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Supersonic Rectangular Over-Expanded Jets of Single and Two-Phase Flows
ISABE 2003-1119
A. Mohamed* and A. Hamed†
Department of Aerospace Engineering & Engineering Mechanics
University of Cincinnati, Cincinnati, Ohio
T. Lehnig‡
Vice President and Director of Engineering and Operations
Coldjet Inc., Cincinnati, Ohio
Abstract
An experimental investigation was
conducted to study supersonic jets from
convergent divergent nozzles with
rectangular cross section.
The flow
regimes and shock structure in the plume
was characterized for jets in quiescent
atmosphere at over-expanded conditions.
Schlieren pictures of the jets are presented
to show the shock structure and jet spread
rate at different nozzle pressure ratios.
LDV measurements are presented for the
jet flow field and the centerline velocity
decay.
The results indicate that the
rectangular supersonic jet spread rate is
greater along the minor axis and increases
with the nozzle pressure ratio.
The
individual shock cell length, as well a, the
total number of shock cells within the jet
plume were found to increase with nozzle
pressure ratio. In two-phase rectangular
jets of gas and dispersed solid particles the
shock strength was found to attenuate with
increased particle loading.
Introduction
Recent interest in rectangular supersonic
jets is motivated by the need to reduce
plume length and acoustically excited
structural loads in the exhaust systems of
high performance aircrafts. Semi-periodic
_____
*Doctoral student
†Professor, Fellow AIAA
‡Member AIAA
shock structures form in the jet plumes of
these vehicles during low speed flight when
the convergent divergent nozzles operate at
off design conditions. These shock cells
affect the jet velocity and temperature decay
as well as the jet spread rate and its acoustic
field.
A number of studies presented experimental
results for the centerline jet velocity decay
and spread rate of subsonic rectangular jets.
Sfier [1] studied air jets issuing from
rectangular channels and slots in quiescent
atmosphere. The results demonstrated that
the jet growth rate in terms of the 50%
velocity spread was greater in the direction
of the minor axis. Sfier also presented
experimental results for the axial variation
of the mean velocity, longitudinal and lateral
turbulence intensity and turbulence shear
stress profiles and compared them to twodimensional jets. Lazanova and Shanov [2]
conducted an experimental investigation to
study the effect of rectangular jet aspect
ratio on subsonic jet velocity and turbulence
intensity. Experimental data obtained from
50 m/sec jets for aspect ratios between three
and ten indicated that jet spreading rate in
higher in the direction of the minor axis and
that the crossover point of the jet half width
moved downstream with increased aspect
ratio.
They also presented the axial
variations in jet entrainment, axial jet
momentum, and centerline turbulence
intensity. By computing separately the mass
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flow in four triangular sections from the
center to each of the four rectangular jet
sides, Lazanova and Shanov determined
that the entrainment in the quadrants
containing the long sides were double that
in the quadrant containing the short side
which confirms the more intensive spread
of the jet in the minor plane. They also
investigated the turbulence intensity
patterns and the establishment of similarity
velocity after distances greater than forty
times the hydraulic diameter from the
nozzle exit plane.
Krothapalli et al. [3] studied the mixing of
incompressible rectangular jets for aspect
ratios between 5.5 and 16.7 up to axial
distances 115 times the jet exit width
(small nozzle dimension). Their results
demonstrated similarity in both the mean
velocity and shear stress profile in the
plane along the minor axis beyond 30
times the width.
Experimental investigations of rectangular
high-speed jets also indicated higher jet
spread rate in the plane of the minor axis.
Von Glahn’s experimental studies [4,5,6,7]
of rectangular and circular high-speed
subsonic jets in quiescent surroundings
confirmed that the spread rate of
rectangular jets in the direction of the
minor axis is greater than in circular jets
with the same area equivalent diameter.
Von Glahn [6] developed correlations for
the plume centerline velocity decay and
50% velocity spread variation with the
axial distance in terms of the jet aspect
ratio (AR), jet Mach number, and jet to
ambient temperature ratio. The correlations
were compared to the data for AR 6
rectangular jets at 0.784 Mach number and
for a heated Mach 1.045 jet. He gave a
different set of correlations in each of the
three jet regions, namely, the initial mixing
region, the transitional region, and the fully
mixed region. He also included flight effects
in the correlations based on velocity
measurements of jets from rectangular
nozzles in secondary streams. Seiner [8]
compared the measured centerline velocity
decay and acoustic efficiency of unheated
jets for circular and rectangular nozzles with
the same area equivalent diameter. The
results for these Mach 0.857 shock free jets
demonstrated the high mixing capability and
beneficial noise reduction of rectangular
nozzle exit geometry. A drastic reduction in
the potential core length of the rectangular
jet was reported compared to the equivalent
circular jet. Seiner [8] reported a less drastic
reduction in the core length of a Mach 1.52
fully expanded elliptic jet to 5.2 equivalent
diameters, as compared to a 7.8 round jet
[9]. Seiner [8] also presented phaseaveraged Schlieren photos of supersonic
elliptic jets at fully expanded and overexpanded conditions. While the Mach 1.52
fully expanded elliptic jet mixing layers
experienced similar growth rate along the
major and minor axes, the shock structure in
the jet plume greatly enhanced the jet
spreading rate along the minor axis in the
case of the over-expanded elliptic jet.
Several experimental and analytical studies
of under-expanded jets have been reported
in the literature. Adamson and Nicholls [10]
proposed a simple one-dimensional model to
calculate the boundaries and distance of the
first shock disk from the nozzle exit. They
reported good agreement between the
computed results and existing experimental
data [11,12]. Pao and Abdolhamid [13]
computed the flow fields of supersonic
under-expanded circular and elliptic jets
using different turbulence models and
compared the computed first shock cell
length with the experimental results for
Mach 2 circular jet [14]. Grenville et al. [15]
used a laser-based imaging method in a
wall-adaptive wind tunnel to define the outer
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edges of supersonic jets. They also
presented computed results that predicted
reductions in the jet core length in underexpanded and over-expanded jets with
increased and decreased nozzle exit static
pressure respectively.
Krothapalli et al. [16], Gutmark et al. [17]
and Zaman [18] conducted experimental
studies of under expanded jets of
symmetric and asymmetric cross sections.
Their results indicate that the presence of
shocks in the jet core further increased the
spread rate along the minor axis compared
to subsonic jets. Zaman [18] instantaneous
schlieren pictures demonstrated that tabs
spanning the narrow edges of the AR 3
rectangular
nozzle
weakened
the
shock/expansion structure, increased jet
spreading along the minor axis, and
reduced it along the major axis. Gutmark et
al. [17] demonstrated transition to flapping
mode at the minor axis plane for circular,
elliptic, and AR 3 rectangular jets. The
presented jet spread rate in the Mach 1-2.4
range demonstrated that the transition to
the flapping mode with increased Mach
number is abrupt in rectangular jets and
more gradual in elliptic and circular jets.
Tam [19] developed a linear shock cell
model in which the mixing layer was
approximated by a vortex sheet. Tam
demonstrated that his linear model
predictions of shock cell spacing agree
with the experimental results of Powell
[20] and Hammitt [21] for under expanded
rectangular jets with aspect ratios greater
than 4. His predications of screech tone
frequencies based on the weakest link
hypothesis [22] were in agreement with the
experimental results of Krothapalli [16]
and Powell [23].
A number of experimental and numerical
studies were conducted to Investigate
under-expanded circular jets of gas particle
flows. Both Lewis et al. [24] and
Sommerfeld [25] observed a forward shift in
the Mach disk with increased particle
loading. However, computational studies
either predicted a rearward shift in the Mach
disk location [26,27,28], or under predicted
[25] the forward shift.
Hamed et al. [29,30] conducted numerical
simulations of gas-particle flows to
determine the effect of particle loading in
supersonic 2DCD nozzles. The computed
results at over-expanded conditions with
internal shocks in the nozzle [29], indicated
that both shock strength and shock induced
flow separation region are reduced with
increased particle loading. Subsequently, the
effects of particle sublimation and interphase energy exchange were included in the
numerical simulations of CO2 pellet-blasting
nozzles [30].
The purpose of the present investigation is
to characterize the shock structures in overexpanded rectangular jets plumes. Schlieren
photographs are presented for overexpanded rectangular jets in quiescent
atmosphere to show the effect of nozzle
pressure ratio on the shock structure and jet
mixing. The results indicate that the mixing
rate is high along the jet’s minor axis at the
higher nozzle pressure ratios, but decreases
as the nozzle pressure ratio is reduced. In
over-expanded rectangular particle-laden
jets, the shock strength was found to
decrease as the nozzle pressure ratio was
reduced.
Experimental Method
Experiments were carried out in a blow
down facility with the jet discharging in the
quiescent laboratory air. The air supplied by
a compressor that pressurizes the ambient air
up to 200 psig was filtered, dried and stored
in a high-pressure reservoir consisting of 7
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tanks with a total volume of 102 m3. The
total temperature was equal to that of the
surrounding, and the total inlet pressure to
the nozzle was controlled and maintained
constant during the testing by a pressure
regulator. A particle feeder was designed
and manufactured to provide steady state
flow of particles at pressures up to 150 psi.
The particles were injected four meters
upstream of the nozzle inlet to insure good
mixing of the particles with the air.
Visualization of the supersonic jet and
shock structure was obtained by
shadowgraph and Schlieren photography,
with 100-watt mercury-vapor lamp as a
continuous light source. Two 12” diameter
parabolic mirrors with a focal length of
72” were arranged in the Z-shape
configuration to redirect the light from the
source through the test section and onto a
screen. In the Schlieren arrangements, a
knife-edge was placed at the focal point of
the mirror and oriented horizontally.
A two-component LDV system with
conventional optics manufactured by
Aerometrics Inc. was used in the present
study. The blue wavelength (488nm) and
green wavelength (514.5nm) lines from a
5-watt Spectra Physics argon-ion laser
were used to create the LDV measurement
volume. Velocities up to 570m/s could be
measured using transmitting optics front
lens with a focal length of 1000mm and a
beam spacing of 32mm. The scattered laser
light from the seeding particles in the test
section was collected in the forward
scattered mode by a 500mm (focal length)
receiving lens situated 20o off the forward
scatter axis. The transmitting and receiving
optics were mounted on two fixed tripods.
Traversing
the
measuring
volume
throughout the flow-field was achieved by
mounting the test nozzle on a computercontrolled 2D traverse mechanism. A two-
channel Real-time Signal Analyzer (RSA)
was used to process the LDV signal.
Doppler frequency information from the
signal analyzer was passed to a personal
computer. Control of the RSA was managed
by the personal computer via Data View
(DV) software package. The software
integrated the data acquisition process with
the nozzle traversing mechanism, yielding
automatic traversing capability during
testing. The high-pressure particle feeder
was used to seed the flow with 1-2m
diameter aluminum oxide particles.
Results and Discussion
The convergent divergent nozzle used in the
current experimental study has an exit-tothroat area ratio of 2.79 for a design Mach
number, Md of 2.5 and a design pressure
ratio, NPRd, of 19.4. The rectangular cross
section is 25.4mm x 4.92mm at the exit
plane for an aspect ratio (AR) of 5.1. Tests
were performed over a range of nozzle
pressure ratios, NPR, between 4-9. The
change in NPR was achieved by changing
the inlet stagnation pressure to operate in the
external over-expanded regime.
Figure 1a and 1b show Schlieren
photographs of the jet in the major and
minor axis planes at different nozzle
pressure ratios. The figure shows that the
shock strength as well as the total number of
shock cells in the jet plume decrease as the
nozzle pressure ratio decreases. The visual
jet spread rate along the minor axis is seen
to decrease as the nozzle pressure ratio
decreases. On the other hand, the visual jet
width in the major plane does not exhibit
noticeable spread, nor does it change with
the nozzle pressure ratio.
Sample contours of the axial jet velocity
from LDV measurements in the major axis
plane at NPR = 9, are presented in Fig. 2.
The velocities are normalized by the speed
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of sound, ao, based on the measured nozzle
inlet stagnation temperature, while the
distance is normalized by the nozzle minor
axis width, h. The measurements were
obtained up to x/h=16.6 on an 81  41
mesh by traversing the nozzle in 2mm
increments in both vertical and horizontal
directions. The corresponding centerline
velocity variation along the nozzle axis is
shown in Fig. 3. The centerline velocity
decay is reproduced in a log-log plot in
Fig. 4. One can see that the decay rate
approaches the classical x-1 line past the
shock cell zone.
NPR=9.0. The photographs clearly show
that as the particle loading increases, the
shock strength as well as the number of
shock cells decreases. Shock attenuation was
also predicted in the case of internal shocks
in a 2DCD nozzle operating at NPR much
less than the design value [29].
The distance from the jet exit to the first
shock intersection with the jet centerline,
L1 and the average distance between
subsequent shock intersections with the jet
centerline, LS, as determined from the
Schlieren photographs at the different
nozzle pressure ratios are presented in Fig.
5. Both first and subsequent shock cell
length are seen to increase with increased
NPR. The shock cell length was also
found to increase with nozzle pressure
ratio in underexpanded jets [31, 17]. The
rate of increase was dependant on the
nozzle design Mach number [31], and on
the shape of the jet cross section [17]. The
rate was higher for elliptic and highest for
rectangular jets, compared to circular jets
of the same equivalent diameter [17].
References
1. Sfeir, A.A., “The Velocity and Temperature
Fields of Rectangular Jets,” International
Journal of Mass Transfer, Vol. 19, pp. 12891297, 1975.
Test results were obtained for two-phase
rectangular jets at different particle loading
ratios. Long grain rice, was used to
simulate the cylindrical shaped CO2 pellets
in Coldjet’s blasting nozzles. The material
density, mean diameter and length of the
particles are 750 kg/m3, 1.5mm , and 5mm
respectively. A particle separator was
placed downstream from the jet to collect
the
suspended
particles.
Schlieren
photographs of the jet at different particle
loading ratios are shown in Fig. 6 for
Acknowledgements
This work was sponsored by NSF Grant
CTS-9812837. The authors would like to
acknowledge the valuable help of Prof. S.
M. Jeng, and to thank Mr. R. DiMicco for
his support.
2. Lozanova, M., and Stankov, P.,
“Experimental Investigation on the
Similarity of a 3D Rectangular Turbulent
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Effects on Centerline Velocity Decay for ColdFlow Acoustically Excited Jets,” NASA TM83502, 1983.
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7. Von Glahn, U.H., “Secondary Stream and
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C.J., “Near Acoustic Field and Shock Structure
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Sound and Vibration, Vol. 121, No. 1, pp. 135147, 1988.
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“Proposed relationship between broadband
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Shock Location in Under-Expanded Gas and
Gas-Particle Jets,” AIAA Journal, Vol. 2, pp.
776-777, 1964.
25. Summerfeld, M. “Experimental and
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28. Ishii, R., Umeda, Y., and Yuhi, M.,
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30. Hamed, A., Mesalhy, O., and Lehnig, T,
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Jets,” AIAA Paper 84-2275, 1984.
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NPR=9.0
NPR=8.5
NPR=8.0
NPR=7.5
NPR=7.0
Major axis plane
Minor axis plane
Figure 1a. Schlieren photographs of a rectangular jet at different nozzle pressure ratios (7.0-9.0).
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NPR=6.0
NPR=5.5
NPR=5.0
NPR=4.5
NPR=4.0
Major axis plane
Minor axis plane
Figure 1b. Schlieren photographs of a rectangular jet at different nozzle pressure ratios (7.0-9.0).
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Figure 2. Axial velocity contours (NPR=9.0).
Figure 3. Jet centerline velocity variation (NPR=9.0).
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Figure 4. Jet centerline velocity decay (NPR=9.0)
L1
Ls
Ls
Figure 5. Effect of nozzle pressure ratio on shock cell length.
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Particle loading = 0%
Particle loading = 12%
Particle loading = 15%
Particle loading = 30%
Particle loading=60%
Figure 6. Schlieren photographs of rectangular jet at different particle loadings (NPR=9.0).