1. Proceedings of the 25th CANCAM
London, Ontario, Canada, May 31 – June 4, 2015
EFFECT OF ASPECT RATIO ON THE NEAR FIELD DYNAMICS OF FREE
SURFACE JET
Anuvrat Mishra
Department of Mechanical
Engineering
University of Manitoba
Winnipeg, MB, Canada
Mark F. Tachie
Department of Mechanical
Engineering
University of Manitoba
Winnipeg, MB, Canada
mark.tachie@umanitoba.ca
David C.S. Kuhn
Department of Mechanical
Engineering
University of Manitoba
Winnipeg, MB, Canada
david.kuhn@umanitoba.ca
ABSTRACT
The interaction of a rectangular turbulent jet with the free
surface for three jet-exit aspect ratios is experimentally
investigated using PIV. The jet exits from a sharp edged
rectangular orifice plate parallel to the free surface and has an
equivalent diameter De=10 mm. Aspect ratios of 1, 2 & 4 are
studied with a fixed offset of 3 De from the free surface.
Reynold’s and Froude numbers based on the bulk velocity
are 7300 and 1.35 respectively. Detailed 2-D velocity fields
are captured using the PIV in the central x-y plane for
0<X/De<23.5. The center-line velocity decay, velocity
profiles and turbulence intensities at several axial location are
compared to investigate the effect of jet exit aspect ratio on
jet – free surface interaction.
KEYWORDS: Free surface jets, aspect ratio
INTRODUCTION
The presence of a lateral free surface near a jet causes an
unequal entrainment on the two sides of the jet. As shown in
figure 1 a recirculation region is created in the fluid confined
between the jet and the free surface which creates a local low
pressure zone and deflects the jet towards the boundary. The
jet attaches to the free surface and emerges as a free surface
jet. This phenomenon is of particular interest since it has
potential engineering applications ranging from remote
sensing to the design of water dam spillways so as to mitigate
the effects of hydraulic shock.
Walker et al [1] reported the effect of Reynolds and Froude
numbers on circular turbulent jets discharged at a fixed offset
from the free surface and found the evolution of low
Reynold’s number jets faster as a free surface jet and higher
Froude number to create violent surface deformation thus
reducing the turbulence kinetic energy. The selective
tendency of an offset jet to deflect towards the solid wall or
the free boundary depending upon the offset from the either
boundary was investigated by Tsunoda et al [2] for a plane jet.
A circular turbulent jet with a fixed offset of 5 from the free
surface was investigated and compared against a free jet by
Tian et al [3]. Wen et al [4] reported the dynamic structure of a
submerged jet using POD analysis, they compared flows at 2
different Reynold’s number and found the scale of vortical
structure is much smaller in high Reynolds number jet. Most
of the previous literature have focused on relatively simple
configurations of plane or axisymmetric nozzles. There is
recent interest in orifice type nozzles owing to its superior
mixing properties. The present study focuses on the effect of
rectangular orifice plate aspect ratio on jet – free – surface
interaction.
In the present study submerged turbulent water jets of
different aspect ratios are discharged at a finite and fixed
depth from the free surface and are investigated
experimentally using a PIV system. The jets have a tendency
to deflect towards the free surface. The effect of variation of
aspect ratio is studied and mean velocity profiles, turbulence
intensities and Reynolds shear stresses are reported at various
axial locations, covering the deflecting jet/recirculation
region, impingement point and the wall jet region.
Figure 1: A typical free surface jet
EXPERIMENTAL PROCEDURE
Submerged turbulent water jets of different aspect ratios are
discharged at a fixed depth and are investigated
experimentally using a PIV system. In the present study, ‘h’
is the depth of centerline from the free surface, ‘d’ is the jet
width and the aspect ratio is defined as the width to height
ratio of the orifice plate opening. The water channel has a
width and height of 200 mm and is made of acrylic glass for
optical access. Orifice plates are constructed from 3 mm
thick acrylic glass with sharp edge rectangular openings and
are fixed flush to the vertical entrance wall. A single

2. equivalent orifice diameter of De = 10 mm is studied and
centered at height h = 3 De. The orifice aspect ratios studied
are 1, 2 and 4. A constant flowrate is set to maintain a
Reynolds number, based on the bulk jet velocity, of 7300 and
a Froude number, based on the depth of the jet centerline, of
1.35. An equivalent area of all nozzles is maintained to
ensure a constant momentum flux through all the jets.
Three 2-D velocity fields are captured between the jet exit
and X/De<23.5 using a high resolution Planar PIV system.
Each plane has a field of view of 84.1x84.1 mm, with a 5
mm overlap between the first and second planes. The flow
was seeded with m silver coated hollow glass spheres
having a specific gravity of 1.4. The flow field was
illuminated with a New Wave Solo Nd: YAG double-pulsed
laser that emits green light up to a maximum of 120 mJ/pulse
at 532 nm wavelength and at 4 Hz repetition rate. The laser
sheet was aligned with the mid-span of the channel, and a 12-
bit high-resolution charge-couple device (CCD) camera with
2048 pixel X 2048 pixel array and 7m pixel pitch was used
to image the flow field. A sample size of 5000 instantaneous
image pairs was acquired in each plane and post-processed
using the adaptive correlation option of Dynamic Studio. The
flow images were post-processed using interrogation
window size 32 pixels X 32 pixels with 50% overlap in both
the x and y directions.
RESULTS
Figure 1: Normalized Mean streamwise velocity
contours in x-y plane
The above figure show the normalized mean streamwise
velocity contours (0<X/De<15) in the x-y plane. The velocity
is normalized by the maximum of centerline velocity Umax
and the axial distance by the equivalent diameter De. The
effect of the free surface is not pronounced in the near field
and the profiles retain a typical Gaussian shape as that of a
free jet. As the aspect ratio increases the jet becomes more
and more slender. The maximum jet exit velocities on the
centerline for Aspect Ratio AR2 and AR4 are similar and
greater than AR1. In this study the PIV yields dense enough
instantaneous velocity fields to characterize higher order
turbulence statistics such as Reynolds stresses or even their
derivatives vorticity, swirling strength. These multi point
statistics give a better understanding of the flow as they give
an estimate of spatial and temporal extent to which the
turbulence field is correlated.
Figure 2: Mean streamwise velocity profiles in x-y plane
The mean streamwise velocity profiles at 4 different axial
locations (X/ De=4, 8, 12, 20) are plotted in Figure 2. At X/
De=4 the profiles are symmetrical about the jet centerline
similar to that of a free jet. As the axial distance increases the
shear layer is increasing skewed towards the free surface and
the jet finally attaches itself to the free surface and evolves as
a wall jet. For aspect ratios of 2 and 4 the jet maximum shifts
towards the free surface but not for the case of aspect ratio 1.
All the jets impinge the free surface between X/ De=8 to 12.
It can be observed from the plots the higher aspect ratio jets
evolve more quickly as a free surface jet
Figure 3: Centerline velocity decay in x-y plane.
-2 0 2
0.0
0.2
0.4
0.6
0.8
-2 0 2
0.0
0.2
0.4
0.6
-2 0 2
0.0
0.2
0.4
-2 0 2
0.00
0.05
0.10
0.15
0.20
0.25
-2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Umean/Umax
Y/De
AR1
AR2
AR4
X/De=4
AR1
AR2
AR4
Umean/Umax
Y/De
X/De=8
AR1
AR2
AR4
Umean/Umax
Y/De
X/De=12
AR1
AR2
AR4
Umean/Umax
Y/De
X/De=20
Umean/Umax

3. The center-line jet velocity decay is shown in the figure 3.
The mean streamwise velocity is normalized by U max
which is the maximum jet exit velocity on the center-line.
The axial distance is non-dimensionalized by the equivalent
diameter De. It is observed that the velocity decay rate of
aspect ratio 2 is higher than aspect ratio 1 in the region of
X/De = 3 to 17. At the initial stage of jet development
(X/De<2.25) the center-line velocity decay for the aspect
ratio 4 is the highest, with the shortest potential core. This
can be attributed to the slender vortical structures near the jet
exit plane in the aspect ratio 4 case, which interact strongly
with the potential core and dissipate its momentum in the
near field by entrainment of the ambient fluid thus reducing
its length. Similar observations are reported by Quinn et al [5]
for sharp edged rectangular free jets. In the far field
(X/De>12) the mean stream wise velocity decays at a still
higher rate for aspect ratio 2 while the decay rate for aspect
ratio 4 approaches to that of aspect ratio 1. Similar results are
reported for an elliptical free jet aspect ratio study by Lee et
al [6]. In the near field the interaction with free surface is
minimal and thus various analogies are seen with aspect ratio
studies of free jets, Tian et al [3] showed the jet retains a
profile closely similar to a free jet in the deflecting region.
Figure 4: Streamwise and transverse turbulence intensities in
the near and far field of the jet.
The streamwise and transverse turbulence profiles, figure 4,
in the near field have a typical double peak similar to
observed in a free jet. At further downstream locations the
peaks decay to form a broader peak indicative of increased
turbulence penetration of the jet by the entrained flow. It is
interesting to note that the magnitude of turbulence
intensities for aspect ratio 2 is highest in the near field region
but falls below that of aspect ratio 4 in the far field. This is
similar to observations reported by Lee et al [6] for an elliptic
jet study of aspect ratios of 1, 2, 4 & 8 study the elliptic jet of
aspect ratio 2 was reported to have the most intense
turbulence characteristics in the near field region.
Figure 5: Streamwise development of normalized Reynold`s
shear stress.
Figure 5 shows the contour plots of normalized streamwise
Reynolds shear stress normalized by the square of maximum
centerline velocity. The peaks of the shear stresses are
located in the shear layer regions but are not symmetric in the
inner and outer shear layer in contrast to a free jet [3]. The
smaller magnitude of shear stress near the free surface is
attributed to the proximity of the free surface which
diminishes the surface normal turbulent intensities [1] [3]. The
shear stress decreases in the downstream direction as the jet
expands.
Figure 6: Impingement point
-2 0 2
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
-6 -4 -2 0 2 4
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
-6 -4 -2 0 2 4
0.00
0.02
0.04
0.06
0.08
0.10
0.12
-6 -4 -2 0 2 4
0.00
0.02
0.04
0.06
0.08
0.10
-2 0 2
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-2 0 2
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
-2 0 2
0.01
0.02
0.03
0.04
0.05
0.06
Urms/Umax
Y/De
AR1
AR2
AR4
X/De=4
Urms/UmaxUrms/Umax
Urms/Umax
Y/De
AR1
AR2
AR4
X/De=20
Vrms/Umax
Y/De
AR1
AR2
AR4
X/De=4
Vrms/Umax
Y/De
AR1
AR2
AR4
X/De=20
0 5 10 15 20 25
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
AR1
AR2
AR4
U/Umax
X/De
x/de
y/de
x*
8 10 12 14 16
u2/ub2Frame 001  27 Jan 2015 
8 10 12 14
U/UmFrame 001  27 Jan 2015 
0.2
-0.2
8 10 12 14
Wz/(ub/De)Frame 001  27 Jan 2015 
-0.006
8 10 12 14
Vmean/UbFrame 001  27 Jan 2015 
8 10 12 14
U2/Ub2Frame 001  27 Jan 2015 
8 10 12 14
v2/Ub2Frame 001  27 Jan 2015 
0.002
8 10 12 14
uv/Ub2
Frame 001  27 Jan 2015 
0.8 0.6
0.4
0.2
0.05
0
0 2 4 6
-2
0
2
Umean/UbFrame 001  27 Jan 2015 
3 2 0.8
-3 -2 -0.8
0.8 0.5
-0.8
0.1
0.1
0.3
0 2 4 6
-2
0
2
Wz/(ub/De)Frame 001  27 Jan 2015 
-0.04
-0.08 -0.06 -0.04
-0.02
0
-0.02
-0.015
y*
0 2 4 6
-2
-1
0
1
2
Vmean/UbFrame 001  27 Jan 2015 
0.02
0.0005
0.01
0.005
0.06
0.02
0 2 4 6
-2
0
2
U2/Ub2Frame 001  27 Jan 2015 
0.010.02
0.002
0.005
0 2 4 6
-2
0
2
V2/Ub2Frame 001  27 Jan 2015 
0
0.008 0.006
0.004
-0.006
-0.004
-0.002
y*
0 2 4 6
-2
0
2
uv/Ub2
Frame 001  27 Jan 2015 
AR1
0.05
8 10 12 14
Umean/UbFrame 001  28 Jan 2015 
0.02
0.04
0.02
-0.02
-0.02
0
0
x*
y*
8 10 12 14
-2
0
2
Vmean/UbFrame 001  28 Jan 2015 
8 10 12 14
Wz/(Ub/De)Frame 001  28 Jan 2015 
8 10 12 14
v2/Ub2Frame 001  28 Jan 2015 
8 10 12 14
u2/Ub2Frame 001  28 Jan 2015 
-0.002
0.0020.004
8 10 12 14
uv/Ub2
Frame 001  28 Jan 2015 
x/de
y/de
0
0.04
0.04
0.04
-0.04-0.04
-0.06-0.08
-0.02
0
x*
y*
0 2 4 6
-2
0
2
Vmean/ubFrame 001  28 Jan 2015 
-3 -2
2
0.8
0.3
0.1
-0.3 -0.2
-0.1
3
-0.8
0 2 4 6
-2
0
2
Wz/(Ub/De)Frame 001  28 Jan 2015 
0.8 0.6
0.4
0.2
0.05
0 2 4 6
-2
0
2
Umean/UbFrame 001  28 Jan 2015 
0.02 0.01
0.02
0.005
0.002
0 2 4 6
-2
0
2
v2/ub2
Frame 001  28 Jan 2015 
0.02 0.02
0.01
0.01 0.04
0.06
0.0050.0005
0 2 4 6
-2
0
2
u2/ub2Frame 001  28 Jan 2015 
-0.008
0.01
-0.004
0.008
0.006
0
0 2 4 6
-2
0
2
Frame 001  28 Jan 2015 
AR2
x/de
y/de
x*
8 10 12 14
Vmean/UbFrame 001  28 Jan 2015 
0.2
0.2
0
0
-0.2
-0.2
-0.3
x*
8 10 12 14
WzFrame 001  28 Jan 2015 
8 10 12 14
u2/Ub2Frame 001  28 Jan 2015 
8 10 12 14
v2/Ub2Frame 001  28 Jan 2015 
8 10 12 14
Umean/UbFrame 001  28 Jan 2015 
8 10 12 14
Frame 001  28 Jan 2015 
3 2
1
0.2
0.2
-3 -2
-1
-0.3
-0.2
x*
y*
0 2 4 6
-2
0
2
Wz*Frame 001  28 Jan 2015 
-0.02
-0.01
-0.01
0.01 0.02 0.04
0.04
0.04
-0.04
-0.02
0.01
x*
y*
0 2 4 6
-2
0
2
Vmean/UbFrame 001  28 Jan 2015 
2 2
0.8 0.5
0.3
0.2
-3 -0.8
-0.8
-0.5 -0.3
0.1
0 2 4 6
-2
0
2
Umean/UbFrame 001  28 Jan 2015 
0.04 0.02
0.01
0.005
0.02
0.02
0 2 4 6
-2
0
2
u2/Ub2Frame 001  28 Jan 2015 
0.01
0.015
0.002
0.005
0.01
0 2 4 6
-2
0
2
v2/Ub2Frame 001  28 Jan 2015 
0.8 0.6
0.4
0.2
0.05
0 2 4 6
-2
0
2
Umean/UbFrame 001  28 Jan 2015 
-0.002
-0.006
0.002
0.008 0.006
-0.004
0
0 2 4 6
-2
0
2
uv/Ub2
Frame 001  28 Jan 2015 
AR4

4. The impingement point is the point where the offset jet
finally impinges and attaches to the free boundary (air-water
interface) and emerges as a free surface jet. The impingement
point is calculated as the axial location where the mean
streamwise velocity changes sign along at the free surface. It
was found that aspect ratio 1 had the longest reattachment
length of 10.87De, while it is 10.48De and 9.69De for aspect
ratios 2 & 4. The jet of aspect ratio 1 is expected to have the
longest reattachment length since, despite having sharp
corners, the orifice is most comparable to an axisymmetric
nozzle. As the aspect ratio increases the rate of mixing
increases in the near field [5] and thus the jet experiences a
higher entrainment from the surrounding fluid and reattaches
to the free surface earlier.
CONCLUSIONS
Mean flow in the near field is not much modified by the
presence of the free surface and the normalized mean
streamwise velocity profiles retain shapes similar to that of a
free jet. The centerline velocity decay and turbulence
intensity results indicate the aspect ratio 2 to have highest
mixing in the near field region. The length of potential core
for the aspect ratio 4 is the smallest which can be attributed
to needle like vortices which strongly interact with the
potential core and dissipate its momentum to the adjacent
shear layers. As the axial distance progresses the outer and
inner shear layers distort progressively with a continuous
shift of the maximum velocity to the free surface. The
Reynold’s shear stresses are suppressed in the outer shear
layer due to the vertical confinement.
ACKNOWLEDGMENTS
This work was supported by research grants from National
Science and Engineering Council of Canada.
REFERENCES
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D.T.Walker, C.-Y.Chen, W.W.Wilmarth Journal of
Fluid Mechanics 1995
2. Plane offset jet discharged into water of finite depth:
Hiroyuki Tsunoda, Yoshihito Shimizu, Takeshi
Kashiwagi JSME International Journal 2006
3. Characteristic of a jet in the vicinity of a free
surface: Jiahao Tian, Vesselina Roussinova, Ram
Balachandar. Journal of Fluids Engineering 2012
4. Dynamic structures of a submerged jet interacting
with the free surface: Qian Wen, Hyun Dong Kim,
Ying Zheng Liu, Kyun Chun Kim. Experimental
thermal and fluid science 2014
5. Turbulent jet flow issuing from sharp edged
rectangular slots: The influence of slot aspect ratio
W.R. Quinn. Experimental thermal and fluid science
1992
6. The effect of aspect ratio in the near field turbulence
structure: Sang-joon lee, Seung Jo Baek. Flow
Meas. Intrum. 1994.