Flow Turbulence Combust (2011) 87:115–132
DOI 10.1007/s10494-011-9332-5
Experimental Studies on Co-flowing Subsonic
and Sonic Jets
Pinnam Lovaraju · E. Rathakrishnan
Received: 17 May 2010 / Accepted: 4 February 2011 / Published online: 24 February 2011
© Springer Science+Business Media B.V. 2011
Abstract Effect of an annular co-flow jet on the center jet at subsonic, correctly
expanded and underexpanded sonic conditions was studied experimentally. It is
found that the co-flow retards the mixing of the primary jet, leading to potential
core elongation. The characteristic decay of the jet is also retarded in the presence of
co-flow. With co-flow core length elongation of 40% and 80% were achieved for correctly expanded and underexpanded (NPR 7) sonic jets, respectively. Shadowgraph
pictures show that the co-flow is effective in preserving the shock-cell structures of
the inner jet, making the jet to propagate to a greater axial distance which otherwise
would have decayed faster.
Keywords Co-flow · Shocks · Jets · Mixing
Nomenclature
D
M
Me
NPR
Pa
Pb
inner nozzle (primary) exit diameter
local Mach number
jet Mach number
nozzle pressure ratio
atmospheric pressure
backpressure
P. Lovaraju (B)
Department of Mechanical Engineering, Lakireddy Balireddy College of Engineering,
Mylavaram, India
e-mail: lovaraju@gmail.com
E. Rathakrishnan
Department of Aerospace Engineering, Indian Institute of Technology Kanpur,
Kanpur, India
e-mail: erath@iitk.ac.in
116
P0
Pt
R
X
Y
Z
Flow Turbulence Combust (2011) 87:115–132
stagnation chamber pressure
pitot pressure
co-ordinate along jet radial direction
co-ordinate along jet axis
co-ordinate along transverse direction
co-ordinate along normal direction
1 Introduction
Considerable amount of research has been reported on the mixing enhancement
techniques for subsonic and supersonic jet flows by many researchers [1–4]. However, mixing inhibition of jet flows also has been identified as important in several
industrial applications such as, disposal of exhaust gases from the silencer of heavy
automobile vehicles to higher altitudes, dispersion of exhaust plumes from a chimney
to large heights, flame length elongation of welding torch used for metal cutting
applications, to spray water to longer distances from hoses of fire fighters, etc. The
hot supersonic jets exhausting from the engines of high-speed aircraft are powerful
noise generators, especially during take-off, which is one of the major technological
hurdles facing the supersonic air transport. It has been found that the near and far
field supersonic jets are much noisier than the subsonic jets, due to the intense Mach
wave radiation [5–7]. In addition to Mach wave noise, screech becomes dominant
for both underexpanded and overexpanded jets with strong shocks in the core.
To reduce the Mach wave radiation of the supersonic jets, co-flow is found to be
promising. The principle of Mach wave elimination is to surround the jet exhaust
with a layer of co-flowing stream whose properties are tailored such that the jet
eddies become subsonic with respect to the co-flow and the co-flow eddies are
subsonic with respect to the ambient air stream [6–10]. The flow structure of a co-flow
jet configuration is considerably complex, because the surrounding jet drastically
influences the inner jet characteristics. The mixing between the streams is connected
with and controlled by the dynamics and interactions of the vortical structures that
are present in the shear layers developing between the two jet streams and between
the surrounding jet and the ambient fluid [11]. Sundaravadivelu et al. [12] reported
that co-flow retards the mixing of the primary jet, without giving any physical
reason for that. Recently Sharma et al. studied the effect of co-flow on the primary
supersonic jet from Mach 2 nozzle at different levels of overexpansion [13]. It was
found that the co-flow inhibits the mixing at all levels of overexpansion for Mach
2 nozzle. Thus, study of co-flow jet characteristics are of great interest from both
academic and practical application points of view and a thorough understanding of
the relative influence of the various parameters on the near-field development of
jets is essential for such applications. To gain an understanding about the mixing
inhibition capability of co-flow on subsonic and sonic jets, the flow development
and mixing characteristics of a circular jet at subsonic and correctly expanded and
underexpanded sonic conditions, without and with co-flow were investigated in the
present study.
Flow Turbulence Combust (2011) 87:115–132
117
2 Experimental Details
The experiments were conducted in an open jet facility at the High-Speed Aerodynamics Laboratory, Indian Institute of Technology Kanpur. A convergent circular
nozzle surrounded by an annular convergent circular nozzle with an annular gap
of 4.4 mm was used in the present investigation. The center nozzle inner diameter
was 11.6 mm and had a lip thickness of 2.65 mm. Outer nozzle inner diameter
was 25.7 mm and had a thickness of 5 mm. The exits of both inner and outer
nozzles were in the same plane and were mounted on a common base plate of
thickness 12 mm. The base plate has 30 small circular holes of diameter 2.5 mm
placed at a periphery radius of 20 mm from the center of the inner nozzle. These
small holes feed the annular jet. Co-flow nozzle used in the present investigation is
shown in Fig. 1. Figure 2 shows schematic diagram of co-flow model. Experiments
were conducted using the inner nozzle along with annular flow termed co-flow.
Without the annular flow, the inner nozzle flow is termed without co-flow. Pressure
measurements were carried out using a Pitot probe of 0.4 mm inner diameter and
0.6 mm outer diameter mounted on a traverse mechanism. The field pressure and the
stagnation chamber pressure were measured with a 9016 model pressure transducer.
Application software was used to interface transducer and computer. Experiments
were conducted using the inner nozzle alone (without co-flow) and with both inner
and outer nozzles (with co-flow). Both the nozzles get the pressure from the same
stagnation chamber. The stagnation pressure at the entry is the same for both the
nozzles. At the exit of the central nozzle the inlet stagnation pressure loss is almost
negligible as the flow through this nozzle satisfies the isentropic flow properties.
However, the flow through the surrounding nozzle is not isentropic, as there is an
inbuilt frictional loss due to the central nozzle inside. At the exit of the annular
passage, only around 45% of the running stagnation pressure is recovered. For
subsonic and correctly expanded sonic conditions, measurement of centerline Mach
number decay was carried out for the central jet without co-flow and in the presence
of co-flow at Mach numbers 0.6, 0.8 and 1.0. This gives general overview of the
primary jet development (without co-flow) in comparison with co-flow. To get an
insight into the flow development and mixing characteristics, grid study was carried
out (by measuring the pitot pressure at different grid locations in the jet field) at
Mach number 0.8 at axial locations of X/D = 2.0, 5.5, 8.0, 12.0, 15.0, 18.0 covering
Fig. 1 Experimental model
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Flow Turbulence Combust (2011) 87:115–132
Fig. 2 Schematic diagram of co-flow model
all regions of jet development. Iso-Mach contours in cross-sectional planes were
obtained using this grid study. Iso-Mach contour studies in axial plane were carried
out for Mach numbers 0.6, 0.8 and 1.0. To find out the rate of jet propagation, the
half-width was plotted for Mach numbers 0.6, 0.8 and 1.0. For underexpanded sonic
conditions, experiments were conducted for NPRs (NPR is the ratio of the inlet
stagnation chamber pressure (P0 ) to the ambient pressure (Pa ) to which the jet is
discharged) 3, 5 and 7. Radial pressure measurements normal to the jet axis were
carried out and plotted as pitot pressure profiles for NPR 5. Finally, shadowgraph
visualization was taken to visualize the wave structure in the primary jet and their
interaction with the co-flow jet.
2.1 Data accuracy
The possible sources of error of the present investigation are due to
•
•
•
•
Linear movement of traverse along X, Y and Z directions.
Settling chamber stagnation pressure measurement.
Error in the measurement of total pressure in the jet field.
Possible inaccuracies in nozzle dimensions.
The room temperature was almost constant with maximum variation of ±0.5◦ C
during one experimental run. The stagnation pressure was maintained manually
with an accuracy of ±0.1% through the application software developed in Lab
Flow Turbulence Combust (2011) 87:115–132
119
VIEW. Finally, although great care was taken in pitot pressure measurements, the
possibility of some inaccuracy in these measurements, in a highly turbulent and threedimensional flow field as in the present case cannot be ruled out. But it may be
justifiably assumed that, this slight inaccuracy may not effect the results significantly
as the results are primarily of comparative nature.
The pressures measured were accurate within ±2%.
3 Results and Discussion
3.1 Subsonic and correctly expanded sonic jet characteristics
3.1.1 Centerline Mach number decay
Centerline Mach number decay for subsonic and correctly expanded sonic jets are
presented in Fig. 3. The measured pitot pressures have been converted to Mach
number using isentropic pressure Mach number relation. The local static pressure
is taken as the pressure of the environment to which the jets were discharging. This
assumption is valid since all the subsonic jets are correctly expanded. The local Mach
number (M) is normalized with the jet Mach number (Me ) and axial distance (X)
is non-dimensionalized with the inner nozzle exit diameter (D). Figure 3a gives the
centerline Mach number decay of Mach 0.6 jet with and without co-flow. When there
is no co-flow, the potential core (the axial distance up to which the jet Mach number
is preserved) extends to about X/D = 5. In the presence of co-flow the core gets
elongated and extends up to X/D = 5.6. This implies that the co-flow protects the core
of the central jet. For Mach 0.8 jet (Fig. 3b), the jet core length of without and with coflow cases are X/D = 4.5 and X/D = 5.3, respectively. The centerline decay for Mach
1.0 jet is shown in Fig. 3c. It is seen that the central jet core of X/D = 5 is extended
to X/D = 7, by the co-flow. This is because when a jet is surrounded by the co-flow,
the central jet does not have direct contact with the surrounding environment. The
surrounding environment for the present study is the stagnant atmosphere (at zero
momentum). Only the outer boundary of the co-flow is in direct contact with the
surrounding environment. Thus, only the outer jet (co-flow) encounters entrainment
to begin with. The entrained mass is transported towards the inner jet, as the flow
propagates downstream. Before the mass entrained by the outer jet reaches the
boundary of the inner jet, the inner jet would be able to travel some downstream
distance without encountering any differential shear. Only from the downstream
location where the jet velocity at the inner boundary of the outer jet becomes less
than the velocity at the outer boundary of the inner jet, the inner or main jet would be
able to entrain the mass from the outer jet. Thereafter, the main jet also experiences
mixing. In other words, the co-flow, which surrounds the main jet, shields the jet from
interacting with the surrounding atmosphere up to some downstream distance from
the nozzle exit. Due to this shielding, the main jet experiences entrainment only from
the downstream location where the mixing initiated at the outer boundary of the coflow reached the outer edge of the main jet. Because of this delayed entrainment
experienced by the main jet, its mixing process of the main jet is greatly delayed by
the co-flow.
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Flow Turbulence Combust (2011) 87:115–132
1.1
1
With out co-flow
With co-flow
0.9
0.8
M/Me
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
X/D
(a) Mach 0.6
1.1
1
Without co-flow
With co-flow
0.9
0.8
M/Me
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
X/D
(b) Mach 0.8
1.1
1
Without co-flow
With co-flow
0.9
0.8
M/Me
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2.5
5
7.5
10
12.5
15
17.5
20
X/D
(c) Mach 1.0
Fig. 3 Centerline Mach number distributions for subsonic and transonic jets
22.5
25
Flow Turbulence Combust (2011) 87:115–132
121
3.1.2 Mach number prof iles
Figure 4 presents the radial Mach number variation of Mach 0.8 jet at axial distances
of X/D = 2.0, 5.5, 8.0, 12.0, 15.0 and 18.0, without and with co-flow cases. These plots
clearly show the effect of co-flow on central jet in the radial direction. Figure 4a
shows the radial distribution of Mach number for without co-flow case. The effect
of co-flow is clearly shown in Fig. 4b. The co-flow influences the Mach number
variations at all the axial stations compared to the without co-flow case. As the flow
travels downstream, the co-flow begins to interact with the main jet as seen in the plot
for X/D = 2 in Fig. 4b. With progressive increase of axial distance, the co-flow and the
1.2
X/D = 2.0
X/D = 5.5
X/D = 8.0
X/D = 12.0
X/D = 15.0
X/D = 18.0
1
M/M e
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
3.5
4
R/D
(a) Without co-flow
1.2
X/D = 2.0
X/D =5.5
X/D = 8.0
X/D = 12.0
X/D = 15.0
X/D = 18.0
1
M/M e
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
R/D
(b) With co-flow
Fig. 4 Mach number profiles at Mach 0.8
3
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Flow Turbulence Combust (2011) 87:115–132
main jet confluence, heading towards attaining equal Mach number. In the further
downstream stations, co-flow jet continues to be running with higher centerline Mach
numbers compared to the core jet in the absence of co-flow. These features clearly
demonstrate that, even in the far-field, the co-flowing jet has more kinetic energy
compared to without co-flow. This implies that co-flow delays the jet mixing activity
of the central jet both in the near and far fields significantly.
3.1.3 Iso-Mach contours of Mach 0.8 jet in cross-sectional plane
The centerline Mach number decay can be regarded as a gross measure of jet decay.
However, to account for mixing it is conventional to analyze the jet spread in planes
normal to the jet axis. The pressure distribution measured at different grid points in
the YZ-plane (normal to jet axis) at different axial locations are presented as isoMach contours in Fig. 5. In this the iso-Mach contours of main jet without and with
co-flow are compared. In these plots the innermost contour corresponds to M/Me =
1.0 and the outermost is for M/Me = 0.1. With the increase of axial distance X/D the
main jet without co-flow exhibits faster shrinkage of potential core region compared
to with co-flow. Iso-Mach contour levels in the plots are the measure of mixing of the
jet. Smaller spacing between the Mach number contours indicates lesser entrainment
into the jet and vice versa. In Fig. 5c for X/D = 8.0 location for without co-flow the
innermost contour is with M/Me = 0.8 and for with co-flow it is 0.9. Smaller spacing
at inner layer in the presence of co-flow indicates that there is lesser mixing because
it is bounded by the co-flow and spacing is more for without co-flow implying more
mixing.
3.1.4 Iso-Mach contours of co-f low jet in axial plane
To get a better picture of the jet propagation, iso-Mach contours were constructed
in the X/D and R/D directions for Mach numbers 0.6, 0.8 and 1.0. These results are
presented in Fig. 6. The result for Mach 0.6 jet is shown in Fig. 6a. It is evident from
this plot that the co-flow protects the main jet core because of the reduced mixing
caused by it. For example the contour level of M/Me = 0.9 ends at about X/D =
7.2 for without co-flow. In the presence of co-flow the contour level of M/Me = 0.9
extends up to about X/D = 9.5. Similar extension is seen for other values of M/Me .
Contour plot of Mach 0.8 jet is shown in Fig. 6b. For without co-flow the contour
level of M/Me = 0.9 extends up to X/D = 7 and for co-flow case it extends up to
X/D = 9.5. The contour levels for Mach 1.0 jet are up to X/D = 7.68 and X/D = 10.18
for without and with co-flow, respectively. Furthermore, the spread of the jet in the
radial direction is greater for without co-flow. This clearly demonstrates the reduced
mixing leading to lesser spread and longer core of the main jet in the presence of
co-flow at all the jet Mach numbers of the present study.
3.1.5 Jet half-width
Even though the core length, spread in the plane normal to the jet axis and radial
plane (mixing process) were analyzed based on centerline Mach number distribution
and iso-Mach contours, the quantification of mixing becomes authentic only when
the half-width (the radial distance at which the local Mach number is half of the
centerline Mach number) is measured. Therefore, jet half-width for different Mach
numbers were measured and analysed at a number of axial locations for both without
Flow Turbulence Combust (2011) 87:115–132
-2
-1
0
1
2
33
3 -3
2
2
2
2
1
1
1
1
1
0
0
Z/D
Z/D
3-3
123
-2
-1
-1
-1
-2
-2
-2
-3
-3
-1
0
1
2
3
2
33
0
0.9
-1
-2
1
0
0.9
0.1
-3
-3
0
-1
0.1
-2
-3
-2
-1
0
1
Y/D
Y/D
(a) Without co-flow
(b) With co-flow
2
-3
3
2
33
(a) X/D = 2.0
-2
-1
33
3 -3
2
2
2
2
1
1
1
1
0
0
1
2
0
0.9
-1
-1
0.1
Z/D
Z/D
3-3
-2
-1
0
1
0
0
0.9
-1
-1
0.1
-2
-3
-3
-2
-1
0
1
2
3
-2
-2
-3
-3
-2
-3
-2
-1
Y/D
0
1
2
-3
3
2
33
Y/D
(a) Without co-flow
(b) With co-flow
(b) X/D = 5.5
-2
-1
33
3 -3
2
2
2
2
1
1
1
1
0
0
1
2
0
0.8
-1
-1
0.1
Z/D
Z/D
3-3
-2
-1
0
0
1
0
0.9
-1
-1
0.1
-2
-3
-3
-2
-1
0
1
2
-2
-2
-3
-3
-3
3
-2
-2
-1
0
1
Y/D
Y/D
(a) Without co-flow
(b) With co-flow
(c) X/D = 8.0
Fig. 5 Iso-Mach contours of co-flow jet in cross-sectional plane for Mach 0.8 jet
2
-3
3
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Flow Turbulence Combust (2011) 87:115–132
-3
3
2
2
2
2
1
1
1
1
Z/D
-2
-1
0
0
1
2
3
Z/D
3
-3
3
0
0.6
-1
-2
-1
0
3
0
-1
0.1
-2
-1
3
-1
-1
-2
2
0.8
0
0.1
-3
-3
1
0
1
2
-2
-2
-3
3
-3
-3
-2
-2
-1
0
2
-3
3
2
3
1
Y/D
Y/D
(a) Without co-flow
(b) With co-flow
(d) X/D = 12.0
-2
-1
0
1
2
3
2
Z/D
1
0.4
0.5
0
3
-3
3
2
2
1
1
Z/D
-3
3
0
-1
-2
-1
-3
-3
-1
0
1
2
3
1
0.6
0
0
-1
-1
-2
1
2
-1
0.1
-2
0
0.1
-2
-2
-3
3
-3
-3
-2
-1
0
-2
1
2
Y/D
Y/D
(a) Without co-flow
(b) With co-flow
3
-3
(e) X/D = 15.0
-2
-1
0
1
2
3
Z/D
2
3
-2
-1
0
1
2
3
3
2
1
1
0
0
0.4
-1
0.1
-2
-3
-3
-3
3
-2
-1
0
1
2
3
Z/D
-3
3
2
2
1
1
0
-1
-2
-2
-3
-3
-3
Y/D
-1
-2
0.1
-2
-1
0
1
Y/D
(a) Without co-flow
(b) With co-flow
(f) X/D = 18.0
Fig. 5 (continued)
0
0.5
-1
2
-3
3
Flow Turbulence Combust (2011) 87:115–132
125
3
3
2
2
0.1
0.1
0.2
1
0.2
0.3
1 0.4
0.3
0.4
0.5
0.9
0
0.8
R/D
R/D
0.4
0.5
0.6
0.7
-1
-2
-2
0
3
6
9
12
15
-3
0
18
0.8
0.9
0
-1
-3
0.6
0.7
3
6
9
X/D
12
15
18
X/D
(a) Without co-flow
(b) With co-flow
(a) Mach 0.6 jet
3
3
2
0.1
2
0.1
0.2
0.2
1
0.3
1 0.4
0.3
0.4
0.5
0.5
0
0.9
1
0.7
0.8
R/D
R/D
0.4
0.6
-1
-1
-2
-2
-3
0
3
6
9
12
15
-3
18
0.8
0.9
0
0
3
6
X/D
9
0.6
0.7
12
15
18
X/D
(a) Without co-flow
(b) With co-flow
(b) Mach 0.8 jet
3
3
2
2
0.1
0.1
0.2
0.2
1
0.9
1
0
0.8
0.4
R/D
0.5
R/D
1 0.4
0.3
0.6
0.7
-1
-2
-2
-3
0
3
6
9
12
15
18
-3
0
X/D
3
0.8
0.9
1
0
-1
0.3
0.4
0.5
0.6
6
9
0.7
12
15
18
X/D
(a) Without co-flow
(b) With co-flow
(c) Mach 1.0 jet
Fig. 6 Iso-Mach contours of co-flow jet in axial plane
and with co-flow cases. It is important to realize that because of the co-flowing jet, the
jet half-width becomes authentic only from the beginning of the characteristic decay
of the central jet. The characteristic decay begins at around X/D = 7 for most of the
cases. Therefore, starting from X/D = 8, the half-width variation for without and with
co-flow for different Mach numbers are shown in Fig. 7. At all jet Mach numbers the
126
Flow Turbulence Combust (2011) 87:115–132
2
Without co-flow
With co-flow
R/D
1.5
1
0.5
0
8
12
16
20
16
20
16
20
X/D
(a) Mach 0.6
2
Without co-flow
With co-flow
R/D
1.5
1
0.5
0
8
12
X/D
(b) Mach 0.8
2
Without co-flow
With co-flow
R/D
1.5
1
0.5
0
8
12
X/D
(c) Mach 1.0
Fig. 7 Jet half-width variation
Flow Turbulence Combust (2011) 87:115–132
127
co-flow is found to retard the mixing beyond X/D = 8. However, extent of co-flow
influence is strongly governed by the jet Mach number. These results substantiate
the inference derived from the centerline Mach number distribution and the contour
plots.
3.2 Underexpanded sonic co-flowing jet characteristics
3.2.1 Centerline pitot pressure distribution
To study the effect of co-flow at underexpanded conditions, sonic jet at NPR 3,
5 and 7 were studied. It is well known that for sonic jets, NPR below 3.5 is low
underexpanded state. Above 3.5 is highly underexpanded state. Thus, the present
range of NPRs covers low to highly underexpanded states. For the underexpanded
jets, calculating Mach number from the measured pitot pressure is not possible since
the local static pressure varies from one point to another. Therefore, it is a usual
practice to analyze the jet decay in terms of pitot pressure variation. The measured
pitot pressure (Pt ) is made non-dimensional with settling chamber pressure (P0 ) and
plotted against the axial distance (X) which is non-dimensionalized with the central
(inner) nozzle exit diameter (D). These results are shown in Fig. 8, for without and
with co-flow. In these pressure plots, the core length is the axial extent up to which
pitot pressure oscillations prevail. In other words, the axial extent of supersonic zone
is taken as the core length for wave dominated jets (it should be noted that, even
though the Mach number at nozzle exit is sonic because of underexpanded state, the
flow expands through expansion fan at the nozzle exit and thus becomes supersonic).
Centerline pitot pressure decay for NPR 3, shown in Fig. 8a, exhibits oscillations up
to X/D = 6.5 for without co-flow. When the co-flow is introduced the oscillatory
nature of the pitot pressures continues up to X/D = 10.5. Also, in the characteristic
decay region the mixing of jet without co-flow is much higher than with co-flow.
At NPR 5, being highly underexpanded condition, a Mach disc is formed (seen as
the 1st lowest flat zone in Fig. 8b for without co-flow) at the end of the first shockcell. This is typical of highly underexpanded state. When the co-flow is introduced,
the Mach disc itself is not forming properly. This can be taken as an advantage from
core-length protection point of view. When the Mach disc is formed the flow crossing
the Mach disc experiences severe pressure loss. This prevents the jet from recovering
its momentum to the extent it would recover, if the Mach disc were not formed.
With co-flow, the Mach disc degenerates into a shock cross-over point (seen as single
point minimum). This may be because the expansion fan in the presence of co-flow
is unable to expand the flow to the extent it does when there is no co-flow. Because
of this, the jet in the presence of co-flow would be able to regain momentum to a
larger extent after the shock cross-over point. The core length for without co-flow is
up to X/D = 11.5, whereas in the presence of co-flow it extends up to X/D = 16.5. At
NPR 7, the Mach disc for without co-flow becomes much stronger and core is up to
X/D = 11.5. For co-flow there is no Mach disc formation and the core length extends
to about X/D = 19.5. The percentage increase of core length is 86% at NPR 7.
3.2.2 Pressure prof iles in radial direction for NPR 7
For the underexpanded sonic jets, to get an idea about the restriction encountered by
the main jet because of the co-flow, pitot pressure distribution in the radial direction
128
Flow Turbulence Combust (2011) 87:115–132
1.1
1
Without co-flow
With co-flow
0.9
0.8
Pt/P0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
X/D
(a) NPR 3.0
1.1
Without co-flow
With co-flow
1
0.9
0.8
Pt/P0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
X/D
(b) NPR 5.0
1.1
1
Without co-flow
With co-flow
0.9
0.8
Pt/P0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2.5
5
7.5
10
12.5
15
17.5
X/D
(c) NPR 7.0
Fig. 8 Centerline pitot pressure distributions for underexpanded jets
20
22.5
25
Flow Turbulence Combust (2011) 87:115–132
129
were measured at axial distances of X/D = 2, 4, 10 and 24. The non-dimensionalized
pitot pressure variation (Pt /P0 ) with non-dimensionalized radial distance (R/D) for
with and without co-flow cases for NPR 7 is presented in Fig. 9. At this NPR (Fig. 9a)
Mach disc has formed. For the case of this high underexpansion level there is no
Mach disc formation in the presence of co-flow. To understand the effect of co-flow
on the central jet shock structure and its influence on far-field, pressure distributions
in the radial directions were taken for both without and with co-flow cases. In Fig. 9a,
it is seen that there is a sharp rise in the pressure followed by decay at X/D = 2.0.
This indicates the presence of barrel type shock. This abrupt rise in pressure, seen
as off-center peaks, continues up to about X/D = 10.0, which implies the extent of
1
X/D = 2.0
X/D = 4.0
X/D = 10.0
X/D = 24.0
0.9
0.8
0.7
Pt /P 0
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
2.5
3
R/D
(a) Without co-flow
1
X/D = 2.0
X/D = 4.0
X/D = 10.0
X/D = 24.0
0.9
0.8
0.7
Pt /P 0
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
R/D
(b) With co-flow
Fig. 9 Pitot pressure profiles at NPR 7
2
130
Flow Turbulence Combust (2011) 87:115–132
supersonic region of the main jet without co-flow. Figure 9b presents the pressure
profiles for the jet with co-flow. These profiles clearly show the effect of co-flow
on the central jet characteristics at all axial locations. The variation of pressure is
distinctly different at all the locations, which suggests that the co-flow is effective in
modifying the shock-structure and mixing characteristics of the central jet. For jets
with co-flow the abrupt rise in pressure is observed in the near-field, however the
rate at which the pressure rises is lower compared to the jet without co-flow. This
means that, the strength of the shocks is less compared to the jet without co-flow. In
the far-field, the decay of the jet with co-flow is delayed to a larger extent compared
to the jet without co-flow.
(a) Without co-flow
(a) Without co-flow
(a) NPR 3
(b) NPR 5
(a) Without co-flow
(b) With co-flow
(b) With co-flow
(c) NPR 7
Fig. 10 Shadowgraph pictures
(b) With co-flow
Flow Turbulence Combust (2011) 87:115–132
131
4 Flow Visualization
Figure 10 shows shadowgraph pictures of the sonic jet operated at NPRs 3, 5 and 7
without and with co-flow. At NPR 3 (Fig. 10a), large number of weak waves are
observed. At NPR 5 and 7, shocks become stronger and distinct shock-cells are
formed. The barrel shock formed is clearly seen. In the presence of co-flow, because
of the restriction to expansion of the central jet, the flow is unable to accelerate to the
extent of without co-flow case. Also, there are just five cross-over points for without
co-flow case. Whereas, in the presence of co-flow the cross-over points become 11.
This clearly demonstrates the reason for the elongation of core length in the presence
of co-flow. It is evident from Fig. 10 that, the influence of co-flow on the central
jet shock-cells is significant. Thus, the co-flow is effective in modifying the shock–
expansion strength and reflection pattern. In addition, the shock-cells, which were
longer, become shorter in the presence of co-flow. The number of shock-cells of the
main jet also increases with the co-flow. A close observation reveals that, when the
jet expands right at the exit of the nozzle, the expansion waves get reflected from the
flow boundary created by the co-flow, as compression waves. Thus, the shock-cells
become smaller in size.
5 Conclusions
Co-flow is found to modify the characteristics of central jet development. Jet mixing
is retarded by the co-flow. Thus, the present model acts as mixing inhibitor. The
length of the potential cores of the subsonic and correctly expanded sonic jets
increase in the presence of co-flow. Core of the sonic central jet in the presence of coflow is 40% longer than the jet without co-flow. Jet half-width at all Mach numbers
indicates that the main jet spread is reduced by the co-flow. For underexpanded
sonic condition the shock-cells are protected by the surrounding co-flow, making
the central jet to travel to a greater axial distance. Co-flow is effective in modifying
the shock-structure and mixing characteristics of the central jet. The core length of
the underexpanded sonic central jet increases with increase of NPR. An increase of
86% in core length is obtained at NPR 7. The number of shock-cells increase in the
presence of co-flow and the classic Mach disc at NPRs 5 and 7 (for without co-flow)
is modified as a simple oblique shocks cross-over point.
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