Exp Fluids (2007) 42:941–954

DOI 10.1007/s00348-007-0305-3

RESEARCH ARTICLE

Experimental investigation of planar offset attaching jets

with small offset distances
Nan Gao Æ Dan Ewing

Received: 27 August 2006 / Revised: 28 March 2007 / Accepted: 30 March 2007 / Published online: 26 April 2007

Springer-Verlag 2007

Abstract An experimental investigation was performed Fpp power spectrum of the fluctuating pressure, Pa2/Hz
to characterize the development of planar jets initially Hs offset distance from the lower edge of the jet outlet
issuing parallel to an adjacent wall with offset distances of to the wall, m
up to 1 jet height and Reynolds number of 44,000. The Hj height of the jet, m
results showed that the initial development of the mean P mean pressure, Pa
flow field in the planar offset jets could be divided into five p¢ RMS value of the fluctuating wall pressure, Pa
regions; three associated with the jet attaching to the wall Re Reynolds number of the jet, UaHj/m
similar to other reattaching shear layer flows and two U streamwise component of the local mean velocity,
associated with the resulting planar wall jet flow. The m/s
transition from the reattaching flow to the wall jet flow was Umax maximum local mean streamwise velocity, m/s
also characterized by a significant change in the charac- Ua flow rate averaged velocity of the jet at the exit, m/s
teristic frequency, size, and convection velocity of the u¢ RMS value of the streamwise fluctuating velocity,
large-scale structures in the flows. m/s
u¢max maximum u¢ along the inner shear layer, m/s
Æuv æ turbulent Reynolds shear stress, m2/s2
W channel or facility width, m
List of symbols Xr attachment length, m
CP mean wall pressure coefficient, 2(P–P¥)/q U2a x spatial coordinate in the streamwise direction, m
Cp¢ fluctuating wall pressure coefficient, 2p¢/q U2a x1 location of the reference microphone in the two-
f frequency, Hz point measurements, m
x2 location of the second microphone in the two-point
measurements, m
The research was funded by the Natural Sciences and Engineering y spatial coordinate in the vertical direction, m
Research Council of Canada. y+1/2 outer half width of the jet, m
z spatial coordinate in the cross-stream direction, m
N. Gao
D. Ewing
Department of Mechanical Engineering, ho initial momentum thickness of the jet shear layer, m
McMaster University, Hamilton, ON, Canada L8S 4L7 m kinematic viscosity of air, m2/s
q density of air, kg/m3
Present Address:
qpp correlation coefficient of the fluctuating wall
N. Gao
School of Engineering, Sun Yat-sen University, pressure
Guangzhou 510275, China qpu correlation coefficient of the fluctuating wall
pressure and the streamwise fluctuating velocity
D. Ewing (&)
qpv correlation coefficient of the fluctuating wall
Queens University, Department of Mechanical
and Materials Engineering, Kingston, Canada pressure and the vertical fluctuating velocity
e-mail: ewing@queensu.ca s time interval, s

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942 Exp Fluids (2007) 42:941–954

1 Introduction Driver et al. 1987; Heenan and Morrison 1998; Lee and
Sung 2002; Spazzini et al. 2001) or flows separated from
Turbulent planar jets that are initially travelling parallel to bluff fore bodies (e.g. Kiya and Sasaki 1983, 1985; Cherry
an adjacent wall can effectively form a barrier between an et al. 1984; Hudy et al. 2003). The structures in these flows
outer flow and the wall or cause a maximum in the local are often characterized using measurements of the fluctu-
convective heat transfer rate when they attach to the wall, ating pressure or the fluctuating shear stress on the wall
making them useful in a range of thermal management below the reattaching shear layer. The spectra near the
applications. Previous investigations have characterized the reattachment location have a characteristic frequency at
Reynolds averaged flow fields in turbulent offset planar jets fXr/U¥  0.5–1 (e.g. Kiya and Sasaki 1983; Cherry et al.
analytically (Bourque and Newman 1960; Sawyer 1963; 1984; Farabee and Casarella 1986; Heenan and Morrison
Bourque 1967), experimentally (Sawyer 1960; Hoch and 1998; Lee and Sung 2002; Hudy et al. 2003; Spazzini et al.
Jiji 1981; Lund 1986; Pelfrey and Liburdy 1986; Nasr and 2001) that is associated with the passage of the large-scale
Lai 1997, 1998), and numerically using RANS models structures in the shear layer. The fluctuations near the
(Nasr and Lai 1998). The heat transfer from the wall to the separation point also often have a lower characteristic
flow has also been considered (Kim et al. 1996; Song et al. frequency of fXr/U¥  0.1 (e.g. Kiya and Sasaki 1985;
2000). Most of these investigations focused on jets with Cherry et al. 1984; Castro and Haque 1987; Driver et al.
initial offset distances larger than the jet height (Hj). In 1987; Heenan and Morrison 1998) that is associated with
these cases, the ratio of the reattachment length (Xr) of the the ‘flapping’ of the shear layer or a fluctuation in the size
offset jets to the offset distance (Hs) decreases as the offset of the recirculating flow region. These low frequency
distance increases in agreement with the model proposed fluctuations are not observed in all cases (e.g. Chandrsuda
by Bourque (1967) for fully developed turbulent attaching and Bradshaw 1981; Ruderich and Fernholz 1986), but
jets. modulate the structures in the shear layer when they are
There have been fewer investigations of jets with small present (e.g. Kiya and Sasaki 1985; Cherry et al. 1984;
offset distances where the jet interacts with and attaches Heenan and Morrison 1998).
to the wall in the near field of the jet, typical of the The interaction between the different motions will be
cooling jets used in the blown film manufacturing process further complicated in offset attaching jets by the presence
(cf Gao et al. 2005; Gao and Ewing 2005) that motivated of the large-scale structures in the outer shear layer of the
this investigation. In that application, there is also often a jet. The structures from the reattaching shear layer will also
second co-flowing jet between the main jet and the wall affect the large-scale structures in the wall jet downstream
that affects the interaction of the main jet with the wall. of the reattachment point. The wall pressure fluctuations
This investigation focusses on the development of a single are related to the turbulent fluctuations in the flow field
offset jet to better understand the effect that the offset through a Poisson equation and thus can be used to char-
distance has on the development of the offset jet. The acterize the transition between the different motions as the
effect of adding a co-flowing jet will be considered flow develops. The pressure fluctuations are also of prac-
elsewhere. tical interest for the blown-film manufacturing application,
Heretofore, there does not appear to have been any where the jets cool a pliable thin plastic film, because flow-
investigations that have characterized the flow field in induced vibrations occur even for moderate speed jets
offset jets with small offset distances (less than Hj). Lund considered here. Thus, space and time resolved measure-
(1986) did characterize the reattachment length for offset ments of the fluctuating wall pressure below the offset jets
jets with a wide range of offset distances, including small will provide insight into the nature of the dynamic loading
distances. There was good agreement with Bourque’s that occurs on the film in this application.
model for the jets with large offset distances, but not for This investigation examines the flow field and the large
small offset distances. The ratio of the reattachment length scale structures in planar offset turbulent attaching jets
to the offset height continued to change with the offset exiting long channels with small offset heights, up to Hj,
distance even for distances as small as 0.4 Hj. and Reynolds number of 44,000. The experimental facili-
There also does not appear to have been any investi- ties and methodology used in this investigation are outlined
gations that have examined the dynamics of the large-scale in the next section. Single-point measurements of the flow
structures in offset jets for any offset distance. The large- field are then presented. This is followed by measurements
scale motions in the offset attaching jets with small offset of the fluctuating wall pressure and the correlation between
distances should initially have features in common with the fluctuating wall pressure and the fluctuating velocity
other reattaching shear layer flows, such as flows over that are used to characterize the large-scale structures
backward facing steps (e.g. Farabee and Casarella 1986; present in the flow.

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Exp Fluids (2007) 42:941–954 943

2 Experimental methodology performed for the jet with W/Hj = 41 at a Reynolds number
of 44,000, while the static and fluctuating pressure were also
The development of the planar offset jets in this investi- measured for the jet exiting this channel when Hs/Hj = 1.
gation was examined using the two jets exiting the long The results from the two jets agreed as discussed below.
channels in the facility shown in Fig. 1. The air flow The profiles of mean velocity and turbulent stresses
supplied from a variable speed blower was split into five measured at the exit of the two channels were symmetric
hoses that led to a large upper settling chamber and fully developed. In particular, the Reynolds shear
(122 · 72.4 · 45.7 cm), and three hoses that led to a stress Æuvæ varied linearly across the core region of the flow
smaller lower settling chamber (81.3 · 40.6 · 22.9 cm). at the exit. The profiles measured along the upper channel
The hose connections included gate valves to block flow to outlet were uniform over the central region of the jet from
the channel not in use. The exit of the channel not in use –6 £ z/Hj £ 6, where z is the coordinate out of the page
was also sealed using tape to create a uniform boundary in Fig. 1. The variations in the mean and rms velocities
condition. Both settling chambers included layers of foam were within ±1 and ±2.5%, respectively, that were within
and perforated plates to condition the flow before it entered experimental uncertainty. The effect that the side walls had
the channel. The facility initially included bell mouths at on the development of the jet was examined by measuring
the channel entrances, but the exit profiles were uniform profiles across the jet as discussed below.
across more of the channel for square channel entrances The reattachment location of the jets, defined in terms of
that promote turbulence at the entrance. The height of the the location of zero mean shear stress, was determined
channel outlet (Hj) was 3.8 cm for the upper channel and using a surface oil flow visualization technique (cf
1.8 cm for the lower channel. The width of the channels Naughton and Sheplak 2002). In this approach, Dow
and the facility into the page (W) was 74.3 cm, so the ratio Corning 200 fluid was applied to the surface. The jet was
of the channel width to height (W/Hj) was 19.5 for the then run at the desired condition, while the oil was illu-
upper channel and 41 for the lower channel. The length of minated using a single wavelength light source and ob-
the upper channel was 81 cm or 21.3 times the channel served using a CCD camera. Once the reattachment
height, while the length of the lower channel was 50.8 cm location was evident in the resulting fringe pattern, the jet
or 28.2 times that channel height. was stopped and the reattachment length was measured
The jet exiting the channel in use developed over a using a ruler with a resolution of 1 mm. The repeatability
1.8 m long plate that was mounted parallel to the channels. of the reattachment locations determined through multiple
The height of this plate could be adjusted to change the runs was less than 8% for jets with Hs/Hj = 0.1 and 3% for
offset distance from the wall to the bottom of the channel jets with Hs/Hj = 1.0. The major source of this variability
outlet (Hs). The flow was also confined using an 80 cm was attributed to measurement uncertainty.
high back wall and two 100 cm high by 180 cm long side The development of the flow field in the offset jets was
walls. Most measurements reported here were performed characterized using single and cross hot-wire probes with
using the upper channel (with W/Hj = 19.5) when the an in-house anemometry system based on the designs
average velocity at the exit was 18.4 m/s. This corre- proposed in Perry (1982) and Citriniti (1996). The sensor in
sponded to a Reynolds number based on jet height of the single-wire probe had a diameter of 5 lm and a length
approximately 44,000. Measurements were performed for of 1.25 mm, while the sensors in the cross-wire probe were
Reynolds numbers of 20,000–50,000 for an offset distance 1.5 mm long. The hot wire probes were calibrated in a
of 0.4 Hj. Measurements of skin friction were also separate facility using a jet exiting a contoured nozzle that

Fig. 1 Schematic of the

experimental facility

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944 Exp Fluids (2007) 42:941–954

had a uniform exit velocity profile. The resulting response and 12. The locations used in the measurements were
curves were fit with a four-order polynomial, and a modi- varied according to the offset height.
fied cosine law (Bruun 1995). The microphones were calibrated externally using a
The flow field was measured by moving the hot-wire piston phone at 1,000 Hz. The measurements for one case
probe on a computer controlled traverse that could be were compared with measurements performed using a
positioned with an accuracy better than 0.05 mm. At each different bottom wall where the microphones were flush
point, the output signals from the anemometers were mounted with the surface. The magnitude of the pressure
sampled using a 14-bit A/D board at a frequency of fluctuations for the two configurations agreed to within
4,096 Hz for a total time of 50 s. The uncertainties in the 10%. The spectra also agreed up to 400 Hz that was above
mean velocity and rms velocity measurements due to the frequencies of interest here. The lowest resonance
sample size, evaluated following the approach in Bruun frequency of the cavity observed in the measurements was
(1995), were less than 1 and 3%, respectively, for a 95% 2,000 Hz. There was concern that the flush mounted
confidence interval. The ambient air temperature during the microphones could affect the flow along the wall so that the
measurements was measured using an RTD temperature measurements through the pinholes were used for all the
sensor with a resolution of 0.1C. The temperature varied results reported here. The ambient noise characterized by
less than ±1 C and the effect of the temperature change on leaving one microphone out of the flow in a typical
the velocity measurements was compensated using the experiment was less than 1% of the rms fluctuating pres-
technique proposed by Beuther (1980). sure measured in the wall jet region and a smaller fraction
Rectification in the hot-wire measurements was exam- of the result in the reattaching region. The responses of
ined using the probability density function of the instanta- these microphones were compared with a reference
neous fluctuating velocity for the single-wire measurements microphone using an acoustic chamber.
and using the phase diagram of the effective cooling The signals from the microphones were simultaneously
velocities for the cross-wire measurements (Tutu and acquired with the 14-bit A/D board in 100 blocks of 4,096
Chevary 1975). Rectification affected less than 1% of the data points at a frequency of 4,096 Hz. The uncertainties
data points for the single-point results reported here (other for the mean and fluctuating wall pressure due to the
than the outer most points in the exit profiles) that were sample size were less than 2 and 4%, respectively, for a
taken from the single-wire measurements. Rectification 95% confidence interval, while the uncertainties in the
affected less than approximately 2.5% of the data in the spectra were less than 20%, for a 95% confidence inter-
cross-wire measurements used for the pressure velocity val. The large-scale structures in the flow were further
correlations at the inner half-width. The estimate of the characterized by simultaneously measuring the velocity
cross-flow error in the single-wire measurements in the with the cross-wire probe and the fluctuating pressure on
attaching shear layer were 3–4% for the mean velocity and the wall using the microphones. The signals from the
15–20% for the rms fluctuating streamwise velocity at the transducers were again acquired with the 14-bit A/D
inner half-width near reattachment. The cross-flow error board in 100 blocks of 4,096 data points at a frequency of
was smaller upstream of this point and at the outer half- 4,096 Hz.
width.
The mean pressure on the bottom wall was measured
using a calibrated differential pressure transducer at a 3 Results
series of pressure taps mounted along the jet centerline.
This included 8 equally spaced taps between x/Hj = 0.25 Profiles of the mean velocity near the reattachment point in
and 2 and 16 equally spaced taps between x/Hj = 2.5 and the offset jet with Hs/Hj = 0.6 are shown in Fig. 2. The
12. The fluctuating static pressure on the bottom wall was mean velocities have been normalized using the average
measured using 16 Panasonic WM-60B microphones, that velocity at the jet exit, Ua, determined by integrating the
had flat responses for 20–5,000 Hz. The microphones were velocity profiles measured at the exit. The results show that
mounted directly into a series of blind cavities drilled from the bulk of the jet turns toward and then attaches to the
the bottom of the wall on a line that was 0.75 cm off the jet wall. The location of the maximum mean velocity initially
centerline. The microphones sensed the flow through a continued to approach the wall downstream of the reat-
1 mm-diameter, 5 mm-long pinhole drilled through the tachment location as the flow recovers to a wall jet. This
wall to the top of the cavity. There were 6 cavities at was observed in all of the jets. The effect that the side walls
equally spaced locations between x/Hj = 0.25 and 1.5, 9 in the facility had on the development of the jets was
cavities at equally spaced locations between x/Hj = 2–6, examined by measuring the development of the boundary
and 3 cavities at equally spaced locations between x/Hj = 8 layer on the side walls of the facility for the jet with
Hs/Hj = 1. The thickness of these layers grew to approxi-

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Fig. 2 Profiles of the mean x/Hj=0, x/Hj=1, x/Hj=2, x/Hj=3, x/Hj=4, x/Hj=5, x/Hj=6,
streamwise velocity in the
region x/Hj £ 6 for the jet with
Hs/Hj = 0.6 2

y/Hj
1

0
0 1 1 1 1 1 1 1
U/Ua

mately 5Hj at x/Hj = 12 and 7Hj at x/Hj = 20. Measure- indicating that the differences between the results in this
ments of the velocity distribution on the plane x/Hj = 12 investigation and those reported by Lund were likely due to
showed that the profiles of the mean and turbulent fluctu- the difference in the nozzle shape rather than the presence
ating velocity were uniform over the remainder of the jet. of the wall behind the channel outlet. Similar size differ-
The reattachment length for the jets with Hs/Hj between ences in the reattachment length were observed in jets
0.1 and 1.2 are shown in Fig. 3. The reattachment locations exiting different nozzles with larger offset distances (e.g.
determined for the two jets used here agreed to within Sawyer 1960; Nozaki et al. 1979, 1981; Nasr and Lai
experimental uncertainty. The normalized reattachment 1998).
location Xr/Hs was approximately 6 for jets with The development of the jets with different offset dis-
Hs .0:3 Hj ; similar to the results for a flow over a backward tances can be compared by examining the change in the
facing step (e.g. Eaton and Johnson 1981; Driver et al. maximum mean velocity, Umax, and in the outer jet half-
1987). The normalized reattachment length decreased width, y+1/2, with downstream location shown in Figs. 4 and
gradually with offset ratio for jets with Hs &0:3Hj ; similar 5. Here, y+1/2 is the distance from the wall to the outer
to the results of Lund (1986). The reattachment lengths location where the mean velocity is half the local maximum
here were approximately 15% larger than those reported by velocity. The results show that the development of the mean
Lund for a jet exiting a nozzle with a contoured lower velocity field in the offset jets can be divided into five re-
surface without a wall above the nozzle outlet. Measure- gions, three of which are associated with the reattaching
ments of the reattachment length were also performed here flow region typical of other reattaching shear layer flows,
for jets with Hs/Hj of 0.2–1 when the wall above channel and two of which are associated with the wall jet region. In
outlet was not present. The reattachment length differed by the first region (x/Xr £ 0.65), the maximum velocity is
less than 2% from the results when the wall was present, constant and the outer half width y+1/2 decreases gradually
as the jets curve toward the wall. The jets attach to the wall
in the second region (0.65 < x/Xr £ 1.1), which is char-
acterized by a rapid decrease in both the jet half-width and
6 the maximum velocity. The jet half width and the maximum
velocity initially remain unchanged in the third region
5 (x/Xr > 1.1) for the jets with small offset distances as the
jets reorganize after attaching to the wall. The third region
4 appears to end near x/Hj  6 likely with the interaction
between the outer and the inner shear layers or the end of the
s
X /H

3
near field in the jet. The fourth region ð6.x=Hj .10Þ is
r

characterized by a rapid decrease in the maximum velocity

2
and an increase in the jet half width, suggesting the flows
transition to the wall jets. The jets appeared to undergo a
1
transition to a fifth region near x/Hj  10, characterized by
0
an increase in the growth rate of the jet half-width in the
0 0.5 1 1.5 2 planar wall jet and a decrease of the decay rate of the
H /H
s j maximum velocity in the offset jet with Hs/Hj = 1. The
height of the maximum velocity in these jets also reached a
Fig. 3 Change in the reattachment location with offset height for
open circle the jet with W/Hj = 19.5, open triangle the jet with minimum near x/Hj = 10 providing further evidence that
W/Hj = 41, and filled circle reported by Lund (1986) there was a change in the development of the wall jet flows.

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946 Exp Fluids (2007) 42:941–954

Fig. 4 Change in the maximum (a) 1.5 (b) 1.5

local mean velocity with
streamwise distance for jets
with Hs/Hj = open circle 0 open 1.4 I II III 1.4
(Hs/Hj=0.6)
square 0.2 open triangle 0.4 IV V
inverted open triangle 0.6 open 1.3 1.3
diamond 0.8 and asterisk 1

max
Ua/Umax
1.2 1.2

U /U
a
1.1 1.1

1.0 1.0

0.9 0.9
0 1 2 3 4 0 2 4 6 8 10 12 14 16 18
x/Xr x/Hj

Fig. 5 Change in the outer jet (a) (b)

2.5 2.5
half width with streamwise dy+1/2/dx=
distance for jets with Hs/Hj =
0.065
open circle 0 open square 0.2 2 2
open triangle 0.4 inverted open
0.072
triangle 0.6 open diamond 0.8
and asterisk 1 1.5 1.5
j

j
/H

/H
+1/2

+1/2
y

y
1 1
IV V
III
I II (Hs/Hj=0.6)
0.5 0.5

0 0
0 1 2 3 4 0 2 4 6 8 10 12 14 16 18
x/Xr x/Hj

The measurements were not extended downstream in all of recovered more gradually, consistent with the change in the
the offset jets as the focus here was to examine the transition maximum mean velocity observed in Region III, and there
from the reattaching flow to the wall jet flow in the first four is a change in the development of mean flow downstream
regions. of the reattachment point with the offset height of the jet.
The change in the mean static wall pressure coefficient
with streamwise position in the different offset jets is 0.16
shown in Fig. 6. The results shown here for the jet with
0.12
Hj/Hs = 1 exiting the channel with W/Hj = 19.5 agreed
with results measured for the jet exiting the channel with 0.08
W/Hj = 41. The static wall pressure decreases to a local 0.04
minimum at x/Xr  0.65 or the end of Region I as the jets
0
CP

initially curve toward the wall, before increasing rapidly

through Region II to a maximum slightly downstream of -0.04
the reattachment location as the flow turned away from the
-0.08
wall, similar to other attaching flows (e.g. Eaton and
Johnson 1981; Farabee and Casarella 1986; Driver et al. -0.12
1987; Heenan and Morrison 1998). Both the maxima and
-0.16
minima in the static pressure coefficients increased when 0 1 2 3 4
the initial offset distance of the jet increased due to the x/Xr

differences in the trajectory of the jet toward the wall. The

Fig. 6 Distributions of the static wall pressure coefficient for jets
mean wall pressure downstream of the reattachment point with Hs/Hj = open triangle 0.2 open square 0.4 inverted open triangle
decreased to atmospheric pressure more gradually in the 0.6 open diamond 0.8 and open circle 1.0, and filled circle results
jets with the lower offset distances, indicating these jets from backward facing step (Heenan and Morrison 1998)

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Exp Fluids (2007) 42:941–954 947

The fluctuating wall pressure coefficients shown in suggesting that the turbulent fluctuations from the attaching
Fig. 7 collapse for x/Xr £ 0.65 or Region I. Thereafter, shear layer give way to those associated with the wall jet
the fluctuating pressure increased rapidly as the structures flow. The local minima in the fluctuating pressure did not
in the jets interacted with the surface, reaching a maximum occur at a distinct downstream point indicating that the
slightly upstream of the reattachment location, similar to change in the structures did not necessarily correspond
other reattaching flows. The maxima in Cp¢ here are be- with the change in the evolution of the mean flow field
tween the results for the backward facing step (e.g. Driver observed in Figs. 4 and 5.
et al. 1987; Heenan and Morrison 1998) and those for the The profiles of rms streamwise fluctuating velocity
reattaching flow over a bluff body (e.g. Cherry et al. 1984; measured in the offset jet with Hs/Hj = 0.6 are shown in
Hudy et al. 2003). The maximum in the fluctuating wall Fig. 8. The magnitude of the turbulent fluctuations in the
pressure coefficient increased from Cp¢  0.03 to 0.1 as the inner shear layer increases as the flow evolves downstream
offset distance of the jet increased or the ratio of initial until the jet attaches to the wall. Thereafter, the turbulence
momentum thickness to the offset distance (ho/Hs) de- fluctuations near the wall decrease due to the interaction
creased, consistent with the measurements in the backward with the wall. The change in the magnitude of the fluctu-
facing step (Eaton and Johnson 1981; Vogel and Eaton ating velocity in the shear layers for the different jets can
1985; Heenan and Morrison 1998). The initial momentum be compared by examining the change in the maximum
thickness of the inner shear layer of the offset jets were all value of the rms fluctuating velocity u¢max in the inner shear
approximately 0.027 Hj, so the ratio of ho/Hs decreased layers shown in Fig. 9. The results show that the size of the
from 0.14 to 0.027 as the offset height increased from 0.2 turbulence fluctuations in the inner shear layers of the
to 1. The ratio of ho/Hs did not change significantly for jets offset jets increased rapidly reaching a maximum upstream
with Reynolds numbers between 22,000 and 55,000, and of the reattachment location before decreasing downstream
this change in Reynolds number did not have a significant of the reattachment location. The size of the fluctuations in
impact on the magnitude of the wall pressure fluctuations. the inner shear layer near the reattachment location of the
The fluctuating wall pressure downstream of the reattach- jet increased as the initial offset distance of the jet in-
ment point in the offset jets eventually increases with creased and the shear layer had longer to develop before it
downstream position similar to the planar wall jet flow interacted with the wall.

Fig. 7 Distributions of the (a) (b) 0.12

fluctuating wall pressure
0.16
coefficient for jets with Hs/Hj =
0.1
filled triangle 0 open square 0.1
filled square 0.2 inverted open 0.12 0.08
triangle 0.4 inverted filled
triangle 0.6 open circle 0.8
Cp

filled circle 1.0, backward 0.06

C

0.08
facing steps squared times
Driver et al. (1987) circled 0.04
times Heenan and Morrison 0.04
(1998), and bluff body 0.02
reattachment circled dot Cherry
et al. (1984) circled plus Hudy 0 0
0 1 2 3 4 0 2 4 6 8 10 12
et al. (2003)
x/X x/Hj
r

Fig. 8 Profiles of the rms x/Hj=0, x/Hj=1, x/Hj=2, x/Hj=3, x/Hj=4, x/Hj=5, x/Hj=6,
fluctuating velocity in the region
x/Hj £ 6 for jet with Hs/Hj =
0.6 2
y/Hj

0
0 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2
u'/Ua

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948 Exp Fluids (2007) 42:941–954

Fig. 9 Distributions of the (a) 0.2 (b) 0.2

maximum local rms fluctuating
velocity in the inner shear layer
for the jets with Hs/Hj = filled 0.16 0.16
triangle 0 open square 0.1 filled
square 0.2 inverted open
0.12 0.12

u′max/Ua

a
triangle 0.4 inverted filled

/U
max
triangle 0.6 open circle 0.8 and

u′
filled circle 1.0 0.08 0.08

0.04 0.04

0 0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 1 2 3 4 5 6
x/Xr x/Hj

3.1 Measures of the large-scale structures cause it was near the lower end of the flat response region
for the microphones. The spectra for frequencies below this
The wall pressure fluctuations are related to the turbulent range (< 20 Hz) are dotted here for clarity. Higher fre-
fluctuations in the flow field through a Poisson equation quency peaks emerge at x/Xr  0.5, similar to other reat-
and thus can be used to examine the change in the struc- taching shear layer flows. The frequencies of these peaks
tures present in the flow as it evolves downstream. The associated with the large scale flow structures in the
spectra of the fluctuating wall pressure, Fpp, for jets with attaching shear layer decrease as the flows evolve down-
different offset distances are shown in Fig. 10. The pres- stream. The characteristic frequency near the attachment
sure spectra at x=Xr .0:4 show evidence of a significant point was fXr/Ua = 0.5–1.0 (depending on the offset dis-
low frequency peak at fXr =Ua .0:2; consistent with the tance) consistent with the results near the reattachment
previous measurements in some reattaching shear layer location in other reattaching flows.
flows (e.g. Kiya and Sasaki 1985; Cherry et al. 1984; Fluctuations with the characteristic frequency associ-
Driver et al. 1987; Heenan and Morrison 1998), that was ated with the reattaching shear layer persist in the pres-
also seen for the jet exiting the channel with W/Hj = 41. sure spectra until x/Hj = 6–8 but gradually disappear as
The precise frequency was difficult to determine here be- the flow evolves downstream, unlike other reattaching

Fig. 10 Spectra of the (a) (b) (c)

fluctuating wall pressure x/Xr
x/X x/Xr
normalized using length scale Xr r
0.16 0.11
for jets with Hs/Hj = a 0.2 b 0.6
and c 1.0 0.39
0.31 0.22

0.78
0.33
0.47
Fpp Ua /p,2 X r , arbitrary scale

1.2 0.43
0.62
1.6 0.78
0.54
1.9
0.93 0.65
2.3
0.76
1.1
2.7
0.87
1.2
3.1

1.6 1.1
0.5 0.75 1
H /H =0.2 H /H =0.6 H /H =
=1
s j s j s j
0.1 1 10 0.1 1 10 0.1 1 10
fXr/Ua fX /U fXr/Ua
r a

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Exp Fluids (2007) 42:941–954 949

flows (e.g. Cherry et al. 1984; Hudy et al. 2003). A lower Uc Dx=Hj
frequency peak also appeared upstream of this region. ¼ ; ð2Þ
Ua DsUa =Hj
The spectra of the fluctuating pressure from the offset jets
with Hs/Hj = 0.2 and 1 and the planar wall jet (Hs/Hj = 0) where Dx = x2–x1. The speed within each region was com-
plotted in terms of fHj/Ua are shown in Fig. 11. The puted by selecting two locations, x1 and x2, within the region
pressure spectra from the offset jets have peaks at fHj/Ua being considered. In region I, there was evidence of a
= 0.07–0.1 that began to emerge at x/Hj = 3–6 and downstream convection velocity of Uc  0.55Ua, and an
dominate the spectra in the wall jet region. A similar peak upstream convection velocity of U¢c  –0.2Ua similar to the
occurs in the spectra from the planar wall jet for x/Hj ‡ 3 results of Heenan and Morrison (1998) and Hudy et al.
suggesting the structures at this frequency are associated (2003) in flows over a backward facing step and a bluff
with the wall jet flow. body, respectively. The propagation velocity in region II
The correlation coefficients of the fluctuating pressure initially decreased to Uc  0.45Ua before increasing through
along the wall given by the reattachment region reaching Uc  0.8Ua in Region III
downstream of the reattachment point. The propagation
qpp ¼ pðx1 ; tÞpðx2 ; t þ sÞ=p0 ðx1 Þp0 ðx2 Þ; ð1Þ velocity then decreased to Uc  0.6Ua at x=Hj &6 or Region
IV, indicating again that there is a change in the passage of
for different points in the offset jet with Hs/Hj = 0.6 are
the large-scale motions as the flow travels from Region III to
shown in Fig. 12. The different regions of development in
Region IV. The propagation velocity of 0.6Ua was similar to
the mean flow defined previously are shown on this figure
the velocity observed at 4 £ x/Hj £ 12 in the planar wall
as a reference. The fluctuating wall pressures are well
jet (Fig. 13), where Uc  0.7Ua.
correlated in the different regions of mean flow
The results indicate that the correlation coefficient of the
development in this jet, but are not well correlated
fluctuating pressure along the wall can be used to charac-
between the regions, indicating that the structures change
terize where the structures near the wall change from those
as the flow evolves downstream. The propagation
associated with the attaching shear layer to those associated
velocity of the pressure fluctuations also changed
with the wall jet flow. Correlation coefficients of the
between regions. The propagation velocity of the most
fluctuating pressure measured downstream of the reat-
correlated fluctuations was determined from the slope of
tachment location in the jets with Hs/Hj = 0.2 and 1.0 are
the locus of the main positive peak in the cross correlation
shown in Fig. 14. The correlation coefficient and the
contour given by (Heenan and Morrison 1998; Hudy et al.
propagation velocity of the pressure fluctuations changed at
2003)

Fig. 11 Spectra of the (a) (b) (c)

fluctuating wall pressure
normalized using length scale x/Hj x/Hj(x/Xr) x/Hj(x/Xr)
Hs for jets with Hs/Hj = a 0 0.5(0.11)
b 0.2 and c 1.0 1 0.5(0.39)
2(0.43)
2
1.5(1.2)
FppUa /p Hj, arbitrary scale

3(0.65)
3 3(2.3)
4(0.87)
4 4(3.1)

6(4.7) 6(1.3)
6
,2

8(6.2) 8(1.7)
8
10(7.8) 10(2.2)
10
12(2.6)
12 12(9.3)

0.07 0.07 0.07

0.2
0.35
Hs/Hj=0 Hs/Hj=0.2 Hs/Hj=1.0
0.01 0.1 1 0.01 0.1 1 0.01 0.1 1
fH /U
j a

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950 Exp Fluids (2007) 42:941–954

Fig. 12 Correlation (a) 12 (b) 12 ρpp

coefficients, qpp, of the 0.5
11 V 11 V
fluctuating wall pressure for the 10 10 0.4
3 3
reference microphone at x1/Hj = 9 9 0.3
(x1/Xr) a 1.5 (0.5) b 3 (1.0) c 5 8 IV 8 IV 0.2
(1.7) d 7 (2.1) for an offset jet 7 7

x2 /H j
2 2 0.1
6 6

x2 /H j
with Hs/Hj = 0.6

x 2 /X r

x 2 /X r
0
5 III 5 III
4 4 -0. 1

3 II 1 3 II 1 -0. 2
2 2 -0. 3
1 I 1 I
-0. 4
0 0
-20 -10 0 10 20 -20 -10 0 10 20 -0. 5

τ U a/Hj τ U a/Hj

(c) 12 (d) 12
ρpp
11 V 11 V 0.5

10 10 0.4
3 3
9 9 0.3
8 IV 8 IV
0.2
7 7
2 2

x2 /H j
0.1

x 2 /X r
6 6

x 2 /X r
x2 /H j

5 5 0
III III
4 4 -0. 1
3 II 1 3 II 1
-0. 2
2 2
-0. 3
1 I 1 I
-0. 4
0 0
-20 -10 0 10 20 -20 -10 0 10 20 -0. 5
τ U /H τ U a/Hj
a j

Fig. 13 Correlation (a) (b)

coefficients, qpp, of the 12 12 ρpp
0.5
fluctuating wall pressure for the 11 11
10 10 0.4
reference microphone at x1/Hj =
9 9 0.3
a 3 and b 7 in the planar wall jet
8 8 0.2
(with Hs/Hj = 0)
7 7
x2/Hj
x2/Hj

0.1
6 6
0
5 5
4 4 -0. 1

3 3 -0. 2
2 2 -0. 3
1 1
-0. 4

-20 -10 0 10 20 -20 -10 0 10 20 -0. 5

τ U a/Hj τ U a/Hj

x/Hj  4 (x/Xr  3.2) in the jet with Hs/Hj = 0.2, and at qpv ¼ pðx1 ; tÞvðx; y; t þ sÞ=p0 ðx1 Þv0 ðx; yÞ: ð4Þ
x/Hj  8 (x/Xr  1.8) in the jet with Hs/Hj = 1.0. Thus, the
transition in the structures downstream of the reattachment Contours of the correlation coefficients between the fluc-
point does not correspond to the change in the development tuating velocities and the fluctuating wall pressure mea-
of the mean flow field, nor is it fixed in either x/Xr or x/Hj, sured at x1/Hj = 2 (x1/Xr = 0.43) in the offset jet with
likely because its position was determined by the promi- Hs/Hj = 1.0 are shown in Fig. 15. These contours were
nence of the structures formed in the attaching shear layer generated from velocity measurements at 16 · 20 equally
and the wall jet flow. spaced locations. The areas with large positive and nega-
The large scale structures can also be examined using tive correlations are related to the large scale structures in
the correlation coefficients between the fluctuating wall the attaching shear layer flow. The results indicate that the
pressure at a position x1 and the fluctuating velocities at structures are convected along the attaching shear layer and
different locations in the flow for time delays of s; i.e., along the wall in the region x/Hj ‡ 6 after the jet attaches to
the wall.
qpu ¼ pðx1 ; tÞuðx; y; t þ sÞ=p0 ðx1 Þu0 ðx; yÞ ð3Þ The development of the structures downstream of the
and reattachment point can be examined using the correlation

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Exp Fluids (2007) 42:941–954 951

Fig. 14 Correlation (a) 12 (b) 12 ρpp

coefficients, qpp, of the 11 V 11 V 0.5

fluctuating wall pressure with a 10 10 0.4

reference microphone at x1/Hj = 9 9 0.3

(x1/Xr ) a 3 (2.3) and b 5 (3.9) 8 IV 8 IV

6 6 0.2

for the jet with Hs/Hj = 0.2 (top) 7 7

x2/Hj

x2/Xr
5 5 0.1
6 6

x2/Hj
x 2 /X r
and c 7 (1.5) and d 10 (2.2) for 4 4 0
5 5
the jet with Hs/Hj = 1.0 4 III 3 4 III 3 -0.1
(bottom) 3 3 -0.2
2 2
2 2 -0.3
1 II 1 1 II 1
I I -0.4
0 0
-20 -10 0 10 20 -20 -10 0 10 20 -0.5

τ U a/Hj τ U a/Hj

(c) 12 (d) 12 ρpp

0.5
11 V 11 V
10 10 0.4

9 2 9 2 0.3

8 IV 8 IV 0.2
7 7
x2 /H j

0.1

x2/Hj
x 2 /X r

x 2 /X r
6 6
III III 0
5 5
1 1
4 4 -0.1
II II
3 3 -0.2

2 I 2 -0.3
I
1 1
-0.4
0 0
-20 -10 0 10 20 -20 -10 0 10 20 -0. 5

τ U a/Hj τ U a/Hj

3 3
ρpu(τ Ua/Xr=-0.43) ρpv(τ Ua/Xr=-0.43)
0.2 0.2
2 2
0.1 0.1
y/Hj

y/Hj

1 0 1 0

-0. 1 -0. 1
0 -0. 2 0 -0. 2
0 2 4 6 8 0 2 4 6 8
x/Hj x/Hj
3 3
ρ (τ U /X =0.14) ρ (τ U /X =0.14)
pu a r pv a r
0.2 0.2
2 2
0.1 0.1
y/Hj

y/Hj

1 0 1 0

-0.1 -0.1
0 -0.2 0 -0.2
0 2 4 6 8 0 2 4 6 8
x/H x/H
j j
3 3
ρ (τ U /X =0.72) ρ (τ U /X =0.72)
pu a r pv a r
0.2 0.2
2 2
0.1 0.1
y/Hj

y/Hj

1 0 1 0

-0.1 -0.1
0 -0.2 0 -0.2
0 2 4 6 8 0 2 4 6 8
x/H x/H
j j

Fig. 15 Correlation coefficients qpu (left) and qpv (right) for the fluctuating wall pressure at x1/Hj = 2 (x1/Xr = 0.43) and the fluctuating
velocities at different locations for time delays s Ua/Xr  –0.43 to 0.72 in an offset jet with Hs/Hj = 1 and Re  44,000

coefficients between the fluctuating velocities and the £ 16. In this case, the fluctuating pressure on the wall ap-
fluctuating wall pressure measured at x1/Hj = 8 shown in pears to be initially correlated with the fluctuating velocity
Fig. 16. These contours were generated from velocity associated with two different structures; larger structures
measurements at 16 · 20 equally spaced locations at that appear to span much of the outer jet, and smaller
x/Hj £ 8 and 8 · 20 equally spaced locations at 9 £ x/Hj structures near the wall from the attaching shear layer. The

123
952 Exp Fluids (2007) 42:941–954

ρ (τ U /X =-0.72) ρ (τ U /X =-0.72)
pu a r pv a r
0.2 0.2
3 3
0.1 0.1
2 2
j

j
y/H

y/H
1 0 1 0

0 0.1 0 0.1
0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16
x/H 0.2 x/H 0.2
j j
ρ (τ U /X =-0.48) ρ (τ U /X =-0.48)
pu a r pv a r
0.2 0.2
3 3
0.1 0.1
2 2
j

j
y/H

y/H
1 0 1 0

0 0.1 0 0.1
0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16
x/Hj 0.2 x/Hj 0.2

ρ (τ U /X =-0.24) ρ (τ U /X =-0.24)
pu a r pv a r
0.2 0.2
3 3
0.1 0.1
2 2
j

j
y/H

y/H
1 0 1 0

0 0.1 0 0.1
0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16
x/Hj 0.2 x/Hj 0.2

ρ (τ U /X =0) ρ (τ U /X =0)
pu a r pv a r
0.2 0.2
3 3
0.1 0.1
2 2
y/Hj

1 0 y/Hj 1 0

0 0.1 0 0.1
0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16
x/Hj 0.2 x/Hj 0.2

ρ (τ U /X =0.24) ρpv(τ U a /Xr=0.24)

pu a r
0.2 0.2
3 3
0.1 0.1
2 2
y/Hj

y/Hj

1 0 1 0

0 0.1 0 0.1
0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16
x/H 0.2 x/Hj 0.2
j
ρpu(τ U a /Xr=0.48) ρpv(τ U a /Xr=0.48)
0.2 0.2
3 3
0.1 0.1
2 2
y/Hj

y/Hj

1 0 1 0

0 0.1 0 0.1
0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16
x/H 0.2 x/Hj 0.2
j
ρ (τ U /X =0.72) ρpv(τ U a /Xr=0.72)
pu a r
0.2 0.2
3 3
0.1 0.1
2 2
y/Hj

y/Hj

1 0 1 0

0 0.1 0 0.1
0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16
x/H 0.2 x/H 0.2
j j

Fig. 16 Correlation coefficients qpu (left) and qpv (right) for the fluctuating wall pressure at x1/Hj = 8 and the fluctuating velocities at different
locations for time delays s Ua/Xr  –0.72 to 0.72 in an offset jet with Hs/Hj = 1 and Re  44,000

results show that the smaller structures from the attaching Thus, the structures near the wall in the offset jet do tran-
shear layer are convected downstream faster than the larger sition from those associated with the attaching inner shear
outer structures causing the inner structure to approach the layer to lower frequency motions associated with the
slower moving outer structure. The correlation measure- resulting wall jet flow.
ments suggest that the two structures merge and travel The structures in the attaching shear layer and the wall
downstream together in the region x/Hj ‡ 10. The resulting jet region are both three-dimensional in nature. The three-
correlations are similar to those observed in the planar wall dimensional development of the structures was examined
jet shown in Fig. 17, indicating that the merged structures in a separate investigation that considered the lateral cor-
are similar to those that develop in the planar wall jet flow. relation of the fluctuating velocity field and the fluctuating

123
Exp Fluids (2007) 42:941–954 953

ρ (τ U /H =0) ρ (τ U /H =0)
pu a j pv a j
2 2
0.2 0.2
y/Hj

j
0.1 0.1

y/H
1 1
0 0

0 -0.1 0 -0.1

0 2 4 6 8 -0.2 0 2 4 6 8 -0.2
x/H x/H
j j
ρ (τ U /H =2) ρ (τ U /H =2)
pu a j pv a j
2 2
0.2 0.2
y/Hj

j
0.1 0.1

y/H
1 1
0 0

0 -0.1 0 -0.1

0 2 4 6 8 -0.2 0 2 4 6 8 -0.2
x/H x/H
j j
ρpu(τ U a /Hj=4) ρpv(τ U a /Hj=4)
2 2
0.2 0.2
y/Hj

j
0.1 0.1

y/H
1 1
0 0

0 -0.1 0 -0.1

0 2 4 6 8 -0.2 0 2 4 6 8 -0.2
x/H x/H
j j
ρpu(τ U a /Hj=6) ρpv(τ U a /Hj=6)
2 2
0.2 0.2
y/Hj

j
0.1 0.1
1 y/H 1
0 0

0 -0.1 0 - 0.1

0 2 4 6 8 -0.2 0 2 4 6 8 - 0.2
x/H x/H
j j

Fig. 17 Correlation coefficients qpu (left) and qpv (right) for the fluctuating wall pressure at x1/Hj = 1.5 and the fluctuating velocities at different
locations for time delays s Ua/Hj  0–6 in the planar wall jet with Re  44,000

wall pressure and fluctuating velocity field. The results development of the resulting planar wall jet flow. The re-
showed that the integral length scale of the streamwise sults also showed that there was a change in the initial
fluctuating velocity in the lateral direction was growing as development of the attaching flow with the offset height,
the flow evolved downstream, and was approximately 0.3 from one similar to a shear layer attaching to the wall to
Hj (or 1.5% of the facility width) in the core of the wall jet one more characteristic of a fully developed jet attaching to
structure at x/Hj = 16 (from y/Hj  1.0 to 2.2). Thus, it was the wall. Evidence of this change was apparent in the
thought that the three-dimensional development of the reattachment length normalized by the offset height that
structures in the core region should not be affected by the was approximately 6 for jets with Hs =Hj .0:3 similar to
width of the facility. The lateral correlations decayed more flows over a backward facing step, but decreased with
slowly outside this region indicating the spanwise roller offset distance at larger distances similar to fully developed
structures played a more prominent role near the wall and jets attaching to a wall. The decay of the mean velocity and
in the outer region of the wall jet. The three-dimensional the recovery of the mean pressure in the jets with small
development of the structures will be considered in more offset distances after they attached to the wall were also
detail in a later paper. more gradual than those in jets with larger offset distances.
The results showed that there is also a transition in the
prominent structures near the wall as the flow develops
4 Concluding remarks downstream from those associated with the attaching inner
shear layer to a lower frequency motion associated with the
An experimental investigation was performed to charac- wall jet flow. Evidence of the change in the large-scale
terize the development of planar jets issuing parallel to an structures was observed in both the measurements of
adjacent wall with small offset distances. The results the fluctuating wall pressure and the correlation between
showed that the development of the mean flow field in the the fluctuating pressure and the fluctuating velocities in the
jets could be divided into five regions, three associated flow. The location of the transition in the structures did not
with the jet attaching to the wall, similar to other reat- correspond to the change in the development of the mean
taching shear layer flows, and two associated with the flow field, nor was it fixed in terms of x/Xr or x/Hj, likely

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954 Exp Fluids (2007) 42:941–954

because its position was determined in part by the promi- Heenan A, Morrison J (1998) Passive control of pressure fluctuations
nence of the structures formed in the attaching shear layer generated by separated flow. AIAA J 36:1014–1022
Hoch J, Jiji M (1981) Two-dimensional turbulent offset jet boundary
and the wall jet flow. The effect of the offset distance on interaction. J Fluids Eng 103:154–161
the interaction between the structures in the inner and outer Hudy L, Naguib A, Humphreys W (2003) Wall-pressure-array
shear layers as well as the three-dimensional development measurements beneath a separating/reattaching flow region.
of the structures will be considered in more detail in a later Phys Fluids 15:706–717
Kim D, Yoon S, Lee D, Kim K (1996) Flow and heat transfer
paper. measurements of a wall attaching offset jet. Int J Heat Mass
Transf 39:2907–2913
Acknowledgments This work was funded by the Natural Sciences Kiya M, Sasaki K (1983) Structure of a turbulent separation bubble.
and Engineering Research Council of Canada. The authors wish to J Fluid Mech 137:83–113
acknowledge Prof. J. W. Naughton for his assistance in the mea- Kiya M, Sasaki K (1985) Structure of large-scale vortices and
surements of the reattachment location, Dr. J. Hall for his suggestions, unsteady reverse flow in the reattaching zone of a turbulent
and Ms. L. C. Ofiara for her assistance in preparing the manuscript. separation bubble. J Fluid Mech 154:463–491
Lee I, Sung J (2002) Multiple-arrayed pressure measurement for
investigation of the unsteady flow structure of a reattaching shear
layer. J Fluid Mech 463:377–402
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