Second Int. Conference for Environment, Ain Shams University, Cairo, Egypt
10-12 April, 2007
Three – Dimensional Jets in Crossflow
H.Mansour*, S.H.El-Emam*, A.R. Abdel-Rehim*, and M.M.El-Khayat**
**
*
Faculty of Engineering, Mansoura Univeristy, Mansoura, Egypt
New and Renewable Energy Authority, mohamed.elkhayat@yahoo.com
Abstract
In This study three-dimensional jets in crossflow have been studied experimentally and
theoretically, different jet to crossflow velocity ratios, and jet diameters have been
investigated. Sid-view images have been obtained using a high speed digital camera, the
obtained images have been analyzed using image digitizing technique. The following
conclusions have been reached, the obtained correlation for tracing jet centerline for the threedimensional jet in crossflow can be used in both near-and far-field. No crossing has been
occurred for the maximum centerline concentration before reaching the branch point. That is
the decay of the centerline increases by decreasing velocity ratio. Jet fluid is seen to penetrate
into the wake structure at low velocity rations, leading to the reduction of the concentration in
the jet. A shorter potential core length, that is the transverse jet decays earlier makes. Jet in
crossflow is a faster and good mixing mechanism than free jets. At velocity ratio 1:1 the best
mixing mechanism can be occurred.
Nomenclature
A
Parameter issued with jet trajectory
B
C
CVPs
D
dj
DR
dref
Parameter issued with jet trajectory
Parameter issued with jet trajectory
Counter-rotating vortex pairs
Parameter issued with jet trajectory
Jet diameter
Ratio between the current jet diameter and the reference jet diameter
Reference jet diameter, dJ=4mm
JICF
Lpc
m
PLIF
Jet in crossflow
Potential core length
Parameter issued with jet trajectory
Planner-laser induced fluorescent
S
Arc length along the jet centerline, m
VR
Velocity ratio, jet velocity to crossflow velocity
X
Coordinate in initial crossflow direction
X
Y
Horizontal distance measured from the jet exit normalized by jet diameter
Coordinate in jet direction
Ỹ
Vertical distance measured from the jet exit normalized by jet diameter
1) Introduction
A jet exhausting perpendicularly into a crossflow deflects as shown in Figure (1),
increases in lateral extent, distorts in cross sectional shape and evolves into a flow field that is
dominated by a pair of counter-rotating vortex, CVPs. This phenomenon is known as jet in
crossflow, JICF. JICF is the subject of numerous studies because its wide variety of industrial
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Second Int. Conference for Environment, Ain Shams University, Cairo, Egypt
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applications, either in confined or unconfined environments. Examples of confined JICF
include Vertical and short take-off and landing aircraft in translation form hover to forward
flight; in which case, the jets from their engines impinge on the ground surface. Internal
cooling of turbine blades by air jets impinging on the leading edge and dilution air jets in
combustion chambers of gas. Turbine engines, where the jets are injected radialy into the
chamber through discrete holes distributed along its circumference, in order to stabilize the
combustion process near the head, and to dilute the hot combustion products near the end.
Figure (1): Schematic diagram showing the many vortex systems of a JICF. (After Kelso et al
(1996))
Practical examples of jets in unconfined or semi-infinite crossflow are more numerous.
These include, flow situations resulting from the action of crosswinds on effluents from
cooling towers, chimney stacks, or flames from petrochemical plants, film cooling of turbine
blades,
The determination of jet trajectory was a primary goal for many of the experimental and
theoretical studies. Through studies based on imaging, the determination of the jet trajectory,
called jet centerline, is defined to be the loci of points of maximum velocity, or loci of
maximum concentration in the direction of the jet within the flow symmetry, as
recommended by Smith (1996), Simth and Mungal (1998), and Hasselbrink (1999).
El-Emam et al (2003) studied the flow characteristics of a two-dimensional JICF, a slit
jet of 1 mm width has been used. The concentration distribution was obtained
experimentally using image digitizing technique. The velocity distribution was theoretically
studied using a two–dimensional model. A jet centerline trajectory was traced based on
maximum concentration values and maximum velocity values along the flow field. A
reasonable agreement has been indicated between both traces. The recommended to extend
thus result for studying the three-dimensional jets in crossflow. An experimental correlation
has been developed to trace jet trajectory for the two-dimensional jets in crossflow.
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The centerline trajectories, in the near-filed, 0≤S≤4dJVR, of five velocity ratios, jet to
crossflow, ranged from 1:5 to 1:25 have been studied by Smith (1996). The raw data for
each velocity ratio is individually fit to the following trajectory relationship presented by
Pratte and Baines (1967) to produce the curve fits,
~
Y
X
(1)
 m*(
)B
VR d j
VR d j
The values of m that the curve fit selected range from 1.5 to 1.8, meanwhile m values
range from 0.27 to 0.28. Hasselbrink (1999) studied the flame stability by simulating the
flame flwo field by a JICF. Planner-laser induced fluorescent, PLIF, has been used to study
the far-field of a JICF, at two velocity rations. Based on his experimental results in the farfiled, and using results obtained by Smith (1996), for the near-field, he obtained a group of
scaling laws. Using an analytic solution formula to trace jet trajectories in the near and far –
field have been reached, the formula are;
Y
X 0.5
 2.5 * (
)
VR d j
VR d j
0≤S≤4dJVR
(2)
Y
X
 1.6 * (
)0.33
VR d j
VR d j
S>4dJVR
(3)
Roth (1988) depends on a computational method based on the three-dimensional, timedependent Navier-Stokes equations, represented an empirical formula to trace the jet
centerline, injected vertically in a crossflow, for different velocity ratios. Only small
deviations occur between the jet paths according to the number of points in each grid, also
results are the same for both inviscid and viscous cases, Roth’s formula is;
Ỹ =0.9772 * VR0.911*X0.334
(4)
Unfortunately, the most of the presented formula to trace jet trajectory and others
presented by Abramovich (1963), Beer and Chigier (1974), and Schetz (1980) are limited in
use. Limitation sources may due to the presented formula are valid for a specific range of
velocity ratios, or a certain region, (i.e. near-field, or far field). Thus it is needed to develop a
new formula to predict jet trajectory in the near- and far-field at the same time.
Kim and Benson (1992) represented calculations for a three-dimensional turbulent flow
of a JICF using a multiple-time-scale. It has been obtained that the interaction between the
jet and the crossflow creates a strong non-equilibrium turbulence field in the forward region
of the jet. Martin and Meiburg (1996) investigated vorticity concentration, re-orientation,
and stretching in three-dimensional aspects for a swirling jet model. Prestidge and Lasheras
(1996) studied the effect of axial and azimuthal forcing on the spreading and mixing
characteristics for a co-flowing turbulent jet theoretically and experimentally using PLIF.
The decay of the concentration along the centerline of the jet shows a marked increase in the
mixing of the jet as a result of the axial forces.
Smith and Mungal (1998) studied mixing of a round jet to a uniform crossflow in the
near-field. A range of jet-to-crossflow velocity ratios has been applied; with aid of acetone
vapor as a marker for the jet fluid, quantitative two-dimensional images of the scalar
concentration field have been obtained using PLIF. It is concluded that; the CVPs is
asymmetric in shape. Accordingly, the objectives of this paper are studying the
characteristics of the three-dimensional JICF represented by jet concentration at different
radial cross-sections, jet boundaries and introduce a general formula to trace jet trajectory.
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2. The Experimental Set up
An arrangement of the experimental test rig is shown in Figure (2). A Plexiglas 1’ x 1’
square cross section of 2’ length is used to study the concentration variation at different
radial cross sections in both near- and far-fields. The test section is painted with a black
color to avoid external light reflection. Jet is mounted at the center of the test section, and
fitted with a heat exchanger to reduce temperature of the paraffin smoke produced from a
smoke generator to the ambient temperature. In addition, a sheet of light with 0.25 mm in
thickness is produced from a lighting sourece a ligned to the center of the jet, and images are
captured using a high-speed camera.
Pitot
tube
Plexiglas test
section
Crossflow
Jet
Air
Inlet
Air
Outlet
Y
X
CCD
Jet
exit
camer
Light
bulb
Data transfer
a
cable
Monitor
metering
Orifice
A/D converter
Heat
exchanger
LCD
monitor
Hose
pipe
Air control
valve
Central
Processing Unit
Bottle
Digital
Micro-manometer
Air
cover
vessel
Paraffin
oil
Smoke
generator
Heat
element
Power
supply
Air
Compressor
Figure(2): Experimental rig arrangement
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Digital micro-manometer and digital non-contact thermometer have measured pressure
and temperature of the smoke, respectively. Meanwhile a digital illumenance meter has been
used to check test section darkness. Three circular jets with internal diameters 4 mm, 5 mm,
and 6 mm have been used individually, each of them has been mounted in the center of the
test section. Jet velocities are 1,2, 3 and 4 m/s, and crossflow velocity is fixed at 1m/s. In
addition the side-view images taken in this study have been discussed and analyzed using
image digitizing technique introduced by El-Khayat (2002).
3. Results
Side-view images for circular jets discharge perpendicular to crossflow for velocity ratios
range form 1:1 to 4:1. In this section X and Y coordinates have been measured form the
lower left corner of the obtained frame, and normalized by the jet diameter, dj. Using
FLUIDLAB package presented by Abdel-Rahim el al (2004), each mean image is otained by
averaging 15 sequential images, time interval between each of them is 6 seconds.
3.1 Concentration distribution
Figure (3) shows typical mean images for velocity ratios VR = 1 to 4, and dj = 4 mm. The
deflection of the jet path has been started at small distance, near the jet. This distance
increases with increasing velocity ratio. The deflection is due to reduction of the vertical
momentum at the jet boundaries causing the mixing region to deflect.
From Figure (3) it can be noticed that the distribution of the fluid in the region behind the
jet is strongly affected by the velocity ratio. Starting from VR=2, the fluid particles follow a
clearly defined path toward the crossflow and upward along the jet. In addition, the flow
pattern indicates that there is an entrainment, for the fluid in the surrounding environment,
due to the interaction between the jet boundaries and the surrounding fluid.
Moreover, color variation in each image reflects the concentration distribution for each
case. This makes an easy visual comparison between images. The color representation is
based on the issued color palette. This palette has 16 different colors and it has been used to
define the pseudo-color image technique and to represent the concentration distribution, in
near- and far-field. Each color in this palette has 16 different degrees, this means that the total
number of colors presented is 256 colors. Due to using and applying image digitizing
technique the obtained side-view images have been digitized and jet boundaries have been
traced, in addition to the jet centerline as shown in Figure (4).
Concentration profiles through the jet for velocity ratios from 1:1 to 4:1 and dJ = 4mm, are
presented at several locations as shown in Figure (4). These profiles show that, when a
turbulent jet spreads through a crossflow, the profiles of the mixture concentration in the cross
sections of the jet are symmetrical in shape around the jet centerline. Also, it indicates a fast
decay of the jet centerline, which means fast mixing process has been occurred between the
jet and the crossflow. The indicated profiles are nearly Gaussian shaped.
The ensemble-averaged profiles are included on each instantaneous profile shown in these
figure. A smooth shape of these profiles characterizes the average, which is "top hat" when
sliced perpendicularly to the jet centerline. El-Emam et al (2003) mentioned that, the
instantaneous profiles are marked by sharp vertical rises in concentration resulting in small
plateaus of high concentration fluid. It can be noticed also that the velocity ratio affect to a
great extent the concentration profiles, these results are in agreement with Smith (1996).
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Also, it can be seen that concentration distributions in case of velocity ratios 1:1 and 2:1 is
lower than the same distributions compared with that for velocity ratios 3:1 and 4:1. The
reason backs to the wake structure exists in velocity ratios 1:1 and 2:1, which extract the fluid
from the jet.
(A) : V = 1
R
(B) : V = 2
R
15
Jet
Jet
(D) : V = 4
R
(C) : V = 3
R
0
Jet
Jet
Figure (3): Experimental mean jet images. dj = 4mm, for different velocity ratios
In the following a mechanism for the presence of jet fluid in the wake is proposed. At
velocity rations 1:1 and 2:1, the near-field is fully affected by the crossflow, so it is
turbulences dominated. The flow behaves as if a partial inclined cover were put over the front
part of the exit hole. This causes the jet streamlines to start bending while it still in the
discharge tube and the jet to bend over completely right above the exit and also to lift up the
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oncoming flow over the bent over jet as represented in Figure (5). This means that most of the
interaction takes place in the region above the exit where the contributions of the crossflow
are very effective. Also the interface between the pipe flow and the boundary layer is
irregular. However, this concept seems to valid at velocity ratio 1:1.
Figure (4): Experimental jet trajectories, boundaries, and dimensionless mean
concentration distributions. dj=4mm, for different velocity ratios
Figure (5): Illustrative streamlines for VR = 1 and 2
Due to this fact the jet bending may start inside the pipe and is virtually completed at the
downstream end of the exit the effect of crossflow is gradually decrease whenever jet velocity
increase. So, it can be mentioned that jet wake structure is strongly depending on the velocity
ratio.
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Also, it can be seen that concentration distributions in case of velocity ratios 1:1 and 2.:1
is lower than the same distributions compared with that for velocity ratios 3:1 and 4:1. The
reason backs to the wake structure exists in velocity rations 1:1 and 2:1, which extracts the
fluid form the jet. The physical meaning of this result is in the mixing processes either low
concentration ration or high ratios are required. So, for low concentration ratios low velocity
ratios are necessary. Also, these figures give a general trend or concentration ratio if it is high
or low, meanwhile in the practical applications a certain ratio is required this issue will be
discussed in section 3.3.
The results for the dJ =5 mm for velocity ratios from 1:1 to 4:1 is illustrated in Figure (6).
The same observations can be noticed as for the previous case; where dJ=4mm.
30
V =1
R
25
25
20
20
Y/dJ
Y/dJ
30
15
15
10
10
5
5
0
V =2
R
0
0
5
10
15
20
25
30
0
5
10
X/dJ
20
25
30
20
25
30
X/dJ
30
V =3
R
25
25
20
20
Y/dJ
Y/dJ
30
15
15
15
10
10
5
5
0
V =4
R
0
0
5
10
15
20
25
30
0
X/dJ
5
10
15
X/dJ
Figure (6): Experimental jet trajectories, boundaries, and dimensionless mean
concentration distributions. dj=5mm, for different velocity ratios
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In addition, the present experimental investigation reveals the existence of large structures
in the flow of a JICF. These structures are sometimes well organized and sometimes not.
Depending basically on the velocity ratio, this can be explained as follows. Smith (1996)
mentioned that, CVPs developed refers to a progression from a circular jet exit, to an oval
deformation, to a kidney shape, and finally to the position where the peak local jet
concentration moves off the centerline plane. Therefore, at high velocity ratios the formed
vortices have vorticity of the same sign as the flow inside the pipe but opposite to that of the
crossflow and they are well organized. They are subjected to tilting and stretching, and they
breakdown to turbulence within the first couple of jet diameters downstream of the exit. As
the velocity ratio decreases the organization of these large structures reduce, but still there is a
periodicity in their appearance.
In the obtained images, other vortical structure is visualized as well. The jet roll-up shear
layer vortices are shown but resolution is not adequate in the vortex interaction region for a
clear penetration. Abdel-Rahim et at (2004) mentioned that, jet roll-up shear layer vortices
play a great role in the entrainment process. Where they help to withdraw the surrounding
fluid inside the jet.
3.2 Jet centerline
The maximum values of the jet concentration along the jet are available from the images
captured by the high-speed camera. The positions of the maximum values give the trajectory
of the jet. The effect of the jet diameter on the jet centerline for the four velocity ratios are
presented in Figure (7). The trajectories of the same velocity ratio do not coincide on each
other. This is likely the result of jet shape factor. Also, it may due to the effect of crossflow
shear stress exerted upon the jet fluid, where the jet weakness increases whenever the jet
diameter increases.
El-Emam et al (2003) presented an empirical equation to fit data of jet centerline based on
both jet diameter and velocity ratio, the advantage of applying this equation on the raw data,
is at the near-field the trajectory is slightly affected by the crossflow. Meanwhile at the farfield the jet reaches its saturation limit, this means that jet trajectory reaches a maximum limit
then keeps this limit until jet vanishes, totally mixes, with the crossflow. The formula is;
~
XC
~
Y  A * VRB * ~
X  D
(5)
The reason of applying this formula backs to, based on visual observations it has been
noticed that the jet starts vertically then deflects on a result of the interaction with the
crossflow, then takes the direction of the crossflow. This trend has been found similar to the
trend obtained from the presented equation, which called saturation equation. The obtained
experimental data have been normalized by dJ = 4mm, considering it the reference jet
diameter, dref, and, the empirical constants were found as listed in table (1).
Table(1): The constants A, B, C and D
for the three-dimensional jet
A
B
C
D
5.59 * VR * DR
1
0.5
VR
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Figure(7): Experimental jet centerlines, for different jet diameters and different velocity ratios
Therefore, Eq.(5) can be written in the final form as follows;
~
Y 
5.59
* VR * D R
*
~
X  0.5
~
X  VR
(6)
Where, DR is the ratio between the current jet diameter and the reference jet diameter, 4
mm. It is clearly shown that as the velocity ratio increases, the jet extends further into the
flow. At velocity ratios greater than unity the jet is only slightly affected near the exit, this
issue will be discussed by El-Khayat et al (2004).
Moreover, the obtained centerline formula has been put into comparison with equation
presented by Roth (1988), and those introduced by Hasselbrink (1999). The result of this
comparison is highly appreciated as shown in Figure (8). The presented formula shows an
influence by the crossflow in the near-field, and has a reasonable agreement with both
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Figure (8):Comparisons the obtained jet trajectory formula, and the obtained
with others
formulae. Also It can be noticed that, using Eq.(6) jet trajectories reach their saturation limit
in the far-field region, while using the other two equations jet does not reach this limit and
continue their increase in the vertical direction. Thus the presented formula can be used in the
near- and far-field and for different velocity ratios.
3.3 Potential Core
Figure (9) illustrates a schematic diagram for the potential core. Each point of the
trajectory data given in Section 3.2 has a definite concentration value. Figure (10) displays the
maximum centerline concentration decay along the centerline coordinate, S, for VR= 1 to VR=
4, and dJ=4 mm, plotted against the downstream distance, S/dJ. Figure (10) is drawn in log-log
plot, so a power-law decay appears as a straight line.
For each jet the centerline concentration remains unchanged through the potential core
length, LPC. This length increases with increasing velocity ratio, LPC = 1.26 dJ at VR =1, and
LPC = 2.0 dJ at VR = 4. The difference in potential core length make the VR=1 the best mixing
mechanism if the final desired maximum jet concentration is greater than 40%. Below 40%
the branch points cause the decay lines to cross, which makes the choice of the velocity ratio
dependent upon the final desired concentration.
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The physical mechanism which explains the minimum flame is the decay lines when dJscaled, Figure (10). For example if a final concentration of 30% is required, the four velocity
ratios, have a different core length to reach 30% point. Otherwise, Figure (10) indicates that
concentration ratio along the jet centerline is less than 10% or equal can not be reached by
velocity ratios from 1 to 4 (dJ=4mm).
Potential core
Figure (9): Nomenclature for the potential core (After Coelho and Hunt (1989))
Moreover, Figure (10) shows the branch point locations, indicated by symbol ‘ ’, which is
given by X = 4dJ VR. The branch point occurs at S=1.58dJ for VR=1, at S=3.16dJ for VR=2, at
S =5.01 dJ for VR = 3, and at S= 6.30 dJ for VR = 4. Also, it can be noticed that, no crossing
has been occurred before reaching branch points for VR= 1 to 4. That is the decay of the
centerline increases by decreasing velocity ratio. For VR= 2 and VR= 3 crossing has been
started rapidly after the branch points. On contrary for VR= 1 and VR= 4 crossing starts far
after the branch points.
Figure (10):Maximum centerline concentr-ation decay plotted with down-stream distance
S, normalized by dj
Therefore, it can be concluded that the centerline decay rates show that the branch points
are the physical mechanism behind the minimum flame length. In addition, much interest in
the transverse jet results from its enhanced mixing properties, making the regions before and
just after the branch points important areas of study.
Potential core lengths have been measured for VR= 1 to 4, and dj=4, 5 and mm and
represented in Figure (10). The maximum potential core length is about 0.35 S/dj. This plot
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confirms that the transverse jets reduce their peak centerline concentration at a faster rate
than the free jets. Figure (10) indicates that a certain concentration ratio can be reached at
different operating conditions. For example at dj = 4mm, concentration ratio 90% can be
obtained at 1.4 S/dj, and 2.8 S/dj at VR =1 and 4, respectively. These results are very important
for both slow mixing process and fast mixing process.
Conclusion:
- The obtained correlation for tracing jet centerline for the three-dimensional JICF can be
used in both near- and far-field. This correlation includes the effect of jet diameter, in
addition to the velocity ratios.
- No crossing has been occurred for the maximum centerline concentration before reaching
the branch point. That is the decay of the centerline increases by decreasing velocity ratio.
- Jet fluid is seen to penetrate into the wake structure at low velocity ratios, leading to the
reduction of the concentration in the jet.
- A shorter potential core length, that is the transverse jet decays earlier makes JICF is a
faster and good mixing mechanism than the free jet.
- At velocity ratio 1:1 the best mixing mechanism can be occurred.
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a crossflow,” Ph.D. thesis, University of Florida.
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Second Int. Conference for Environment, Ain Shams University, Cairo, Egypt
10-12 April, 2007
Schetz, J. A. (1980), “Injection and mixing in turbulent flow,” Progress in Astronautics and
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