundary Layer in a Channel with
Rough Walls", Journal of Turbulence, Vol. 8, pp. N41.
Sirovich, L., 1987, "Turbulence and the Dynamics ofCoherent Structures Part I: Coherent Structures", Quarterly of
Applied Mathematics, Vol. 45, pp. 561–571.
Violato, D., and Scarano, F., 2011, "Three-dimensional
Evolution of Flow Structures in Transitional Circular andChevron Jets", Physics of Fluids, Vol. 23, pp. 124104.
Violato, D., and Scarano, F., 2013, "Three-dimensional
Vortex Analysis and Aeroacoustic Source Characterization of
Jet Core Breakdown", Physics of Fluids, Vol. 25, pp. 015112.
Wygnanski, I., and Fiedler, H., 1969, "Some Measurementsin the Self-preserving Jet", Journal of Fluid Mechanics, Vol. 38,
pp. 577–612.
Xu, G., and Antonia, R. A., 2002, "Effect of Different Initial
Conditions on a Turbulent Round Free Jet", Experiments in
Fluids, Vol. 33, pp. 677–683.
Zaman, K. B. M. Q., 1996, "Axis Switching and Spreadingof an Asymmetric Jet: The Role of Coherent Structure
Dynamics", Journal of Fluid Mechanics, Vol. 316, pp. 1–27.

CONCLUSION
Volumetric three-component and three-dimensional velocity
measurements are performed for the axisymmetric turbulent
pipe jet case. The dataset is validated extensively with acompletely different and well-established measurement
technique. A positive match between both techniques
emphasizes the suitability of the V3V technique for measuring
this type of flow field.
For leveraging the availability of a complete velocity
gradient tensor, global entrainment in the spanwise plane of thejet is calculated and compared against the available literature.
POD technique is applied for revealing the flow structurearrangements which govern the entrainment and ejection
processes in a jet.

REFERENCES
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