Full text of DOI:10.2514/2.2099

AIAA JOURNAL
Vol. 41, No. 8, August 2003
Sectional Flow Structures in Near Wake
of Elevated Jets in a Cross ow
Rong F. Huang¤ and Ren H. Hsieh†
National Taiwan University of Science and Technology, Taipei 10672, Taiwan, Republic of China
Near-wake  ow structures in the symmetry and horizontal planes of elevated jets in a cross ow are studied
experimentally in a wind tunnel via a laser Doppler velocimeter. The measured velocity vector Ž elds and the
corresponding streamline patterns in the symmetry and several horizontal planes display tremendous variations
in different characteristic regimes of jet-to-cross ow momentum  ux ratios. They are typically termed cross ow-
dominated, transitional, and jet-dominated regimes. The complex  ow behaviors are the result of the interactions
amongthe downwash effect, which is induced by the cross ow passing over the tube tip; the upshear effect induced
by the issuing jet; and the wakes behind the jet and the tube. Topological  ow patterns are proposed to delineate
the measured  ow structures. Impact effects of the cross ow on the jet are discussed in two aspects, that is, the
geometry and the turbulence properties of the central streamline. The geometric characteristics of the de ected
jet in different  ow regimes are presented and compared with previous results. The velocity components and
turbulence properties along the central streamlines of different  ow patterns show that the premier turbulence
generation that is observed in this  ow arrangement occurs in the impingement and jet bend over regions.
Nomenclature
outer diameter of tube, 6.4 mm
inner diameter of tube, 5 mm
maximum height of a central streamline,
measured from level of tube tip to highest
level of central streamline
V/STOL, turbine-bladecooling,etc.An elevatedjetdischarginginto
a cross ow arises in many situationsof technologicalimportanceof
environmentalŽ eld, for example, stack  are and plume dispersion.
The wall-issued case is characterized by three-dimensional  ows,
which are subject to the interactions among the jet, jet wake, and
wall boundarylayer. The  ow structuresin the stack-issuedcase are
subject to the interactionsamong the jet, jet wake, and stack wake.
Flow propertiesofthejetsemittedintocrossows frombothground-
level sources and elevated sources have been examined in detail in
the literature, but with more attention focused on the ground-level
case.
D
d
Hj
=
=
=
R
Rej
Rew
j u2 wu2
=
=
=
=
=
=
=
jet-to-wind momentum  ux ratio, ½ j =½
u d
w
exit Reynolds number of jet,
=º
j
u D
freestream Reynolds number of cross ow,
local velocity components in
average exit velocity of jet
=º
w
u
x y z
, v, w
, , and directions
u j
uw
u0
Most of the studies on the wall-issued jet in cross ow before
the mid-1980s dealt with the shape and centerline trajectory of the
jets. The kidney-shapedcounter-rotatingvortices in the far Ž eld of
the bent jets were also studied.1¡9 Mean and  uctuating velocity
propertiesat jet-to-crossow velocity ratios 0.5, 1, and 2 were stud-
freestream velocity of cross ow
instantaneousvelocity  uctuations
x y
Reynolds shear stress
Cartesian coordinateswith origin at center
of jet exit plane
originated locations on tube-openingplane
from where bifurcation line evolves
de ection angle of jet streamline evolving
from origin on tube-openingplane
kinematic viscosity of air
mass density of jet  uid
mass density of cross ow
0
0
, v , w
z
, , and directions
in
0
u0
w
=
=
x y z
,
x0
µj
º
,
11
ied by Andreopoulosand Rodi10 and Andreopoulos. They used a
three-component hot-wire anemometer and reported the  ow and
turbulence properties in the jet wake and the wall boundary layer.
Reverse  ow was found to be restricted to a region very close to
the wall. Sherif and Pletcher12 conducted measurements of the ve-
locity and turbulence characteristics of the jet in cross ow at jet-
to-crossow velocity ratios 4 and 6 in a water tunnel with hot-Ž lm
probes. Two mean velocity maxima on the distribution proŽ le of
each vertical cross section in the symmetry plane were found. One
is in the jet wake, which is usually a local maximum. The other is
on the jet centerlinetrajectory,which is an absolute maximum. The
double-peakbehaviorin the mean velocityproŽ les has alsobeenob-
served by Andreopoulos and Rodi.10 The turbulence intensity has
an absolute maximum at the location of maximum velocity gradi-
ent and a local maximum near the wall surface in the wake region.
Blanchardet al.13 analyzedthe wall-issuedjet in crossow and con-
cluded that the longitudinal structures must be taken into account
in the mechanism of stability. Examinations of the time-dependent
=
=
=
=
=
½
j
½
w
Introduction
HE subject of the jet in a cross ow has been widely studied
due to its wide range of industrialapplications.It is commonly
T
identiŽ ed in two categories,accordingto the differencebetween the
emerging sources of the jet. The jet may eject from an opening on
a wall or from an elevated stack. A jet issuing from a wall opening
into a cross ow is often encountered in the Ž lm cooling of jet en-
gines,powerplantcombustors,vertical/standardtakeoffandlanding
14¡16
coherentstructureshavebeenlimitedto spectralmeasurements
and  ow visualizations.
17;18
Received 22 March 2001; revision received 6 June 2002; accepted for
For the case of stack-issued jet in cross ow, few investigation
results have been reported. Moussa et al.19 have made similarity
considerations on the Navier–Stokes equations for two geometri-
cally,kinematically,and dynamicallysimilar ows. They concluded
that the bending geometry of two jets must be the same and can be
related directly to the jet-to-crossow momentum  ux ratio. Also,
the dimensionless ratios that govern the similarity in the nonbuoy-
ant  owŽ eld of jet-in-crossow are the Reynolds numbers of the
jet and cross ow, jet-to-crossow momentum  ux ratio, Strouhal
°c
publication 25 January 2003. Copyright 2003 by the American Institute
of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this pa-
permay bemade for personal or internaluse, on conditionthat the copier pay
the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rose-
wood Drive, Danvers, MA 01923; include the code 0001-1452/03 $10.00 in
correspondence with the CCC.
¤Professor, Department of Mechanical Engineering. Senior Member
AIAA.
†Graduate Student, Department of Mechanical Engineering.
1490

HUANG AND HSIEH
1491
number, and the shape factor. Andreopoulos20;21 presentedhot-wire
anemometer-measured velocity proŽ les and statistical turbulence
propertiesin the bent jet and the far-wake region of a cooling tower
at low jet-to-wind velocity ratios. The results disclosed the strong
interaction among the bent plume, cooling tower, and the wakelike
region behind the cooling tower and jet. However, the detailed  ow
structuresin the near-wake region behind the cooling tower and the
de ected jet were not reported because of the limitations of instru-
mentation. More recently, Eiff et al.22 and Eiff and Keffer23 used
the pattern-recognition technique to study the coherent structures
within the near-wake region of a turbulent tube-dischargedjet in a
cross ow. They found that the von Ka´rma´n-like vortexstructuresin
the wake of the pipe are locked to similar structuresin the jet wake.
Because the large structures in the near wake of the tube-issued
jet in cross ow are still unclear, the aim of this paper is to reveal
the characteristicsof the  ows in this area. The streamline patterns,
velocity distributions, and turbulence properties along the central
streamline are investigated.
coordinate system ( ; ; ), as shown in the subset of Fig. 1. The
origin of the coordinate system was centered at the exit plane of
the tube. The stack tube was adapted to the tip of a nozzle assem-
bly. The nozzle assembly served as a  ow-conditioning device in
which honeycombsand three layers of mesh screenswere installed.
The jet  ow rate was measured by a set of rotameters and was con-
stantlycheckedwith a laminar  ow meter. The averageexit velocity
proŽ les measured by a two-component laser Doppler velocimeter
Re
x y z
were parabolic for Reynolds number
larger Reynolds numbers, transitionof  ow occurs. The turbulence
less than about 3000. At
j
x d y d z d D
intensityof the jet at . = ; = ; = / .0; 0; 0:04/ was lower than
Re
0.35% for
less than about 3000. At larger Reynolds numbers,
j
the turbulenceintensity at the jet exit increases to about 2.5%.
Re
w
During the experiment,the crossow Reynolds number
Re
was
set at 2074. The jet Reynolds number
based on the inner diam-
j
eter of the tube was varied from 200 to 8000. The jet-to-crossow
momentum  ux ratio thus covered a wide range from 0.015 to 25.
Velocity Measurements
Experimental Setup
The velocity Ž eld was measured with a two-component laser
Doppler velocimeter(LDV). The blueand green laserbeams, which
were supplied by a Spectra-Physics Stabilite-2017 6-W argon-ion
laser, were separated and focused through the Dantec Fiber-Flow
optical system. The dimensions of the measuring volumes of the
Cross ow and Jet
The cross ow was supplied by an open-circuit wind tunnel, as
£
£
showninFig. 1. Thewindtunnelhada testsection30 30 110cm
in size. The  oor of the test sectionwas made of an aluminum-alloy
plate. The lateral walls and the ceiling were made of glass plates
Re D
e¡2
greenandbluecomponentsestimatedat
lightintensitylevelwere
£
£
£
£
about 0:120 0:120 1:543 mm and 0:114 0:114 1:463 mm,
respectively.The fringe separationsof these componentswere 3.31
and 3.14 ¹m, respectively.The system was conŽ gured to operateat
backscattermode. A Bragg cell was embedded in the system to dis-
tinguish the directionalambiguity. A Dantec  ow velocity analyzer
enhancedtwo-componentcorrelationprocessorwas used to convert
the Doppler signals into frequency data. The frequency data were
fed into a personal computer-controlleddata acquisition system to
calculatethe velocitiesand otherstatisticalproperties.Each velocity
data record consisted of 6000 samples, which would last for about
0.8 s. The average sampling rate was about 7.5 kHz. When 0.21
was taken for the Strouhal number of the tube-wake vortex shed-
Re D
for transmission and receiving of laser lights. At
2074, a
w
parallel  ow velocity proŽ le with a nonuniformility of about 0.8%
x d D ¡
was detected at the stage
=
20 by using a two-component
laser Doppler velocimeter. The turbulence intensity was less than
0.25%. The average wind velocity was detected with a retractable
pitot static tube and a high-precisionelectronicpressure transducer.
The pitot static tube was retracted to the  oor of the test section
when the velocity measurements were conducted to not in uence
the  ow Ž eld.
The elevated stack was a stainless steel tube with an inner diam-
eter 5.0 mm, outer diameter 6.4 mm, and length 560 mm. The tube
protruded perpendicularly 160 mm into the aluminum  oor plate
of the test section. Positions are described in terms of a rectangular
ding at
2074, the shedding frequency was about 150 Hz.
w
Fig. 1 Experimental setup.

1492
HUANG AND HSIEH
Approximately120 cyclesof the wake dynamic structureswas con-
tained in a data record for calculations of average and turbulence
properties.When the frequencyof the coherent structureson the jet
momentum uxratios.Thespacingbetweenthemeasurementpoints
d
is 0.084 in the regioncloseto the tube tip. In otherregions,it varies
d
d
from 0.1 to 0.6 . The measurement points are dense in the near-
wake region and sparse in the far Ž eld. When shown, super uous
velocityvectorsare removedfor clarityof presentation.The stream-
lines are obtained by using the shooting method.
R D
»
was considered, 400 1000 Hz was detected by using a hot-wire
anemometer.Hence, at least 300 cycles would be captured in a data
record for data processing. Two sets of three-component travers-
ing mechanisms with a resolution of 10 ¹m were set up on one
side and on the top of the test section, respectively. Depending on
the measurementsbeing conducted for the symmetric or horizontal
planes, the transmitting/receiving optics of the LDV was installed
and preciselymounted on the side or the top traversingmechanism.
Magnesium oxide particles with an average diameter of 5 ¹m
were introducedintoboththe jetand the cross ow to scatterthe laser
lightvia two separatedparticleseeders.A cycloneparticlegenerator
as described by Glass and Kennedy24 was used for the cross ow
seeding, and a  uidized bed was installed for the jet seeding. The
particles were estimated to be capable of following frequenciesup
to 3.6 kHz (Ref. 25).
At
0:1, as shown in Fig. 2a, the jet momentum is not large
enough to sustain the impingement of the transverse stream so
that the streamlines evolving from the tube opening are de ected
through large angles from the vertical axis of the tube. A down-
wash area is enclosed between a dividing streamline evolving from
x d z d D
. = ; = / .0:04; 0/ and the tube. This dividing streamline is a
bifurcationline in topologicalterms.27;28 At the jet exit, the stream-
lines emanating from the left of the bifurcation line extend down-
stream, whereas those emitting from the right of the bifurcationline
go into the downwash area. With the increase of the jet momentum,
a vortex is formed in the jet wake due to the interaction between
the jet shear and the downwash effect, as shown in Fig. 2b. A bifur-
cation line, which separates the downwash and downstream areas,
x d z d D
evolves from . = ; = / .0:32; 0/. Figure 3 shows the originated
Uncertainties
The accuracy of the measurement of freestream velocity was af-
fected primarily by the alignment of pitot tube and the calibration
of the pressure transducer.With the help of an onlinemicropressure
calibrationsystemand thecarefulalignmentofthe pitottube,the un-
certaintyin the freestreamvelocity was estimated26 to be as large as
3% of reading. The rotameters used to measure the  ow rate of the
air jet were calibratedin the laboratorywith a micro ow calibration
§
system. The accuracy was 1% of full scale. The estimated uncer-
taintiesoftheLDV measurementswerelessthan1% forthemeanve-
locitiesand 7% for the turbulenceintensitiesand Reynoldsstresses.
Results and Discussion
Tomographic Flow Structures
Cross ow-Dominated Regime
Figure 2 shows the velocity vectors and the streamline patterns
in the symmetry plane of the near wakes at various jet-to-crossow
Fig. 3 Locations on the tube opening from where the bifurcation lines
originate, Rew = 2074.
(
)
Fig. 2 Velocity vector Ž eld and streamlines of symmetry plane y = 0 in cross ow dominated regime, Rew = 2074.

HUANG AND HSIEH
1493
R
R
§
locations of the bifurcation lines at various . For < 0:9 0:03,
area. The combined effects of the jet shear and the jet wake cause
x z
all of the bifurcation lines evolve from the tube opening, that is,
the recirculationbubbleto form on the – plane,as shownin Fig. 2.
¡
x
d
R
0:5 < 0= < 0:5. When is greater than about 0.9, all stream-
It is expected from Figs. 2c and 4a that a three-dimensionalrecir-
z d D
lines emitting from the tube opening go directly to the downstream
culation bubble exists in the jet wake. In the plane
=
0:1, as
area. At < 0:9 0:03, part of the jet-issued  uids in the symme-
try plane would be downwashed into the recirculationregion in the
near wake behind the tube, if diffusion and dispersion are not con-
sidered. The uncertainties for the range of the characteristic  ow
regimes were estimated accordingto the  ow patternsof LDV mea-
shown in Fig. 4b, the focus becomes stable27;28 because the stream-
line evolving laterally from the forward stagnation point goes into
z d D ¡
R
§
the focus. On the plane across the tube wake at
=
2:0, as
shown in Fig. 4c, the forward stagnation point attaches to the tube
wall, whereas the aft stagnation point is located far downstream at
R
x d D
d
3:39. The axial bubblelengthbecomes2.76 , which is about
surementsat many . The differencesbetween neighboringregimes
=
were pretty distinct, so that the identiŽcation was not very difŽ cult.
To achieve this,  ow patterns were measured at many around the
30% longer than that in the jet wake. The focus is unstable, as is
that shown in the jet wake of Fig. 4a. The axial locations of the bi-
furcation line in the symmetry plane of Fig. 2c coincide with those
of the aft stagnation points in the horizontal planes of Fig. 4. It is
clear that the bifurcation line in the symmetry plane describes the
loci of the aft stagnationpoints of the recirculationbubble of the jet
and tube wakes.
R
critical values.
R
At larger values of , as shown in Figs. 2c and 2d, the jets shoot
up a little higher than at the values shown in Figs. 2a and 2b before
theyarede ectedintothe cross ow direction.Comparedwith thatin
Fig. 2b, the jet-wakevortexbecomeslarger and is locatedat a higher
level.Itisevenmoreapparentin Fig. 2d.The bifurcationlinesshown
in Figs. 2c and 2d do not evolvefrom the tube opening.Instead,they
evolve from the jet-wake vortices. All of the streamline patterns of
TransitionalRegime
§
R
§
In the regime 1:90 0:03 < < 5:90 0:10, complex behaviors
of  ow transition proceed due to the competition between the up-
shear effect of the jet and the downwash effect that is induced when
the cross ow goes across the tube tip. Figures 5a–5d show three
typesof velocityvectorŽ eld and streamlinesat various . Figure5a
shows type 1 of the transitional  ow at
of the up-shooting jet is strong enough so that the jet-wake vortex
in the cross ow-dominated regime shown in Fig. 2 is stretchedoff.
Two  ow structurefeatures, that is, the reverse  ows in the jet wake
and the recirculation bubble in the tube-wake, are found. The re-
versed streamlines in the jet wake appear in the region near the jet
because of the up-shear effect of the up-shootingjet. Consequently,
because of the shear of the bent jet the streamlines point rightward
and eventuallyextendtothedownstreamarea.Nearthe leesideofthe
tube tip, a clockwise-rotating recirculation region centered around
R
§
the  ows at < 1:9 0:03 show features similar to those shown in
Figs. 2c and 2d. A term cross ow-dominated regime is applied.
R D
The  ow patterns of the horizontalplanes at
0:95 are shown
0:6, the cross ows wrap across the
z d D
in Fig. 4. In Fig. 4a for =
R
jet and turn around to form a recirculation bubble. Two stagnation
points exist on the symmetry axis. A forward stagnationpoint is lo-
R D
2:02. The momentum
x d D
catedat =
x d D
0:56. An aft stagnationpointislocatedat =
2:67.
d
The axial bubble length is about 2.11 . The streamline evolves lat-
erally from the forward stagnationpoint and goes downstream.The
bubblecentersat a focusthatis unstable27;28 becausethe streamlines
evolve from the focal center. The recirculation bubble in the hori-
zontal plane is subjectto the shear effect, which is developedby the
up-shooting jet. The jet shoots up and de ects to the downstream
x d z d D
¡
. = ; = / .1:4; 0:8/ is induced because of the combined ef-
fects of the up-shear jet and the downwash  ow. A bifurcation line
x d ¼
standingat =
3:4 belowthe jetexitplanedescribesthe lociofthe
aft stagnation points of the recirculation bubbles on the horizontal
planes in the tube wake.
Figure 5b shows the velocity vectors and the streamlines of type
R D
2 transitional  ow at
2:40. Because of the increase of jet mo-
mentum, a counterclockwise-rotating vortex located behind the up-
shootingjet and above the lee side of tube tip is formed. The vortex
is formed due to the interactions among the up-shear jet, jet-wake
reverse  ow, and the tube-wake recirculation bubble. A jet-wake
vortex similar to the one observed here has also been found by
Brizzi et al.18 in an experiment for a wall-issued water jet that was
Re D
R D
submergedinto a cross ow at
251 and
6:25. Two saddle
w
points are consequentlyformed to satisfy the  ow topology. One of
them is between the up-shear jet and the counterclockwise-rotating
jet-wake vortex. The other one is located between the clockwise-
rotating tube-wake vortex and the reverse  ow region in the jet
wake. A source point comes up between the bifurcationlines of the
jet-wake and the tube-wake.
Figures 5c and 5d show the velocitiesand the streamlinesof type
R D
3 transitional ow at
2:70 and 4.43,respectively.Huge up-shear
effect developed by the jet suppresses the downwash effect so that
the streamlines, which evolve from the tube-wake bifurcation line
toward the leeside of the tube, become  atter. Consequently, the
tube-wake recirculation vortex and its accompanying saddle point
shown in Fig. 5d disappear.
Figure 6 shows the sectional ow structuresof varioushorizontal
R D
planes in the type 3 transitionalregime at
2:70. The  ow struc-
2:0 and 1.0, as shown in
z d D
tures in the jet wake on the planes =
Figs. 6a and 6b, respectively,are similar to that in Fig. 4a. The bub-
ble structureslocated between the forward and aft stagnationpoints
with unstablefoci27;28 are found.The  ow structurein the tubewake
z d D ¡
on the plane =
2:0, as shown in Fig. 6f, is similar to that in
Fig. 4c. However, the sectional ow structuresshown in Figs. 6c–6e
display quite differentpatternsaroundthe area of interfacebetween
z d D
Fig. 4 Velocity vector Ž eld and streamlines of horizontal planes in
cross ow-dominated regime, R = 0.95 and Rew = 2074.
the jet and the tube wakes. Because the horizontal plane =
0:5

1494
HUANG AND HSIEH
(
)
)
)
)
)
Fig. 5 Velocity vector Ž eld and streamlines of symmetry plane y = 0 in transitional regime, Rew = 2074: a type 1, b type 2, c type 3, and d type 3.
Fig. 6 Velocity vector Ž eld and streamlines of horizontal planes in transitional regime, R = 2.70 and Rew = 2074.
z d D
of Fig. 6c goes across the saddle point and the jet-wake bubble of
=
0:1 of Fig. 5c are positive.Below the tube-tipplane, as shown
y d D
Fig. 5c, four stagnation points on the symmetry axis
=
0 and a
in Fig. 6e, an off-axis saddle and two stagnation points appear on
bubble structureof stable focus27;28 are formed. All four stagnation
points can Ž nd their counterpartsof null axial velocities in Fig. 5c.
The forward stagnation point is located near the jet-wake saddle
x d D
the symmetry axis
0. The forward stagnation point is a sink,
y d D
=
whereas the aft one is a source. It is evident that the detailed  ow
structures around the interface area between the jet and the tube
wakes of the transitional  ows are very complicated. Above and
below the interface area, the sectional  ow structures are similar to
those observed in the cross ow-dominated regime.
point of Fig. 5c. The aft stagnationpoint located at
=
2:80 cor-
u
respondsto the point with a zero velocity component on the level
z d D
across =
0:5 in Fig. 5c. Between the forward and aft stagnation
points of Fig. 6c, there are two extra stagnation points. These two
stagnation points describe the left and the right boundaries of the
z d D
Jet-Dominated Regime
R
§
jet-wake vortex across the line =
z d D
0:5 in Fig. 5c. On the plane
In the regime > 5:90 0:10, the jet momentumis largeenough
to sustain the impact of the transverse stream so that the velocity
vectorsemitting from the jet exit do not de ect appreciablyfrom the
=
0:1, as shown in Fig. 6d, no stagnation point is found on the
y d D
axis =
u
0 becauseall of the velocitycomponentsalong the line

HUANG AND HSIEH
1495
Table 1 Ranges of R values for different
characteristic  ow patterns at Rew = 2074
Characteristic  ow
Range of R
Cross ow dominated
R < 1:9 § 0:03
(R < 0:9 § 0:03 downwash)
1:9 § 0:03 < R < 5:9 § 0:10
5:9 § 0:10 < R
Transitional
Jet dominated
Fig. 8 Velocity vector Ž eld and streamlines of horizontal planes in jet-
dominated regime, R = 17.36 and Rew = 2074.
Maps of Topological Flow Patterns
(
)
Fig. 7 Velocity vector Ž eld and streamlines of symmetry plane y = 0
in jet-dominated regime, Rew = 2074.
Figure 9 shows the pictorialtopological ow patternsof the near-
wake  ows in the symmetry plane. Following Perry and Fairlie27 as
well as Chong and Perry,28 the topological  ow pattern is charac-
terized by critical points, separatrices, and alleyways. In topologi-
cal terminology, a critical point is a point in a  owŽ eld where the
streamline slope is indeterminate, a separatrix is a streamline that
leavesor terminates at a saddle, and an alleyway is a passagewayin
between the two separatrices.When the criticalpoints, separatrices,
and alleyways are correctly described, the  ow map can be clearly
delineated.In the present case, the critical points consist of saddles
and nodes.
vertical direction, as exempliŽ ed in Fig. 7. In Fig. 7a, the de ection
z d
angle of the jet is small in the region 0 < = < 3. In the region
z d
where = is higher than about 3, the up-shooting jet loses a large
amount of momentum  ux so that the velocity vectors are de ected
appreciably to point to the right due to the impingement of the
cross ow. At = > 5, the components of the velocity vectors
become much larger than the componentsbecausethe momentum
z d
x
z
z
x
exchanges signiŽ cantly from the direction to the direction. In
the jet wake, very strong up shear developed by the jet on the wake
regioncausesthe  ow velocitiesnearthe leesidesof the tubeand the
jet to point upward. The jet-wake saddle and the counterclockwise-
rotating jet-wake vortex, which appear in Fig. 5 of the transitional
 ows, hence, are all stretched away. Only one source point located
between the jet-wake and the tube-wake bifurcation lines is left in
the  owŽ eld. The jet-wake bifurcation line becomes short. In the
tube wake, the bifurcation line goes downward and separates the
 owŽ eld into reverse and forward  ow regions. The  ows emitting
from the source point must come from the lateral streams to satisfy
the law of mass conservation. The lateral streams are induced by
R D
Figures 9a and 9b show the topological  ow patterns in the
cross ow-dominatedregime. In Fig. 9a, the bifurcationline evolves
fromthetubeopening,whereasinFig.9bthebifurcationlineevolves
from the jet-wake vortex. In both Figs. 9a and 9b, four three-way
S0
saddles, a leading-edgesaddle 1 on the tube tip, a stagnation point
S0
S0
2 on the tube surface of the up-wind side, a trailing-edgesaddle
3
S0
N
on the tube tip, and a reattaching point 4 on the leeside of the tube
surface, are formed. In addition, a node
is also shown. Because
1
the three-dimensional effect is almost unavoidable in real  ows,29
the focus instead of the center is presented.Hunt et al.30 obtained a
general formula for the relationshipbetween the numbers of nodes
N
N0
(including four-way nodes and three-way nodes ) and saddles
the recirculation bubble, as shown in Fig. 8 for
17:36. When
S
S0
(including four-way saddles and three-way saddles ) for the
Figs. 8a and 8c are compared, the bubble length of the jet wake is
apparentlymuchshorterthanthatofthetubewake.Therecirculation
bubblein the jet wake is an unstable focus,27;28 whereas it is a stable
focus in the tube wake. This situation also occurrs in the crossow-
dominated and transitionalregimes.
 ows around surface obstacles. The topologicalrule is
³
´
³
´
X
X
X
X
1
2
1
2
N C
N0
¡
S C
S0
D
¡ n
1
R
The ranges of
for different characteristic  ow patterns at
2074 are listed in Table 1. Although it is not shown here,
Re D
n
in which is the connectivityof the section of the  ow under con-
w
R
n D
it was observed in the laboratory that the critical values of in-
sideration.In this case,
the  owŽ eld. When the number of the critical points is counted in
2 becauseone solid obstacle presentsin
Re
crease gradually with Reynolds number
.
w

1496
HUANG AND HSIEH
)
)
a
d
)
)
b
e
)
)
f
c
(
)
)
)
)
)
Fig. 9 Topological  ow patterns of symmetry plane y = 0 : a downwash  ow, b cross ow-dominated  ow, c type 1 transitional  ow, d type 2
)
)
transitional  ow, e type 3 transitional  ow, and f jet-dominated  ow.
Fig. 9a or 9b, that is,
The topological  ow patterns of the horizontal planes are pro-
posed in Fig. 10. In the jet wake, as shown in Fig. 10a,  ows in all
X
X
X
X
N D
N0 D
S D
S0 D
1;
0;
0;
4
S
S
)
2
characteristic  ow regimes have two fourway saddles ( and
1
N
N
n D
and two nodes (
and 2). In this case,
1 because no solid
obstacle presents in the sectional  owŽ eld. When the number of
1
the topologicalrule is satisŽ ed.
Figures 9c–9e show the  ows in the transitionalregime. As dis-
cussed earlierin the sectionof velocity vectorŽ eld and streamlines,
a tube-wake vortex, a pair of counter-rotating jet-wake and tube-
wake vortices, and a jet-wake vortex feature the transitional  ows
of types 1, 2, and 3, respectively. These complex  ow patterns are
induced by the competition between the effects of the up shear and
the downwash on the jet and tube wakes. Figure 9f shows the picto-
rial topological  ow pattern in the jet-dominated regime. Only the
N
critical points is counted, that is,
X
X
X
X
N D
N0 D
S D
S0 D
¡ n
2;
0;
2;
0
the topologicalrule
³
´
³
´
X
X
X
X
1
2
1
2
source point
exists in between the jet-wake and the tube-wake
N C
N0
¡
S C
S0
D
1
4
bifurcation lines.

HUANG AND HSIEH
1497
Fig. 10 Topological  ow patterns of horizontal planes.
S
is satisŽ ed. The forwardstagnationpoint 1 is a fourwaysaddle.The
streamlines that evolve laterally from the forward stagnation point
S
1 godownstream.The streamlinesthatgo to the aftstagnationpoint
S2
N
N
.
2
are evolved from the unstable foci
and
1
In the tube wake, as shown in Fig. 10c,  ows in all characteristic
S0 ¡ S0
regimes have four threeway saddles (
4) on the tube wall: one
1
S
N
N
four-waysaddle 1 on the symmetryaxis, and two nodes 1 and
.
2
S0
Theforwardstagnationpoint 3 attachesto the leesideof the tube,so
thatitbecomesa threewaysaddle. 1 isanupstreamstagnationonthe
S0
S0
S0
tube wall, whereas and are separation points of the boundary
layers. The recirculation bu4bbles in the tube wake are centered at
2
)
a
N
N
unstable foci
and 2, which is similar to those observed in the
1
n D
cross ow-dominated regime. In this case,
obstaclepresents in the sectional owŽ eld. When the number of the
2 because one solid
critical points is counted, that is,
X
X
X
X
N D
N0 D
S D
S0 D
¡ n
2;
0;
1;
4
the topologicalrule
³
´
³
´
X
X
X
X
1
2
1
2
N C
N0
¡
S C
S0
D
1
is satisŽ ed.
)
b
Around the interface region, the situation is complex. For both
the cross ow-dominated and jet-dominated regimes, as shown in
Fig. 10b, two features different from Fig. 10a are observed. The
)
Fig. 11 Geometric properties of jet central streamline: a maximum
height of central streamline and b de ection angleof central streamline
at jet exit.
)
S
1
separatrices, which evolve from the forward stagnation point
,
do not go downstream as they do in the jet wake. Instead, they
go into the vortex so that the vortex centers become stable foci.
central streamline, shown in Fig. 11. Figure 11a shows the normal-
H
d
= of the central streamlines evolving
ized maximum heights
j
S
2
The streamlines that go into the aft stagnation point are evolved
from the center of the tubeopening.In the crossow-dominatedand
from upstream  ows. For type 3  ow of the transitionalregime, the
topological  ow patterns around the interface region are complex
because of the existenceof the jet-wake and tube-wake vortices, as
shown in Fig 5.
H
d
R
increasesfast with the increaseof .
the transitionalregimes,
=
j
The increase rate becomes low in the jet-dominated regime. Some
previous works2;6;31;32 concerning the jet centerline trajectories are
R
shown in Fig. 11a for comparison. At low , the experimental re-
sult of Keffer and Baines2 and the semi-analytical prediction of
Sucec and Bowley31 seem to be close to the presentresults. At large
Geometry Characteristics
R
The impact effect of the cross ow on the jet geometry can be
observed from the maximum height and the de ection angle of the
, however, the deviation is notable. The experimental data em-
ployedby Keffer and Baines2 to correlate the trajectoryformula are

1498
HUANG AND HSIEH
z d ¼
obtained from long-exposure smoke-trace  ow-visualization pic-
tures. They may subjectto a great difŽ culty of identiŽcation at large
=
1:5 and bends quickly to the right due to the impingement of
the cross ow. Because of the low jet-to-crossow momentum  ux
ratio, the downwash effect overwhelms the up-shootingmomentum
and “attracts” the central streamline to a level below the tube-tip
R D
R
because of a severe turbulent diffusion problem. The result ob-
tained by Adler and Baron32 using a quasi-three-dimensional inte-
gral method shows a good agreementwith the presentmeasurement
at large jet-to-crossow momentum  ux ratio 14.7. They do not
plane. In the transitionalregime at
shoots up to a level =
mosthorizontalinthedownstreamarea.Inthejet-dominatedregime,
3:49, the central streamline
z d ¼
3, then turns to the right, and remains al-
R
recommend the application of that method to low because of the
R D
inherent deŽ ciency of the integral method. Kamotani and Greber’s
experiment, in which a one-componenthot-wire anemometer was
at
13:83, the centralstreamlineis not de ected by a large angle
z d ¼
6
until it shoots up to a high level, =
3:7. The de ected central
R
applied, grows a little higher than the present result at large
.
streamline still gradually goes up even at the downstream stage
x d D
The in uence of the impact of the cross ow on the jet geometry
can alsobe observedfrom the de ection angle of the centralstream-
line at the jet exit, shown in Fig. 11b. The de ection angledecreases
=
15. It moves eventually in the freestream direction in the far
x d
d
downstream area for
=
greater than about 25 .
u u
= w, as shown in
The normalized local velocity distributions
R
rapidly with the increase of in the crossow-dominated regime.
Fig. 12b, attain peak values where the central streamlines make
u u
R D
When the jet momentum is large in the jet-dominated regime, the
decreasing rate becomes relatively low. In this regime de ection
angle is lower than about 13 deg. It is only 3 deg, which is negli-
R D
turns. The peak value of
=
at
13:83 is smaller than that
w
R D
at
3:49 because the central streamline in the jet-dominated
regime is less de ected around the jet-turning region than in other
two regimes. The normalized local velocity distributions w= w, as
shown in Figs. 12c, decrease rapidly from the jet exit, then ap-
proaches gradually to low constant values in the downstream area.
For the cross ow-dominated  ow, w= remains at small negative
u
gibly small, at
17:36. The jet momentum in the jet-dominated
regime is large enough to resist the impact of the crossow so that
the de ection angle is small and the maximum height of the central
streamline is large.
u
w
x d D
valueseven at the downstreamregion =
25. For the transitional
x d
approaches almost null when = > 10. For the jet-
Turbulence Properties Along Central Streamline
u
 ow, w=
w
u
dominated  ow, w= remains positiveand does not approachzero
Figure 12 shows the central streamlines, normalized local ve-
w
p
u u
u
u02
u
/=
x d D
locities ( = and w= w), and turbulence properties [
.
,
even at the downstream stage =
appears that the change of jet momentum from the component to
25. From Figs. 12b and 12c, it
w
w
p
02
z
u
u0
u2
0
.w /= w, and w = w] along the centralstreamline in three  ow
R D
x
regimes. As shown in Fig. 12a, the central streamline for
in the crossow-dominated regime shoots up a short distance to
0:89
the component in the transitionalregime is most efŽ cient among
three characteristic ow regimes.
Fig. 12 Turbulence properties along central streamline.

HUANG AND HSIEH
1499
p
p
.w /=
02
u02
u
u
,
w
The normalized turbulence properties
.
/=
,
5Ramsey, J. W., and Goldstein, R. J., “Interaction of a Heated Jet with
a De ecting Stream,” American Society of Mechanical Engineers, ASME
Rept. 71-HT-2, 1971.
w
u0
u2
0
and w = of the central streamlines are presented in Figs. 12d–
w
12f. They increasequicklyin a shortaxialdistancebeforethe central
streamlinesare bentdue to the effectsof impingementand shear de-
veloped by the cross ow. The peak values occur where the central
streamlines make turns. The turbulence properties decrease drasti-
cally in a short distance after the jet bends, then approach constant
values in the downstream region. Around the bend over region, the
turbulences, which are induced by the momentum exchange of the
jet from the to the component in the jet-dominated regime, are
signiŽ cantly larger than those in the cross ow-dominatedand tran-
sitional regimes. The axial and lateral normal turbulenceintensities
may even attain 85 and 150%, respectively, which are certainly
beneŽ cial to the mixing between the jet and the cross ow  uids.
The axial and lateral normal turbulenceintensitiesalong the central
streamline around the impact and bend over regions are larger than
6Kamotani, Y., and Greber, I., “Experiments on a TurbulentJet in a Cross-
 ow,” AIAA Journal, Vol. 10, No. 11, 1972, pp. 1425–1429.
7Fearn, R., and Weston, R., “Vorticity Associated with a Jet in a Cross-
 ow,” AIAA Journal, Vol. 12, No. 12, 1974, pp. 1666–1671.
8Rudinger, G., and Moon, L., “Laser-Doppler Measurements in a Sub-
sonic Jet Injected into a Subsonic Cross Flow,” Journal of Fluids Engineer-
ing, Vol. 98, Sept. 1976, pp. 516–520.
9Crabb, D., Durao, D. F. G., and Whitelaw, J. H., “A Round Jet Normal
to a Cross ow,” Journal of Fluids Engineering, Vol. 103, No. 1, 1981,
pp. 142–153.
z
x
10Andreopoulos, J., and Rodi, W., “Experimental Investigation of Jets in
a Cross ow,” Journal of Fluid Mechanics, Vol. 138, 1984, pp. 93–127.
11Andreopoulos, J., “On the Structure of Jets in a Cross ow,” Journal of
Fluid Mechanics, Vol. 157, 1985, pp. 163–197.
12Sherif, S. A., and Pletcher, R. H., “Measurements of the Flow and
Turbulence Characteristics of Round Jets in Cross ow,” Journal of Fluids
Engineering, Vol. 111, June 1989, pp. 165–171.
those in the jet-wake and the tube-wake regions. For instance, al-
p
u02
u
thoughnot shown,
.
/= w is about 70% in the jet wake and 50%
13Blanchard, J. N., Brunet, Y., and Merlen, A., “In uence of a Counter
Rotating Vortex Pair on the Stability of a Jet in a Cross Flow: An Experi-
mental Study by Flow Visualizations,” Experiments in Fluids, Vol. 26, 1999,
pp. 63–74.
p
02
u
in the interface area and tube wake and .w /= is about 50% in
w
the jet wake, 40% in the interface area, and 30% in the tube wake.
Both the axial and the lateral normal turbulence intensities in the
jet wake are higher than those in the tube wake, which is similar to
the resultobtainedby Andreopoulos.20 Nevertheless,the impactand
the shear effects developed by the cross ow around the jet-turning
area can induce larger turbulence strength than the wake region. In
14McMahon, H. M., Hester, D. D., and Palfrey, J. G., “Vortex Shedding
from a TurbulentJet in a Cross-Wind,”Journal of Fluid Mechanics, Vol. 48,
1971, pp. 73–80.
15Kelso, R. M., Lim, T. T., and Perry, A. E., “An Experimental Study
of Round Jets in Cross-Flow,” Journal of Fluid Mechanics, Vol. 306, 1996,
pp. 111–144.
x d
the far downstream area = > 25, the turbulence strengths in the
transitional and the jet-dominated regimes get to almost the same
16Morton, B. R., and Ibbetson, A., “Jets De ected in a Cross ow,” Ex-
periments in Thermal Fluid Science, Vol. 12, No. 2, 1996, pp. 112–123.
17Fric, T. F., and Roshko, A., “Vortical Structure in the Wake of a Trans-
verse Jet,” Journal of Fluid Mechanics, Vol. 279, 1994, pp. 1–47.
18Brizzi, L. E., Foucault, E., and Bousgarbie`s, J.-L., “Vortices Organiza-
tion in the Near Field of a Jet Issuing Normally into a Cross ow,” Journal of
p
p
02
u02
u
u
levels: about 10% for
.
/0= w, 8% for .w /= w, and almost
u0
u2
zero for the shear stress w = w. Impingement and shear devel-
oped by the cross ow and the bend over of the jet are apparentlythe
most important mechanisms for turbulence generation in this type
of  ows.
z
Flow Visuali ation and Image Processing, Vol. 5, No. 1, 1998, pp. 17–28.
19Moussa, Z. M., Trischka, J. W., and Eskinazi, S., “The Near Field in
the Mixing of a Round Jet with a Cross-Flow,” Journal of Fluid Mechanics,
Vol. 80, Pt. 1, 1977, pp. 49–80.
Conclusions
The elevatedjet in thecross ow presentscomplexnear-wake ow
patterns in different regimes of jet-to-crossow momentum  ux ra-
tio. Three characteristic ow regimes, crossow-dominated,transi-
tional,and jet-dominatedregimes,areidentiŽed.Drasticdifferences
between the  ow patterns existing in different regimes are induced
by different extents of jet-shear and tube-tip downwash effects that
in uencethe jet and the tube wakes at differentjet-to-crossow mo-
mentum  ux ratios. In the crossow-dominated regime, the down-
wash effect overwhelms the up-shear effect of the jet. A downwash
area in the tube wake and a vortex in the jet wake are features of
the  owŽ eld. In the transitionalregime, three types of complex  ow
patterns with jet-wake and tube-wake vortices are found. In the jet-
dominated regime, no recirculationbubble is found in the jet wake
or the tube wake due to a strong up-shear effect of the jet. The
 ow structures in the horizontal planes reveal that the recirculation
bubbles in both the jet wake and the tube wake are unstable foci.
Around the interface area, stable foci may be found. The geometry
and turbulence properties of the jet central streamline re ect the
impact effects of the cross ow on the jet. The turbulenceproperties
alongthe centralstreamlinesshowthatsigniŽ cantturbulencesoccur
around the area of impingement, which is induced by the cross ow
on the jet and the region of jet turning. The axial and transverse
turbulence intensities, as well as the Reynolds shear stress around
the impingement and the jet-turning regions, attain large values in
the jet-dominatedregime.
20Andreopoulos, J., “Wind Tunnel Experiments on Cooling Tower
Plumes, Part I: In Uniform Cross Flow,” American Society of Mechanical
Engineers, ASME Paper 86-WA/HT-31, 1986.
21Andreopoulos, J., “Wind Tunnel Experiments on Cooling Tower
Plumes, Part I: In Non-Uniform Cross Flow of Boundary Layer Type,”
American Society of Mechanical Engineers, ASME Paper 86-WA/HT-32,
1986.
22Eiff, O. S., Kawall, J. G., and Keffer, J. F., “Lock-in of Vortices in the
Wake of an Elevted Round Turbulent Jet in a Cross ow,” Experiments in
Fluids, Vol. 19, No. 3, 1995, pp. 203–213.
23Eiff, O. S., and Keffer, J. F., “On theStructures in theNear-Wake Region
of an Elevated Turbulent Jet in a Cross ow,” Journal of Fluid Mechanics,
Vol. 333, 1997, pp. 161–195.
24Glass, M., and Kennedy, I. M., “An Improved Seeding Method for High
Temperature Laser-Doppler Velocimetry,” Combustion and Flame, Vol. 29,
1978, pp. 333–335.
25Mei, R., “Velocity Fidelity of Flow Tracer Particles,” Experiments in
Fluid, Vol. 22, No. 1, 1996, pp. 1–13.
26Steele, W. G., Taylor, R. P., Burrell, R. E., and Coleman, H. W., “Use
of Previous Experience to Estimate Precision Uncertainty of Small Sample
Experiments,” AIAA Journal, Vol. 31, No. 10, 1993, pp. 1891–1896.
27Perry, A. E., and Fairlie, B. D., “Critical Points in Flow Patterns,” Ad-
vances in Geophysics, Vol. 18, No. B, 1974, pp. 299–315.
28Chong, M. S., and Perry, A. E., “A General ClassiŽ cation of Three-
Dimensional Flow Fields,” Physics of Fluids A, Vol. 2, No. 5, 1990,
pp. 765–777.
29Perry, A. E., and Steiner, T. R., “Large-Scale Vortex Structures in Tur-
bulent Wakes Behind Bluff Bodies. Part 1. Vortex Formation,” Journal of
Fluid Mechanics, Vol. 174, Pt. 2, 1987, pp. 233–270.
30Hunt, J. C. R., Abell, C. J., Peterka, J. A., and Woo, H., “Kinematic
Studies of the Flows around Free or Surface-Mounted Obstacles; Applying
Topologyto Flow Visualization,” Journal of Fluid Mechanics, Vol. 86, Pt. 1,
1978, pp. 179–200.
References
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Research Council, R&M 3074, London, Oct. 1956.
2Keffer, J. F., and Baines, W. D., “The Round Turbulent Jet in a Cross-
31Sucec, J., and Bowley, W. W., “Prediction of the Trajectory of a Turbu-
lent Jet Injected intoa Cross owingStream,” Journalof FluidsEngineering,
Vol. 98, Dec. 1976, pp. 667–673.
Wind,” Journal of Fluid Mechanics, Vol. 15, No. 4, 1963, pp. 481–496.
3Margason,R. J., “ThePathofa Jet Directed at Large Anglesto a Subsonic
Free Stream,” NASA TN D-4919, 1968.
32Adler, D., and Baron, A., “Prediction of a Three-Dimensional Circular
TurbulentJet in Cross ow,” AIAAJournal, Vol. 17,No.2, 1979,pp.168–174.
4Pratte, B. D., and Baines, W. D., “ProŽ les of the Round Turbulent Jet in
a Cross Flow,” Journalof the Hydraulics Division, ASCE, Vol. 93, No. HY6,
1967, pp. 53–64.
I. Gokalp
Associate Editor