effects of a low-density weak co-flow on the near field of an a xi symmetric jet_bonarski_ms
TRANSCRIPT
ON THE EFFECTS OF A LOW-DENSITY WEAK CO-FLOW ON THE NEAR FIELD OF AN
AXISYMMETRIC JET
by
Michael G. Bonarski
September 2010
A thesis submitted to the Faculty of the Graduate School of the University at Buffalo, State University of New York in partial fulfillment of the requirements for
the degree of
Master of Science
Department of Mechanical and Aerospace Engineering
Major Professor David J. Forliti, Ph.D.
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ACKNOWLEDGEMENTS
The author wishes to express his gratitude to a number or individuals who were vital to
the success of this project and his graduate studies as a whole. First and foremost, he would like
to thank his advisor, Dr. David Forliti. He has been extremely helpful and supportive, and
provided the insight to pursue this interesting research opportunity. The author would also like
to thank Dr. Paul Desjardin and Dr. Matthew Ringuette for being kind enough to serve as
committee members. He is also very appreciative of the funding received throughout his
graduate studies from the University at Buffalo through the Presidential Fellowship.
Many thanks go out to all the past and present graduate students of the Combustion
Laboratory including, Kareem Ahmed, Zak Carr, Arezoo Hajesfandiari, Dan Jason, Ben Knox,
Rahul Mulinti, Sann Naing, and Joe Richter. Their guidance, and assistance was highly valued,
as was their friendship. Joel Gabrielson and Paul Dack are also acknowledged for volunteering
to help during different phases of this project.
The design, manufacturing, and construction of the coaxial nozzle facility were difficult
and the project may not have materialized as well as it did, had it not been for the expertise of
Ken Peebles. His advice in these areas was second to none and was greatly appreciated. The
author is also grateful for the assistance from Dr. Bahattin Koc of the Industrial Engineering
Department, in manufacturing the nozzles used in this project by means of rapid prototyping.
The author would also like to thank Toni Schumacher and Carole Dentico for all their
administrative help throughout his graduate career.
Lastly, the author wishes to express his most sincere gratitude to all his family, friends,
employers, and all other UB faculty and staff, for their support and motivation throughout his 6+
years at the University at Buffalo, and making it a truly memorable and enriching experience.
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ................................................................................................ ii
LIST OF FIGURES ........................................................................................................... vi
LIST OF TABLES ............................................................................................................. ix
NOMENCLATURE ........................................................................................................... x
ABSTRACT ...................................................................................................................... xii
CHAPTER 1: INTRODUCTION ....................................................................................... 1
1.1 Motivation ................................................................................................................ 1
1.1.1 Mixing Enhancement ....................................................................................... 1
1.1.2 Turbulence and Mixing Suppression ................................................................ 2
1.1.3 Current Study ................................................................................................... 3
CHAPTER 2: LITERATURE REVIEW ............................................................................ 5
2.1 Free Shear Layers ..................................................................................................... 5
2.1.1 Axisymmetric Jets ............................................................................................ 6
2.1.2 Instability .......................................................................................................... 8
2.1.3 Effects of Initial Conditions ........................................................................... 13
2.1.4 Effects of Density ........................................................................................... 16
2.1.5 Effects of Compressibility .............................................................................. 20
CHAPTER 3: FACILITY & INSTRUMENTATION ...................................................... 22
3.1 Nozzle Design ........................................................................................................ 22
3.2 Test Facility ............................................................................................................ 25
3.3 Test Conditions ...................................................................................................... 25
3.3.1 Initial Conditions ............................................................................................ 27
3.4 Instrumentation & Data Collection Techniques ..................................................... 28
3.4.1 Particle Image Velocimetry ............................................................................ 28
3.4.2 Hot-wire Anemometry ................................................................................... 31
3.4.3 Schlieren Flow Visualization ......................................................................... 32
3.4.4 Flow Metering ................................................................................................ 33
CHAPTER 4: RESULTS .................................................................................................. 35
4.1 Schlieren ................................................................................................................. 35
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4.2 Particle Image Velocimetry.................................................................................... 37
4.2.1 Instantaneous Images ..................................................................................... 37
4.2.2 Velocity Field Statistics ................................................................................. 38
4.3 Hotwire Power Spectra .......................................................................................... 45
CHAPTER 5: CONCLUSIONS ....................................................................................... 48
5.1 Conclusions ............................................................................................................ 48
5.2 Future Work ........................................................................................................... 49
APPENDIX A: FIGURES .......................................................................................... 51
REFERENCES .................................................................................................................. xi
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LIST OF FIGURES
Figure 1: Example free shear layer boundaries and evolving velocity profile. ........................... 51
Figure 2: Velocity profiles at 5 downstream locations for an axisymmetric air jet ..................... 51
Figure 3: Vorticity profiles at 5 downstream locations for an axisymmetric air jet .................... 52
Figure 4: Axisymmetric jet structure ........................................................................................... 53
Figure 5: Evolution of vortex growth in the free shear layer. ...................................................... 53
Figure 6: Instantaneous PIV image demonstrating two vortices pairing ..................................... 53
Figure 7: Comparison of an air jet and a helium jet at similar Reynolds numbers ...................... 54
Figure 8: Schlieren photograph of a helium jet exhibiting a side jet. .......................................... 55
Figure 9: The scaled contours of the axisymmetric nozzles used in the experiment. .................. 56
Figure 10: Experimental apparatus setup for PIV. ....................................................................... 57
Figure 11: Cross-sectional view of piping leading up to coaxial nozzle apparatus ..................... 58
Figure 12: Velocity profile of the central air jet at 0.63 mm above the nozzle exit plane. .......... 59
Figure 13: Velocity fluctuations profile of the central air jet at 0.63 mm above the nozzle exit . 60
Figure 14: Setup used for PIV. .................................................................................................... 61
Figure 15: Sample instantaneous vector fields ............................................................................ 62
Figure 16: Schlieren setup ........................................................................................................... 62
Figure 17: Sample schlieren images ............................................................................................ 63
Figure 18: Sample PIV images for a central air jet with a 50 m/s mean velocity ....................... 66
Figure 19: Sample PIV images for a central air jet with a 17 m/s mean velocity ....................... 68
Figure 20: Streamwise velocity contours. ..................................................................................... 69
Figure 21: Streamwise centerline velocities. ............................................................................... 70
Figure 22: Transverse velocity contours. ..................................................................................... 71
Figure 23: Linear region of the shear layer width. ....................................................................... 72
Figure 24: Shear layer spreading rate for varying mass flow ratios. ........................................... 72
Figure 25: Streamwise velocity fluctuation contours. ................................................................. 73
Figure 26: Transverse velocity fluctuation contours. .................................................................. 74
Figure 27: Centerline transverse velocity fluctuations. ................................................................ 75
Figure 28: Centerline streamwise velocity fluctuations. ............................................................... 75
Figure 29: Turbulent kinetic energy production contours. .......................................................... 76
Figure 30: Peak transverse velocity fluctuations. ........................................................................ 77
Figure 31: Peak streamwise velocity fluctuations. ...................................................................... 77
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Figure 33: Maximum vorticity per streamwise location. ............................................................. 79
Figure 34: Instantaneous vorticity contours ................................................................................. 80
Figure 35: Power spectra at x/D=.45, y/D = .45. ......................................................................... 81
Figure 36: Power spectra at x/D = 2, y/D = .25. .......................................................................... 82
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LIST OF TABLES
Table 1: Annular to Inner Coaxial Jet Parameters ....................................................................... 26
Table 2: PIV Test Conditions ...................................................................................................... 26
Table 3: Measured Shear Layer Properties .................................................................................. 42
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NOMENCLATURE
a speed of sound
B shear layer width
D jet diameter
f focal length
vortex passage frequency
L nozzle contraction length
Lp potential core length
M annular to inner momentum flux ratio
Mc convective Mach number
PIV particle image velocimetry
volumetric flow rate
r nozzle contraction radius
rQ annular to inner mass flow ratio
rv annular to inner mean velocity ratio
R planar velocity ratio
R0 nozzle inlet radius
Re Reynolds number
RL nozzle outlet radius
R.xx radial location of xx% the local centerline velocity
S annular to inner density ratio
St Strouhal number
u local streamwise velocity component
U mean jet exit velocity
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Uo jet centerline exit velocity
v transverse velocity component
x streamwise distance
x0 virtual origin location
y transverse distance
Greek Symbols
∆t laser pulse separation
ρ density
θ momentum thickness
kinematic viscosity
Notations
( )i relative to inner jet
( )a relative to annular co-flow
( )’ root mean square of the velocity fluctuation component
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ABSTRACT
The near-field flow characteristics of an axisymmetric air jet issuing into ambient air
were studied, with a focus on the structure and growth of the instabilities and vortices within the
shear layer. Changes in the jet’s stability characteristics and spreading properties were observed
with the application of small levels of a helium co-flow shroud. The addition of the low-density
gas served to introduce density gradients within the shear layer, altering the density-weighted
vorticity profile, and a subsequent suppression of the Kelvin-Helmholtz instability. Density
gradients, visualized by the schlieren technique, indicated an increased delay in the formation of
vortex roll-ups and a greater suppression of the vortex pairing process for increased low-density
co-flow. Power spectra plots, obtained using hot-wire anemometry, suggest that the initial
instability frequency of the air jet remains constant throughout all conditions examined, however,
they are made more stable with increased annular flow. The effects of a more stable jet and
changes to the vortex dynamics brought on by a density gradient in the shear layer were revealed
in mean and instantaneous flow data obtained using particle image velocimetry. Co-flowing
mass flow rates of 2.5% resulted in a potential core length increase of 41% due to a 20%
reduction in the shear layer spreading rate. Reduced mixing and entrainment, and an overall
change of the turbulence profile also resulted from the applied annular flow.
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CHAPTER 1: INTRODUCTION
1.1 Motivation
The coaxial jet, or co-flowing axisymmetric jet, consists of a central jet surrounded by an
annular fluid flow. Each of the two streams exit a nozzle, where they are initially separated by a
thin splitter plate and undergo mixing and develop to a turbulent state typical of free shear flows.
This flow configuration is relevant in the aerospace industry and has been studied for roughly the
past 60 years. Many efforts have been made in the near-field region of the jet exit (less than
approximately 10-20 diameters downstream), where large coherent vortical structures are
generated due to flow instabilities. These structures facilitate mixing and shear layer growth and
ultimately break down to a fully-developed turbulent state. The round jet near-field region is of
particular interest for applications that would benefit from enhanced mixing (e.g. combustion
chamber design), as well as reduced turbulence intensity (e.g. jet exhaust noise suppression).
The aim of the current study is to investigate the near-field mixing characteristics of an
axisymmetric air jet with the presence of a density variation in the shear layer, generated via an
annular nozzle issuing varying amounts of helium co-flow. This simple configuration is
employed to achieve a density profile similar to one seen in jet flames, the inspiration for this
study, but without any of the associated temperature gradients.
1.1.1 Mixing Enhancement
Air-breathing engines in aerospace applications rely on flow dynamics to create a mixture
of fuel and air necessary for combustion. In an industry where weight is a major factor in
driving costs, it is desirable to minimize the required distance to thoroughly mix the two fluids
rapidly to a homogenous condition, as to permit a shorter and more efficient combustion
chamber design. Since bulk mixing and shear layer growth are directly governed by the
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behavior of the coherent vortex structures in the early stages of shear flow evolution, emphasis
for enhanced mixing (or reduced mixing, for that matter) has been placed on efforts that alter the
expression of jet instabilities. Passive control can achieve this through geometric modifications,
while active control accomplishes this with energy addition to the flow by means of excitation:
acoustics, a flapping ribbon, thermal techniques, or hydrodynamic methods, for example(Ho and
Huerre 1984). Using schlieren flow visualization and pressure measurements, Kedia and
Kurian(Kedia and Kurian 2005) showed that tabbed and lobed nozzles, a form of passive mixing
control, result in supersonic jets with reduced potential core lengths and greater mixing
capabilities. Samimy et al.(Samimy, Kim et al. 2007) demonstrated control over instability
mode expression of a jet, and was able to decrease the potential core length and enhance mixing
with electrical excitations from arc filament plasma actuators, located azimuthally around the
nozzle exit and using less than 1% of the jet flow power. These are but two accounts
demonstrating different methods of control.
1.1.2 Turbulence and Mixing Suppression
Reduced mixing and reduced turbulence via active or passive control is also of interest to
the aerospace industry. Tam(Tam, Viswanathan et al. 2008) identified both fine-scale turbulence
and the large coherent turbulent structures, produced from jet instabilities, as the sources of noise
in axisymmetric jets. It was also concluded that the dominant source of noise is located
immediately downstream of the jet potential core, in agreement with others(Laufer 1976;
Schaffar 1979) who identified it to be confined between one and two potential core lengths
downstream of the nozzle exit. Acoustic theory first put forth by Lighthill(Lighthill 1952)
speculated jet noise changes proportionally to the exit velocity to the eighth power. It was later
shown that noise reduction could also be achieved by introducing an annular jet of the same
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fluid. A regime of annular to central jet velocities below one resulted in reduced noise levels as
observed experimentally by Williams, Ali, and Anderson(Williams, Ali et al. 1969), with the
maximum attenuation near a velocity ratio of one half. Balsa and Gliebe(Balsa and Gliebe 1977)
also demonstrated reduced noise levels for velocity ratios less than one using numerical methods,
citing reduced turbulence as the cause. More recently, other intricate methods, such as water
injection(Krothapalli, Venkatakrishnan et al. 2003) and microjets(Arakeri, Krothapalli et al.
2003), suppressed turbulence by 10-30% in a Mach 0.9 round jet, resulting in near-field noise
reductions of 2 to 6 dB. In both experiments, the injection of secondary flow was small in
comparison to the central jet: mass flow rates of approximately 5% and 1%, respectively.
A relevant mixing suppression application has been developed and patented by Praxair
Inc. for electric arc furnaces in the steel industry. Engineers developed a process and apparatus
called CoJet™ to deliver oxygen at supersonic speeds into molten metal baths. The technique
uses an oxy-fuel flame shroud and special injector nozzle to maintain original oxygen jet
diameter and velocity up to 70 diameters(Mathur and Messina 2001). This type of active
control, which has an overwhelming impact on the original oxygen jet dynamics, is similar to
those being utilized in the present investigation.
1.1.3 Current Study
Similar to some of the more recently developed methods eluded to, the current
investigation attempts to explore an active control technique to alter jet mixing behavior, using
an input that is small in magnitude in relation to the jet. Specifically, the goal of the study is to
explore the impact of a density variation in the shear layer of an axisymmetric jet. This is
achieved by introducing a weak co-flow of helium through an annular nozzle in a coaxial jet
configuration with the assumption that the low-density gas is entrained into the shear layer of the
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jet. Motivation for studying this technique of introducing a density variation comes from the
insight of Day, Reynolds, and Mansour(Day, Reynolds et al. 1998), who showed through
numerical simulations that the behavior of the mixing layer can be described and predicted from
the density-weighted vorticity profile, which is altered from the effects of both compressibility
and heat release. In addition, Rehm and Clemens(Rehm and Clemens 1999) demonstrated a
striking difference in jet structure between reacting and non-reacting planar jets, also indicating
that density variation within the shear layer may influence jet behavior; in this case a result of
heat release. Although density variation in the shear layer, as a means of control is a key point of
the study, direct measurements of density/composition within the flow-field are not made.
Instead, qualitative and quantitative techniques are used to compare jet structure and behavior,
with and without helium co-flow. Mean and instantaneous measurements are made using
particle image velocimetry to extract velocity, vorticity, and turbulence properties of the flow. In
addition, schlieren is used to visualize the flows, and a hot-wire probe is used to measure jet exit
conditions and obtain power spectra measurements.
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CHAPTER 2: LITERATURE REVIEW
2.1 Free Shear Layers
A free shear layer, or mixing layer, is the region in an unbounded fluid flow,
characterized by transverse velocity gradients, high levels of fluctuating velocity, and intense
mixing. It originates from the detachment of a boundary layer from the end of a surface, usually
a sharp splitter plate or trailing edge in the experimental setting, and it spreads approximately
linearly(Brown and Roshko 1974). Although not experimentally realistic, a shear layer can also
originate from an abrupt discontinuity in velocity, in the idealized inviscid condition(Lugt 1983).
Initial and downstream mean velocity profiles are shown in Figure 1 for a generic free shear
layer consisting of a single semi-infinite planar stream with some arbitrary velocity, U, coming
into contact with a stagnant fluid. Progressing downstream, the velocity profile broadens and the
shear layer grows in thickness, resulting in increased mixing between the main flow and ambient
fluid. The broadening of the velocity profile is coupled with the diffusion of vorticity as
governed by the vorticity transport equation (see Figure 2 and Figure 3 for profiles of the
axisymmetric shear layer from the current study). Due to the large velocity gradients at the
separation point, the vorticity will be at a maximum there in the absence of vorticity-generating
mechanisms within the flow. Progression downstream also leads to the evolution of a fully-
developed mixing layer, regardless of the initial conditions. Bradshaw(Bradshaw 1966) found
this to transpire at approximately 1000 initial momentum thicknesses downstream of the shear
layer separation point.
Aside from the simplistic single stream shear layer, emphasis has recently been placed on
the study of free shear layers between multiple interacting streams, as there are many practical
applications where two streams at different conditions are experiencing mixing. Ko et al.(Ko and
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Kwan 1976; Ko and Au 1985) for example, investigated co-flowing shear layers in the
axisymmetric jet, while Strykowski et al.(Strykowski and Niccum 1991; Strykowski and
Wilcoxon 1993; Forliti, Tang et al. 2005) has extensively studied the counter-flowing shear layer
for both planar and axisymmetric geometries.
2.1.1 Axisymmetric Jets
The axisymmetric shear layer is more complex than its planar counterpart, however, the
principles governing its behavior are essentially the same. In most experimental efforts, focus is
placed on the round jet exiting from a contraction nozzle, such that only a small boundary layer
exists near the wall, giving way to a top-hat velocity profile at the trailing edge. Due to this
geometry, the shear layer spreads radially both away from and towards the jet axis in the
downstream direction. Unlike the planar case, the axisymmetric shear layer eventually
converges on itself, shown experimentally to occur at the jet axis between 4 and 5 diameters
downstream(Dimotakis, Miakelye et al. 1983; Gutmark and Ho 1983). This pinches off a region
referred to as the potential core. The conical core of flow is nearly inviscid, maintaining the
initial jet exit velocity, and it is only weakly influenced by vorticity within the shear layer. The
extent of the potential core can be measured by the intersection of the constant and the
hyperbolic decrease in jet centerline velocity(Hinze 1959). Turbulence intensity, and more
specifically, the centerline turbulence intensity, is shown to reach a maximum at a location
between the end of the potential core and approximately 10 diameters downstream due to the
merging of shear layers(Boguslawski and Popiel 1979; Warda, Kassab et al. 1999).
While the shear layer inner boundary intersects at the end of the potential core, the outer
boundary continues to spread indefinitely, influencing a greater region of fluid. Downstream of
the potential core is a development or transition region, followed by a region of fully-developed
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turbulent flow and self-similarity(Hinze 1959) (see Figure 4). The self-similar solutions for both
mean velocity and turbulence quantities correspond to flow induced by a point source of
momentum located at a point on the jet axis, called the virtual origin (x0), which is found to vary
in location between upstream, downstream, or at the jet exit as a result of differing jet exit
conditions(Hussain and Zedan 1978; Revuelta, Sanchez et al. 2002).
2.1.1.1 Coaxial Jets
The structure of the coaxial jet varies from the single round jet by the presence of a
secondary or outer potential core and mixing region from the existence of the annular jet.
Interaction between the central and annular jets occurs within the inner mixing layer of the jet,
while the outer or secondary shear layer combines annular and ambient fluids. This type of
configuration was utilized in the current investigation as a means of introducing helium in close
proximity to the shear layer of an air jet. Because of the flows studied, focus is strictly placed on
coaxial jets with small outer to inner velocity ratios.
The homogenous coaxial jet structure and behavior was extensively studied by
Champagne and Wyganski(Champagne and Wygnanski 1971), and Ko and Kwan(Ko and Kwan
1976; Kwan and Ko 1977). They found the velocity and turbulence profiles far downstream
reach a self-similar state that depends only on virtual origin location and total jet momentum, in
agreement with single free jet results. They also established that a velocity ratio less than one
lengthens the potential core, while a velocity ratio greater than one shortens it, enhancing mixing
between the two streams. Hinze(Hinze 1959) presents an empirical relation established by the
experimental work of W. Forstall and Shapiro(Forstall and Shapiro 1950), correlating the length
of the potential core to velocity ratios over the range of 0.2 to 0.5, which will be referenced to in
Chapter 4. According to the relation, a trend of increasing potential core lengths should be
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observed for increasing velocity ratios, λ, (below one) of annular to inner jet flow. Subsequent
studies have gone on to examine how jet dynamics are affected by the velocity ratio in more
detail and over a broader range, as well as other parameters such as the ratio of exit areas, lip
thickness, density ratio, and momentum flux ratio (taking both density and velocity ratios into
account). One particular focus was placed on determining the effect of coaxial jet parameters
on acoustic noise production. Williams and Ali(Williams, Ali et al. 1969) and Balsa and
Gliebe(Balsa and Gliebe 1977) identified attenuation of jet noise for velocity ratios less than one,
both experimentally and computationally, and cited reduced mean shear and turbulence levels in
the inner mixing region as the cause. Maximum reductions were found for velocity ratios
between 40% and 50%. Dahm et al.(Dahm, Frieler et al. 1992), utilizing flow visualization,
suggested that variation in jet structure and behavior from changes in velocity ratio are due to
changes in the instability characteristics in the near field of the flow. A more general discussion
on the effects of velocity ratio on a free shear layer will follow in section 2.1.3.
2.1.2 Instability
The mechanism governing the interaction of parallel streams of fluid is the Kelvin-
Helmholtz instability. It dictates the behavior of the flow in uniform density shear layers, as well
as the configuration in the current investigation, which is a variable density shear layer. The
stability characteristics of a particular flow are determined when small disturbances are
introduced, naturally or artificially, and disrupt the equilibrium base flow. If those disturbances
are amplified, the flow is termed unstable, and subsequently if the disturbances are suppressed,
or not amplified, it is termed a stable flow (with respect to the type of disturbance introduced).
The interaction of numerous parameters results in the specific stability characteristics of a
flow. A fluid’s viscosity has both a stabilizing effect by means of energy dissipation, while at
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the same time a destabilizing one by means of momentum diffusion(Drazin and Reid 1981).
Nonetheless, the Reynolds number, whose lengthscale is defined according to the type of flow, is
attributed to driving the behavior. Above some critical Reynolds number, a flow is unstable, and
even above this value, the exact behavior of the instability is Reynolds number dependent.
Multiple investigations showed the instability of round jets evolve from a sinuous to pulsatile, or
varicose behavior at a critical Reynolds number (based on jet diameter) near the order of 103 for
both Pouiseuille flow jet exit conditions in water(Crow and Champagne 1971) and a top-hat
velocity profile in air(Becker and Massaro 1968). Therefore, experimental results suggest that at
Reynolds numbers above approximately 103, a round jet may be considered
turbulent(Boguslawski and Popiel 1979). However, other research has demonstrated flaws with
this train of thought. Heeg, Dijkstra, and Zandbergen(Heeg, Dijkstra et al. 1999) for example,
established that differences in pressure gradients resulted in drastically different critical
Reynolds numbers, varying by orders of magnitude. Lower critical Reynolds numbers resulted
from the presence of shear layer inflection points (where the derivative of vorticity equals zero),
explaining why counterflowing geometries are typically a more unstable flow. A wide range of
critical Reynolds numbers were also found for a number of different fluids under the same
Hagen–Poiseuille flow conditions by Novopashin and Muriel(Novopashin and Muriel 2002),
further demonstrating a universal independence of the Reynolds number on stability.
2.1.2.1 Vortex Evolution
At and above moderate Reynolds numbers in free shear flows, the appearance of large
coherent vortical structures or eddies in the shear layer is an inherent property of the Kelvin-
Helmholtz instability and they play an integral role in the transition of an initially laminar jet to
turbulence. The evolution of vortices in a free shear flow was described by Sato(Sato and Okada
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1966) and Freymuth(Freymuth 1966) as consisting of four distinct development regions or
processes and is pictured(Lugt 1983) in Figure 5. The free shear layer originates from the
separation of the boundary layer from the surface of a trailing edge and is followed by
exponential growth. Due to non-linear growth downstream, vortices roll up and this
phenomenon occurs at regular intervals, referred to as the vortex shedding frequency. Becker
and Massaro(Becker and Massaro 1968) determined that the distance from a nozzle exit to the
location of vortex roll-up, or the “wave-breaking” length, is a function of the jet diameter and
Reynolds number. As instability waves form, less dominant fluid stream (or the ambient fluid) is
engulfed into the shear layer by the more dominant one, and a larger interface between the fluids
facilitates greater mixing. This process, termed entrainment, is more generically defined as the
inclusion of fluid from outside the jet boundaries into the main turbulent stream(Falcone and
Cataldo 2003). The final region in the evolution of the shear layer is characterized by vortex
pairing and transitioning to turbulence. A sample instantaneous PIV image is provided in Figure
6, which shows two vortices of equal size rolling around each other and pairing to create a larger
vortex, similar in size to the one seen downstream. In an axisymmetric jet, the final vortex
merging occurs near the end of the potential core(Gutmark and Ho 1983). Winant and
Browand(Winant and Browand 1974) showed that the pairing process between two vortices
results in a vortex structure doubled in both size and spacing (frequency) and occurs repeatedly
until they breakdown to turbulence. A more significant finding is that the pairing process
directly controls the growth of the shear layer. In fact, the growth between vortex pairings is
relatively small, giving rise to the appearance of a step in the shear layer thickness at the site of
vortex mergings. Ho and Huang(Ho and Huang 1982) expounded on this concept when they
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demonstrated that a forcing mechanism could be used to significantly increase the shear layer
growth by the coalescence of multiple vortices at once, termed ‘collective interaction’.
2.1.2.2 Vortex Frequency
Besides controlling the growth of the shear layer, vortex structures also play an important
role in jet energy transport. Within the shear layer, vortices contain the largest amount of
turbulent kinetic energy, and transport this energy my means of inertial forces. Dominant vortex
passage frequencies are generally indicated by peak(s) within spectral density plots.
Determination of the vortex frequency within a flow is dependent upon the disturbances
(naturally or artificially produced) initiating the growth of instabilities in the flow. Wave
formation is dominated by a discrete frequency, corresponding to the most amplified (most
unstable) frequency predicted by linear theory. Forcing, or creating artificial disturbances,
commonly achieved by means of a mechanically oscillating ribbon or flap, or acoustic excitation
by an array of speakers, has been shown to influence a flow to express specific frequencies
and/or modes of instability; i.e. axisymmetric, helical(Ho and Huerre 1984). In the absence of
forcing, the peak frequency was demonstrated by Ko and Davies(Ko and Davies 1971) to be a
function of jet exit velocity, as well as axial and radial position in the near field (of an
axisymmetric jet).
Frequency is typically reported in the non-dimensional form of the Strouhal number, and
is given by , where is the preferred or peak frequency, U is the mean jet exit velocity
and L is some characteristic length scale. For a jet, the characteristic length is chosen to describe
the passage frequency for one of two sizes of instabilities, one on the order of the boundary
layer, scaling with the momentum thickness, and the other involving the jet column and scaling
to the jet diameter or width(Crow and Champagne 1971). In axisymmetric jets, Crow and
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Champagne(Crow and Champagne 1971) found that the most amplified frequency occurring at
the end of the potential core, or the preferred mode, has a Strouhal number based on jet diameter
of 0.3. Gutmark and Ho(Gutmark and Ho 1983) acknowledged that a wide range of Strouhal
numbers, from 0.24 to 0.64, have been reported in other studies, and attributed this to scatter in
the location of measurement and the range of frequencies that could be encountered as a result
due to jumps in frequency from the vortex pairing process. Ho and Huerre(Ho and Huerre 1984)
note that the range of data could be a result of data processing techniques, noise present in
individual facilities, or varying initial conditions (momentum thicknesses). Instabilities on the
order of the initial boundary layer, referred to as the shear layer or initial instability mode, also
show scatter in reported values, but maintains a Strouhal number of approximately 0.017 for the
axisymmetric jet(Gutmark and Ho 1983).
2.1.2.3 Linear Stability Theory
An analytical/numerical means has been established which analyzes the origins of
instability within a shear flow, and can be a useful means for studying factors influencing their
formation. The basis of this technique, termed linear stability theory, is to determine when a
flow becomes unstable due to the introduction of infinitesimal perturbations. The equations
governing the behavior of the flow are derived from a linearization of the Navier-Stokes
equations, where second order or higher fluctuating quantities are assumed negligible. This
assumption limits the relevance of linear stability theory to the very early stages of shear flow
instability. The resulting linearized equations for the parallel shear layer include the Orr-
Sommerfeld equation for viscous flows and the Rayleigh equation for inviscid (high Reynolds
number) flow. Solving the fourth order differential equation eigenvalue problem requires the
utilization of advanced approaches such as the shooting method, or projection method; a popular
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projection method is to use Chebyshev polynomials, for example. Because of the complexity of
the governing equations, early analyses have only been performed on a number of simple
velocity profiles for parallel and axisymmetric shear flows, including Blasius, Pouiselle, and
hyperbolic tangent profiles. However, advancement in techniques and computing has led to the
study of more complex velocity profiles and even variable density shear layers(Colucci 1993;
Srinivasan, Hallberg et al. 2010).
To successfully model a flow using linear stability theory, one must choose between
using spatial or temporal theory, which refers to the disturbances evolving in either space or
time(Huerre and Monkewitz 1985). Disturbances in unstable flows that grow and develop into
large vortex structures form at some preferred frequency depending on the conditions of the
flow. This frequency can be approximated by linear stability theory by mapping wavelength
amplification rates, as Ho and Huerre(Ho and Huerre 1984) have done (in their Figure 2). The
dominant instability forms at only the most amplified wavelength. Comparisons to experimental
results confirm the usefulness of this analytical tool. For example, one can compare the
experimental results of Strykowski and Niccum(Strykowski and Niccum 1992) to the linear
stability theory predictions by Pavithran and Redekopp(Pavithran and Redekopp 1989).
Nonetheless, there is still much ground to cover in gaining a more complete understanding of the
overall interaction between the numerous possible initial conditions and the resulting instability
behavior of a free shear flow.
2.1.3 Effects of Initial Conditions
The spatial developmental behavior of the free shear layer is determined by the initial
conditions. Consequently, the large scatter in jet data between similar studies has been attributed
to the varying initial conditions between jet facilities(Hussain and Zedan 1978; Gutmark and Ho
- 14 -
1983; Ho and Huerre 1984), as previously mentioned. The velocity ratio, density ratio, laminar
or turbulent initial boundary layer, facility disturbances, and the velocity profile and associated
flow properties are believed to be key initial condition parameters influencing the shear layer and
jet development. The influence of the jet Reynolds number and velocity ratio were previously
discussed: the velocity ratio effect was earlier described in terms of jet development, and will be
briefly touched on again with a focus on vortex structures. A thorough discussion on density
ratio will follow this section, as density is the focus driving the current research.
The initial laminar or turbulent state of the boundary layer was found to play a key role in
the jet near-field, specifically in shear layer development. It is suggested that the far-field
behavior is relatively unaffected by this characteristic, as self-similarity and asymptotic
turbulence levels were shown to occur at approximately the same x/D value for both cases(Ho
and Huerre 1984; Antonia and Zhao 2001). The state of the boundary layer is not a clear-cut
classification process, but has been defined based on a collection of factors including the
frequency spectrum, shape factor, and fluctuation intensity magnitude and profile(Hussain and
Zedan 1978). The criteria used in this study to classify the initial boundary layer will be
described later. A turbulent boundary layer, however, is typically achieved via a tripping
mechanism and is found to disrupt vortex formation and pairing during early nonlinear growth,
resulting in smaller spreading rates. This is attributed to turbulence being spread over a wider
range of wavenumbers(Russ and Strykowski 1993; Xu and Antonia 2002). Adversely, the
initially laminar boundary layer leads to regular pairing of coherent, organized structures and
thus, usually a larger shear layer growth rate in the developing region.
- 15 -
The shear layer growth rate is also highly dependent on the ratio of velocities across
streams of fluid. The velocity ratio is given by , where ∆U is the velocity difference
and provides a measure of the shear that drives amplification of instabilities, and Uav is the
average velocity, and provides a measure of the convection velocity of the structures(Ho and
Huerre 1984). Brown and Roshko(Brown and Roshko 1974) made the argument that R related
linearly to the shear layer growth rate, but that dependence is also based on the density ratio
across the streams. For lower values of R, vortex structures are stretched and flow development
is extended(Ho and Huerre 1984). This corresponds to increased potential core lengths in
axisymmetric jets. Dahm et al.(Dahm, Frieler et al. 1992) investigated the mechanisms behind
such trends using a laser-induced-fluorescence technique to visualize a coaxial jet configuration
over a wide range of velocity ratios. He found that vortex size and structure were greatly
affected across varying velocity ratios due to competition between instability modes.
Dominance of either the inner or outer shear layer, the mode of streamwise vortices (e.g.
axisymmetric or helical), and rotational interaction in the shear layer were all found to be
dependent upon the velocity ratio. Rotational interaction within the shear layer was defined by
the velocity profiles and termed shear-layer-like where dominated by vorticity concentrations of
one sign of circulation (e.g. coflowing streams) or wake-like where dominated by vorticity
concentrations of both signs of circulation (e.g. counterflowing streams). Although a smaller
range of velocity ratios were considered, Ko and Au(Ko and Au 1985) also observed competition
between the inner and outer shear layer structures, which led to varying mean jet properties.
Thus, it has been established that the jet shear layer is highly dependent on the exiting conditions
at the trailing edge because of varied vortex dynamics and instability mode competition.
- 16 -
2.1.4 Effects of Density
2.1.4.1 Single Shear Layers
The effects of density on the free shear layer have been studied both in terms of an initial
or freestream condition (i.e. variable density jets) as well as a more complicated entity entailing
compressibility (i.e. high mach number flows) and heat transfer (i.e. combustion and jet flames)
over the entire field of the jet. Brown and Roshko(Brown and Roshko 1974) studied the effects
of the ratio of the density of the freestream fluids on the plane mixing layer and found increased
spreading rates, based on vorticity thickness, when the high speed stream has lower density than
the low speed stream. Correspondingly, axisymmetric jet studies have demonstrated that the
low-density helium jet(Amielh, Djeridane et al. 1996) and heated jet(Russ and Strykowski 1993)
increase the spreading rate, decrease the potential core length, and result in more rapid velocity
decay compared to constant density jets.
More intense mixing and a quicker breakdown to turbulence was observed by the author
in some preliminary schlieren flow visualization in a helium jet compared to that of an air jet at
equal Reynolds numbers (see Figure 7). Observed trends result from changes in the stability
characteristics of the flow. Kyle and Sreenivasan(Kyle and Sreenivasan 1993) cited the
energetic and regular vortex pairing process, occurring closer to the jet exit, as the cause of early
potential core breakdown in low-density jets. Russ and Strykowski(Russ and Strykowski 1993)
also concluded a more organized vortex formation and pairing process taking place at lower jet
densities from narrower spectral distributions of disturbances. Kyle and Sreenivasan found the
vortex passage frequency to be dependent on density as well, as they observed a decrease in the
Strouhal number with jet density. This finding agrees with linear stability theory predictions:
see Trouve(Trouve, Candel et al. 1988) for a heated jet example.
- 17 -
Variation in density can also alter the type of instability within the flow. Kyle and
Sreenivasan(Sreenivasan, Raghu et al. 1989; Kyle and Sreenivasan 1993) observed a shift to a
more intense oscillatory instability, occurring for jet-to-ambient density ratios less than 0.6. This
compares to the linear stability theory analysis of Monkewitz and Sohn(Monkewitz and Sohn
1988), who determined a transition from convective to absolute instability to occur in hot jets for
density ratios less than a critical value of 0.72. Absolutely unstable flows are characterized by
exponential growth of disturbances everywhere in the flow, whereas disturbances are convected
away as they amplify, and leave the flow undisturbed, in the case of convectively unstable
flows(Huerre and Monkewitz 1985). Absolutely unstable flows also exhibit frequency spikes in
the spectral density plot with a dominant peak corresponding to the main disturbance frequency
and numerous harmonic and subharmonic peaks(Sreenivasan, Raghu et al. 1989).
Enhanced spreading and mixing in low-density jets is also facilitated by the formation of
side jets. Side jets result in radial ejection of fluid from the jet and subsequent entrainment.
Sreenivasan, Raghu, and Kyle(Sreenivasan, Raghu et al. 1989) captured photos of these side jets
using laser induced fluorescence, as did the present author using the schlieren flow visualization
(see Figure 8). Monkewitz et al.(Monkewitz, Lehmann et al. 1989) observed anywhere between
2 and 6 of these non-axisymmetric structures and attributed their formation to the Widnall
instability of the primary vortex rings. He also suggested that side jets are similar to, but more
intense than the formation of streamwise vortices, which result from azimuthal instabilities and
are found in unforced homogenous jets; observed by Yule(Yule 1978) and shown by Liepmann
and Gharib(Liepmann and Gharib 1992) to enhance entrainment.
2.1.4.2 Variable Density Coaxial Jets
- 18 -
The study of coaxial jets with large density differences has been limited, and usually
considers only a very specific configuration and range of parameters. Favre-Marinet et
al.(Favre-Marinet, Camano et al. 1999; Favre-Marinet and Schettini 2001) investigated the
regime of large momentum flux ratio coaxial flows with a low velocity, high-density central jet
and high velocity, low-density annular jet configuration, in order to model the conditions of
liquid propellant rocket engine injectors. It was suggested that the dynamics of a variable
density coaxial jet is governed by the momentum flux ratio (which takes the velocity ratio and
the density ratio into account) as it was found that the location of a regime of recirculation and
the potential core length were highly dependent on it. For the case of the single jet in coflow, a
trend of enhanced mixing was observed when the high-velocity stream was lower density. This
same trend was also confirmed for the coaxial jet configuration by Favre-Marinet, as well as by
Gladnick. In addition, Gladnick et al.(Gladnick, Enotiadis et al. 1990) concluded that the near
field mixing of a variable density coaxial jet is dominated by the large structures in the primary
shear layer, which he found to vary drastically for ratios between the co-flow and jet velocity
above, below, and equal to one. Transition to absolute instability has also been observed for the
right combination of velocity and density ratios in coaxial jets(Sreenivasan, Raghu et al. 1989;
Kyle and Sreenivasan 1993). Critical density ratios on the absolute/convective instability
interface for axisymmetric counterflowing streams were experimentally found and mapped for
varying velocity ratios by Strykowski and Niccum(Strykowski and Niccum 1992), with the trend
of decreased density ratios (greater than one) needed to obtain an absolutely unstable flow for
increased velocity ratios.
2.1.4.3 Reacting Jets
- 19 -
Reacting jets exhibit strikingly different behavior than a similar non-reacting jet as a
result of heat release. The heat release results in volumetric expansion in a localized region near
the flame, exhibiting low density and reduced viscosity. Debate ensues as to the specific cause
for the consequential changes in jet behavior. Nonetheless, reacting jets are a more complicated
subject matter because their behavior is no longer solely dominated by their initial conditions;
rather they are highly influenced by the combustion process in or near the free shear layer. For
round jet flames, the combustion process has a stabilizing and laminarizing effect on jet
structure, causing reduced shear layer growth rate, slower decay of the jet centerline velocity,
and reduced entrainment(Rehm and Clemens 1999; Han and Mungal 2001). Savas and
Gollahalli(Savas and Gollahalli 1986) demonstrated that these effects may be due to stark
differences in the behavior of the vortex structures formed in the shear layer. Schlieren
photographs showed that in the case of an attached flame, the formation and roll-up of the
vortices is delayed and pairing less frequent than those in a non-reacting jet, resulting in a slower
growth rate. However, he notes the lifted flame case displays a structure more similar to that of
the non-reacting case, implying that flame location matters. Furi et al.(Furi, Papas et al. 2002)
also concluded that flame location has a significant effect on the Kelvin-Helmholtz instabilities
and attributed it to a redistribution of the density-weighted vorticity profile, ρ du/dy (where
dv/dx is assumed negligible). Day, Reynolds, and Mansour(Day, Reynolds et al. 1998)
performed numerical simulations on a compressible, reacting mixing layer and demonstrated that
the density-weighted vorticity profile is a useful characterization to explain and predict growth
trends of the shear layer. He established that density variation from heat release could result in
multiple peaks in the density weighted vorticity profile, giving rise to the development of inner
and outer instability modes corresponding to the high and low speed side of the shear layer
- 20 -
2.1.5 Effects of Compressibility
A high-speed, compressible flow is a complex entity where large velocity, density, and
pressure gradients are present within the shear layer. The magnitude of the effects of
compressibility are generally described in terms of the convective Mach numbers, Mc, of the
turbulent shear layer, defined by Papamoschou and Roshko(Papamoschou and Roshko 1988) as
Mc1=(U1-Uc)/a1 and
Mc2=(Uc-U2)/a2, where a is the speed of sound and the subscripts 1 and 2 are the two free
streams. The general trend observed both experimentally and through numerical means is
reduced growth rates with increased convective Mach numbers(Papamoschou and Roshko 1988;
Gutmark, Schadow et al. 1995; Freund, Lele et al. 2000; Pantano and Sarkar 2002). Spreading
rates drop steadily until an asymptotic value approximately 20% of the spreading rate of
incompressible shear layers is reached near a convective Mach number of 0.8(Gutmark,
Schadow et al. 1995). Gutmark, Schadow, and Yu(Gutmark, Schadow et al. 1995) point out that
density ratios of 49 produced by Brown and Roshko(Brown and Roshko 1974) resulted in
changes in the growth rate by less than a factor of 2, implying density is not the only significant
parameter in compressible flows. However, just like variable density flows, the compressible
shear layer is greatly influenced by the coherent structures formed by jet instabilities.
Numerous studies find vortex structure and behavior in the compressible shear layer
begin to deviate from what is typical for the incompressible case somewhere in the range of
convective Mach numbers between 0.5 and 0.6(Sandham and Reynolds 1990; Papamoschou
1991; Elliott, Samimy et al. 1995; Gutmark, Schadow et al. 1995). Gutmark(Gutmark, Schadow
et al. 1995) notes that compressibility results in less organized and less coherent structures. In
addition, Papamoschou and Roshko(Papamoschou and Roshko 1988) observed suppression of
- 21 -
vortex pairing within the shear layer and suggest energy loss from supersonic convective Mach
numbers may play a role. Linear stability theory was used to show the dominant instability
modes to transition from a 2-D to 3-D entity above convective Mach numbers of 0.6(Sandham
and Reynolds 1990). The transport of compressible shear layer instabilities also varies in the
convection velocity. Papamoschou(Papamoschou 1991) found the convection velocity of
structures to be close to one of the free streams under high speed conditions, as opposed to an
average of the free streams for the incompressible case. The combination of these differences in
compressible free stream vortex behavior results in a drastically reduced spreading rate.
Determining how the varying conditions of free streams interact still remains the struggle. The
current investigation is an attempt to isolate density from velocity, temperature, and
compressibility effects on shear layer instabilities and growth.
- 22 -
CHAPTER 3: FACILITY & INSTRUMENTATION
3.1 Nozzle Design
The purpose of this experiment was to fashion a means to modify the density profile
within the free shear layer of an axisymmetric jet, without also inducing any significant
temperature gradients, velocity gradients, or compressibility effects in the system. The intent of
this action was to observe coherent vortex structures emanating from the Kelvin-Helmholtz
instability, record their changes in structure and behavior due to density gradients, and determine
their influence on the growth of the shear layer. In order to accomplish this, the nozzle of the jet
was designed to produce a clean boundary layer with certain specific parameters to aid in the
investigation.
The momentum thickness of the boundary layer was minimized (D/θ maximized) such
that the different instability modes scaled with either the jet column or shear layer could be
identified separately. An ideal facility would yield a thin boundary layer with a density
inhomogeneity present at separation. While more complex modifications to an axisymmetric jet
could have been used to better achieve this, it was decided that a coaxial jet was an effective and
simplistic approach to accomplish not ideal, but sufficient conditions. With the addition of a
weak variable density co-flowing jet, the boundary layer of the main jet separates with a uniform
density profile, but it quickly entrains low-density fluid, early in the development of the shear
layer, creating the desired flow conditions slightly downstream of the jet exit.
The nozzles used in this study were designed by the author to accommodate appropriate
flow conditions; a discussion of the more specific considerations made during the design process
will follow. The ultimate goal was the design of coaxial nozzles facilitating an initially laminar
- 23 -
central air jet with a thin exiting laminar boundary layer, surrounded by a weak annular low-
density jet that could be manufactured and run economically. To assure a uniform jet would
issue from the nozzle with only a thin boundary layer, approximations for the boundary layer
development along the nozzle were made using Thwaites’ method(Thwaites 1960) where the
momentum thickness, θ, could be found at any location using the relation, ,
where ν is the kinematic viscosity, u the local mean velocity, and x the streamwise direction with
the origin at the nozzle inlet. The displacement thickness was then estimated by finding the
shape factor, H, using the relation H = 2.61 – 3.75λ + 5.24λ2, where λ is given as
. Boundary layer growth of the main jet flow was minimized with a large inlet-
to-exit area contraction ratio of 75, to produce favorable pressure gradients and result in a small
boundary layer Reynolds numbers based on displacement thickness to maintain a laminar
boundary layer state(Schlichting and Gersten 2003) over a moderate range of jet exit Reynolds
numbers. A compromise on the length of the nozzle contraction was made between a short
design to hinder boundary layer growth and lower manufacturing costs, and a longer design to
avoid flow separation(Mehta and Bradshaw 1979).
After selecting a nozzle contraction length, L, and inlet and exit radii, R0 and RL, a
smooth contraction contour was designed using a 5th order polynomial curve, which was found to
be the optimal geometric choice by Bell and Mehta(Bell and Mehta 1988) for low-speed wind
tunnels. Satisfying all boundary conditions ( r(0)=R0, r(L)=RL, and first and second derivatives
of r with respect to x are zero) leads to the solution of the polynomial coefficients yielding
, where r(ξ) is the contraction radius at the
non-dimensional location ξ = x/L. This chosen design method resulted in the contours depicted
- 24 -
in Figure 9. A final design consideration concerning the inner nozzle was the thickness of the
lip, or trailing edge. Mehta(Mehta 1991) argued that the finite thickness of a splitter plate
between co-flowing streams creates a wake region which affects mixing layer development.
Therefore, lip thickness was designed as thin as possible to minimize any of these effects, but it
was also limited by the fabrication technique. The nozzle was fabricated in ABS plastic by Dr.
Bahattin Koc of the Industrial Engineering Department at the University at Buffalo using a
Stratsys FDM 3000 rapid prototyping machine, which cannot create features smaller than 1.27
millimeters.
The focus of the secondary flow was more on mean quantities of velocity and mass
flowrate than on the velocity profile itself, contributing to a decision to use a moderate
contraction ratio. The purpose of the annular co-flow is simply to provide the presence of a low-
density fluid next to the main jet, and would contribute very little to the total momentum or
vorticity at the interface of the two streams due to velocity differences. To minimize the “co-
flow” or “velocity ratio” effects of the annular jet, a large exit area, approximately 1.8 times
larger than the main flow exit area was designed, such that the velocity of the annular jet was
less than 10 to 15 percent of the central jet for all experimental cases. Coupled with this velocity
requirement was a constraint for the annular mass flow rate to be small in relation to the main jet:
less than 5%. This was imposed for both economic reasons and because other recent
studies(Arakeri, Krothapalli et al. 2003; Krothapalli, Venkatakrishnan et al. 2003; Samimy, Kim
et al. 2007) on the active control of axisymmetric jets have shown significant changes in jet
behavior with minimal inputs.
- 25 -
3.2 Test Facility
A test facility was fabricated and assembled in house to study the effects of a low-density
co-flow on an axisymmetric air jet within the confines of the Combustion Laboratory at The
State University of New York at Buffalo. The facility is pictured in Figure 10 along with the
camera used for taking PIV images. Unistrut metal framing was used to create a stable support
for the test facility in a vertical orientation, with the nozzle exit plane standing at a height of
approximately 50 inches. A vertical orientation was chosen to avoid a situation where Rayleigh–
Taylor instabilities may have been a dominant feature of the flow, due to variable density layers
of fluid perpendicular to the gravitational vector. Air was delivered to the facility from the
building air supply through ½” I.D. braided tubing. Air then passed through 22 inches of 3¼”
I.D. polycarbonate tubing and a total of five 60 x 60 metal screens to condition the flow before
entering the nozzle inlet (see Figure 11). The screens assure uniform flow within the jet and
reduce turbulence levels to approximately 1.5% at the nozzle exit (see section 3.3).
The gas used for the annular co-flow was Praxair UN1046 helium, initially compressed to
2640 psig in a size T Praxair cylinder. A Praxair model # PRX31233 regulator was used to
control the output pressure of the tank. The helium flow was divided up into 4 separate streams
through two sets of tees and entered the annulus between the nozzle walls through four inlets
perpendicular to the nozzles and spaced 90 degrees apart.
3.3 Test Conditions
Results are presented in Chapter 4 for a single axisymmetric air jet with no co-flow as
well as for the same air jet with five cases of increasing amounts of helium co-flow. Properties
of the flow were scaled and non-dimensionalized according to the jet centerline exit velocity, Uo.
Regardless, the conditions of the central air jet were maintained approximately constant for all
- 26 -
cases. The mean velocity of the air jet, determined by dividing the volume flow rate by the
nozzle exit area, was roughly 50 m/s yielding a Reynolds number based on exit diameter, given
as of approximately 36,000.
The selection for the maximum amount of helium co-flow, as well as the incremental
steps in co-flow to be studied were selected after preliminary data was taken with schlieren flow
visualization and PIV, respectively. A schlieren technique (described in section 3.4.3) was
useful in determining the amount of co-flow (determined to be 2.5% helium by mass) necessary
to have a reasonably significant impact on the behavior of the axisymmetric air jet, while being
able to run experiments economically.
Table 1: Annular to Inner Coaxial Jet Parameters
Density Ratio Mean Velocity Ratio Momentum Flux Ratio Mass Flow Ratio
The (variable density) coaxial jet may be characterized by a number of different
parameters; four of which are defined in Table 1. Correspondingly, the experimental values for
each test case considered are given in Table 2.
Table 2: PIV Test Conditions
Case Base 1 2 3 4 5
Annular Mean Velocity (m/s) 0.0 1.0 2.0 3.0 4.0 5.1
Velocity Ratio (%) 0.0 2.0 4.1 6.4 8.1 10.2
Mass Flow Ratio (%) 0.0 0.5 1.0 1.5 2.0 2.5
Momentum Flux Ratio (%) 0.0 0.0056 0.0225 0.0510 0.0907 0.1415
- 27 -
In the case of most homogenous coaxial jet studies (e.g. Ko and Au(Ko and Au 1985);
Dahm et al.(Dahm, Frieler et al. 1992); Rehab, Villermaux, and Hopfinger(Rehab, Villermaux et
al. 1997)), the outer to inner velocity ratio is used to characterize different flow regimes.
Although few studies have focused on variable density coaxial jets, the work of Favre-Marinet et
al.(Favre-Marinet, Camano et al. 1999; Favre-Marinet and Schettini 2001) suggests that
momentum flux ratio is a more appropriate parameter used to describe the flow dynamics of that
configuration. Nonetheless, the results from this investigation are mainly given in terms of the
mass flow ratio. Although this term scaled linearly with the velocity ratio, it is more appropriate
to use to describe the conditions that are driving the changes. It is the presence and amount of
density variation within the shear layer, and not the speed of the low-density co-flow that is
responsible for the observed behavior changes, which is best expressed in terms of the mass flow
ratio.
3.3.1 Initial Conditions
A hotwire technique, described in section 3.4.2, was used to characterize the initial
conditions of the central jet, and specifically the exiting boundary layer by probing the plane
0.63 mm above the nozzle exit. It should be noted that measurements were taken above the exit
plane, and therefore the separated boundary layer of the free jet, although minimal, had some
distance from the nozzle exit in which growth could have taken place. The center of the jet was
located after probing with the hotwire and assuming a symmetric velocity profile across the jet.
High precision travel of the hotwire probe was achieved with a one axis ;spatial uncertainty of
.0005” using a 3-axis micrometer positioning stage. The axis of the jet was used as a starting
point to probe along four paths 90 degrees apart. The resulting mean velocity profile, given in
Figure 12 shows overlap at all four angles, indicating symmetry in the exiting flow. The thin
- 28 -
boundary layers due to the large contraction in the nozzle design result in a top-hat velocity
profile. The average boundary layer thickness on the perimeter of the nozzle, defined by 99% of
the freestream velocity, is approximately 0.49 mm or 15% of the nozzle radius. Using the
standard definition, given by , the initial momentum thickness of the jet
was found to be 0.047 mm, giving the ratio D/θ equal to 225. Velocity fluctuation intensity
profiles are plotted in Figure 13 for all four angles probed. The peak fluctuation intensity, found
to be less than 3% of the jet velocity, is located away from the wall and near the center of the
boundary layer thickness indicating an initially laminar boundary layer(Hussain and Zedan
1978).
3.4 Instrumentation & Data Collection Techniques
3.4.1 Particle Image Velocimetry
Particle image velocimetry (PIV) was the primary means of data collection in the present
investigation. Particle image velocimetry is a non-intrusive optical technique used to measure
instantaneous velocity vectors within a flow-field that can be used to extract information on
turbulence and velocity-dependent flow properties. The method employs a high-speed camera to
record pairs of images of tiny particles within a seeded flow, which are illuminated by a laser
light sheet. The technique produces a vector field by tracking the displacements of groups of
localized particles between image pairs separated by a known time. A hotwire technique is a
simple and typical way to sample flows; however, PIV was chosen to be the main means of data
collection in the current study due to multiple benefits over the hotwire technique. A hotwire
technique uses an intrusive probe, which has been shown to affect instability characteristics
when placed at small x/D(Sreenivasan, Raghu et al. 1989). In addition, a single hotwire probe
can only be used to sample a single point over a discrete time period. Additionally, hotwire
- 29 -
signals are dependent on fluid velocity and concentration(Kyle and Sreenivasan 1993), so due to
the inhomogeneity of gases within the shear layer of this study, hotwires could not be used in this
region. Despite these shortcomings, a hotwire probe was used to characterize the initial
conditions of the jet, particularly the boundary layer, due to its spatial resolution.
For the current study, tracer particles were introduced into the two flows using pressure-
regulated Laskin nozzles to create finely atomized droplets of olive oil. Olive oil was selected
due to its nontoxic properties and relatively constant mean diameter droplet size of 1µm under a
wide range of operating conditions(Kahler, Sammler et al. 2002). For the given particle size, a
compromise is made between the tracer adequately following the flow (a trait of smaller
particles) and providing a strong signal-to-noise ratio from the scattering of light (a trait of larger
particles)(Hart 1998). The building compressed air supply drove the Laskin atomizer for the
central air jet, and seeding density was controlled independently of the flow rate with an air
bypass across the atomizer. All of the helium co-flow passed through a second Laskin atomizer,
which was modified to produce an adequate seeding concentration for the low flowrates. A
reliable seeding concentration is suggested to be greater than approximately 15 tracer particles
per interrogation region(Keane and Adrian 1990). Due to entrainment of ambient air into the jet
flow, it was also necessary to seed the ambient environment using a third Laskin atomizer.
Seeding of the ambient was accomplished again using the building pressurized air supply and
was done prior to, and in between experimental runs, so as not to introduce any ambient velocity
gradients in the vicinity of the jet. A schematic of the PIV setup is provided in Figure 14.
A 50 mJ/pulse New-Wave research Solo III Nd:YAG laser, operating at a rate of 15 Hz,
was utilized for the present study. The 532 nm wavelength laser beam was turned into a
vertically planar light sheet by passing the beam through a spherical lens (f = 500 mm) and a
- 30 -
plano-concave cylindrical lens (f = -25.4 mm). Positioning of the laser sent the light sheet
through the coaxial jet axis and illuminated particles in a plane approximately 1 mm thick. The
time separation between laser pulses was determined to allow particles to be displaced
approximately ¼ of the size of the interrogation region at the maximum flow velocities, based on
the recommendation by Keane(Keane and Adrian 1990) to optimize the correlation between
images, and was calculated using the following equation: .
Images were captured using a high-speed IDT X-Stream XS-5 CCD digital camera with a
1280x1024 resolution. Synchronization between the laser and camera system was controlled
with IDT ProVISION-XS software through an HP xw4300 PC Workstation and an IDT
MotionPro X timing hub. The camera was oriented such that the larger viewing area
corresponded with the vertical or streamwise direction. Three camera positions, overlapping by
approximately 20% along the streamwise direction, were needed in order to obtain data up to 10
diameters downstream of the nozzle exit. At each camera position, 812 image pairs were
collected and correlated to acquire mean and turbulent velocity statistics. Data from the three
positions were later merged to produce the plots given in Chapter 4.
Image pairs were correlated using IDT ProVISION-XS software after applying a
brightness and contrast adjustment to improve correlations. Interrogation regions of 32x32
pixels (with a pixel equivalent in size to 33.96µm per side) were utilized with a 50% overlap,
improving the spatial resolution of the flow-field and eliminating correlation errors(Hart 1998),
and resulting in an 80x64 grid of velocity vectors. Evaluation of sample instantaneous vector
fields (Figure 15) reveal numerous spurious vectors close to the nozzle exit plane due to poor
image correlation as a result of light reflection off the nozzle as well as lack of penetration of the
- 31 -
laser sheet on the far side of the nozzle. As a result, reported data excludes information for the
first 0.3 diameters downstream of the exit plane.
3.4.2 Hot-wire Anemometry
A hotwire technique was used to characterize the initial conditions of the central jet, and
specifically the boundary layer by probing the plane 0.63 mm above the nozzle exit. Hotwire
was used instead of PIV for its high sensitivity, quick response time, spatial resolution, and
because of spurious vectors produced from PIV near the nozzle due to laser reflections. A
downside of hot-wire anemometry is that components of the velocity vector are
indistinguishable, and only the magnitude of the velocity can be obtained. It is assumed that near
the nozzle exit where measurements were taken, the transverse velocity component is negligible,
and measurements can be approximated as streamwise components only.
Data acquisition was conducted using a five micron diameter probe with an active sensor
length of approximately 1.2 mm, operating in constant temperature mode with an overheat ratio
of 50%. Signals from the Standard U-Wire Probe A55P01 from Auspex Scientific were acquired
with a DISA type 55M10 CTA standard bridge. A DISA 55D26 Signal Conditioner removed
noise from the signal using its low-pass filter mode. Output voltages from this configuration
were monitored with LABVIEW on a PC using a National Instruments BNC-2111 Data
Acquisition system. The hotwire sensor was initially calibrated with a pitot tube, using a Fluke
111 multimeter to monitor the voltage output from a Setra model 239 pressure transducer.
Power spectra measurements were made via a fast Fourier transformation of the auto-correlation
function, and sampling occured at 20,000 Hz to obtain a frequency range up to 104 Hz.
- 32 -
3.4.3 Schlieren Flow Visualization
Schlieren is a technique used to visualize gradient disturbances of inhomogeneous
transparent media resulting from temperature differences, high-speed flows, or mixing of
dissimilar materials(Settles 2001). The technique exploits variations of the refractive index
within transparent media to visualize density gradients in a spatial direction (i.e. ) with
varying degrees of light intensity. In order to generate the schlieren effect, parallel light rays
must pass through the region of interest and be focused to a point where a knife edge blocks a
portion of the original light. Without the use of a knife-edge, the shadowgraph technique results,
which shows the second derivative of density (i.e. ), and produces less contrasted
images. Schlieren can be done with a nominal point light source and different combinations of
lenses and mirrors. The schlieren setup for the current study is depicted in Figure 16 in a top
view. An Osram 150W xenon arc lamp was used as the light source and situated in an Ealing
Stabilarc 250 Lamphouse. An aperture on the lamphouse was used to focus light onto a 25.4 cm
diameter concave mirror approximately 203 cm away. The mirror collimates the light, which
then passes through the gases dispersing from the coaxial jet arrangement, and is refocused by an
identical concave mirror. At the focal point, a razor blade is oriented in the vertical direction,
partially blocking some of the light source to create the schlieren effect, and indicates density
gradients in the transverse direction of the jet. Light passing the razor blade is focused by a lens
and images are captured with the same IDT X-Stream XS-5 digital camera used for PIV.
Resulting images display high intensity (bright) regions corresponding to positive density
gradients and low intensity (dark) regions corresponding to negative density gradients.
- 33 -
Five total cases were investigated, each involving a central air jet with a mean velocity of
approximately 22 m/s and Reynolds number of 16,000. The base case with no co-flow, required
the addition of 0.5% helium by mass to introduce a slight density variation from the ambient air
and produce a great enough contrast for the schlieren system, while not significantly altering the
momentum or instability characteristics of the jet. The subsequent cases consisted of increasing
the ratio of helium co-flow to main air flow by increments of 0.74% by mass up to a maximum
of 2.96%.
3.4.4 Flow Metering
Gas flow rates entering the experimental setup were monitored using Dwyer Series RM
Rate-Master® Flowmeters at the locations depicted in Figure 14. The air supply for the center
jet passed through a model RMC-104-SSV flowmeter. A model RMB-51 flowmeter was used to
monitor the helium co-flow for cases 1-3, as defined in Table 1, and a model RMB-52-SSV for
cases 4 and 5. Westward 60 psi max pressure gages were installed near the rotameter exits to
monitor the pressure and account for gas density variation using the ideal gas law, assuming a
deviation from standard temperature was negligible. Flow rates could then be corrected using
the following: .
- 34 -
- 35 -
CHAPTER 4: RESULTS
4.1 Schlieren
A high intensity light source and a series of lenses and mirrors were set up as described in
section 3.4.3 to produce a schlieren effect, and images were captured using a high-speed camera.
The knife-edge used to produce the schlieren effect was oriented vertically, parallel to the axis of
the jet, in order to highlight transverse density gradients. Qualitative comparisons in jet structure
and behavior are conducted by examining images from each trial; images representative of
typical behavior are provided in Figure 17. These 2-D images can be considered an idealized
cross-sectional view of the jet, however there are some features resulting from the 3-
dimensionality of the jet structure.
The images taken for the co-flowing jets show high intensity bright and dark horizontal
strips near the exit plane on either side of the central jet, and correspond to positive and negative
density gradients, respectively. These strips visualize the significant reduction and then increase
of density in moving radially from the jet axis: going from the air jet, to the helium co-flow, and
finally to the ambient air. The regions on either side of the jet axis are symmetric in shape, but
opposite in intensity due to opposing signs in the spatial direction of the density variation. In all
cases, the symmetry of the jet behavior is further visualized by examining the instability
structures, especially in Figure 17(e). Symmetry of the vortex structures and the presence of
faint transverse bands in the jet core, a line of sight integration effect, confirm that axisymmetric
modes of instability are being expressed (and not helical or azimuthal modes). Although the
expressed mode of instability is consistent throughout the cases, the vortex behavior and
interaction is significantly different, comparing the base case to the 2.96% co-flow case. In the
base case, a definite growth in size of the vortex structures as they progress downstream is
- 36 -
clearly seen, and is due to the pairing process described by Winant and Browand(Winant and
Browand 1974). This causes growth of the shear layer, leading to a relatively quick merging and
degradation of the jet to a turbulent state. The addition of increased low-density co-flow is
observed to result in a transition to turbulence farther downstream, which also corresponds to the
approximate end of the large density gradients (seen at the interface of the central and annular
jets). However, changes in density gradient go hand-in-hand with the spreading of the shear
layer and transition to turbulence, analogous to the influence of velocity gradients on vorticity
and vice versa. Transition to a turbulent state appears to take place in image (e) even in the
presence of a relatively thick intense band (i.e. a large density gradient). This suggests that a
turbulent state is still able to transpire in the presence of a large density gradient, and without
significant vortex pairing.
Images of increased co-flow also show an increased number of rolled-up instabilities
present, which appear to have a smaller wavelength and transverse height. Although the vortices
appear to show different frequencies, they are not necessarily representative of the initial
instability frequency and this issue will be addressed in more detail with hotwire spectral plots
presented in Chapter 4.3. For the higher co-flow cases, numerous vortices in a row appear to be
the same in size, indicating that the mechanism inducing vortex pairing has been damped and
amalgamation is not taking place. Thus shear layer growth has been inhibited by the presence of
the low-density gas.
The smaller structures seen in the high co-flow cases don’t penetrate as far into the core
of the central jet, are less capable of inducing entrainment, and leave a more coherent column of
fluid. The helium appears to have an overall stabilizing effect on the jet, resulting in a more
laminar, unsteady behavior near the exit. These trends were also observed by means of schlieren
- 37 -
by Savas and Gollahalli(Savas and Gollahalli 1986), who achieved a similar density profile due
to heat release. The wave-breaking length, the distance from the exit plane to vortex roll-up
formation, is also observed to increase with the addition of a low-density annular flow. The
magnitude of this effect is apparently density driven and correlates well with the trends observed
by Kyle and Sreenivasan(Kyle and Sreenivasan 1993), who found wave-breaking lengths of jet
instabilities decrease as the ambient fluid was made denser.
4.2 Particle Image Velocimetry
A total of six flow cases with the same central jet properties but varying amounts of
helium co-flow were examined with particle image velocimetry, as defined in Table 2. Mean
flow properties were obtained using 812 image pairs at each of three camera locations in order to
capture data extending up to ten diameters downstream of the nozzle exit plane and 1.6 diameters
radially from the jet axis. Both mean and instantaneous PIV data are presented in the following
sections. All figures containing six contour plots correspond to the six cases aforementioned,
with the base case (no co-flow) on top and increasing co-flow from top to bottom.
4.2.1 Instantaneous Images
Sample instantaneous PIV images are provided which highlight differing seeding
densities between the three experimental fluid domains by adjusting image brightness and
contrast. Although not as informative as the schlieren images, the PIV images illustrate similar
near field behavior and dynamics. Images are referenced to in Figure 18 and Figure 19 for cases
corresponding to the central air jet mean velocity of 50 m/s and 18 m/s, respectively. The no co-
flow and low co-flow cases (approximately (a) through (c)) demonstrate large structures that
penetrate deep into the core of the air jet, pinching off the column of fluid, and causing a quick
transition to turbulent behavior. Again, the latter cases of relatively higher co-flow velocities
- 38 -
(approximately 1.5% co-flow by mass and above) exhibit smaller, more frequent vortices and a
more coherent jet column
Although absent from the schlieren cases, but typical of coaxial jet behavior, vortex
formation and instability growth is present in the secondary shear layer of the PIV images.
Nonlinear growth and the rolling-up of vortex structures begin to emerge at a mass flow ratio
around 2.0% and above. The provided images only show one or two vortex roll-ups each,
however they are multiple times larger than the instabilities of the inner shear layer, possessing a
longer wavelength. The formation of these secondary structures is not related to the initial
objective of this research, which was to limit the influence of coaxial jet behavior. However,
these additional structures facilitate the entrainment of ambient air into the annular column of
helium, reducing its ability to shroud the air jet in a pure low-density gas. Despite this, it is
assumed the outer structures have minimal effects on the overall behavior of the central jet
instabilities and spreading dynamics. Thus, the coaxial configuration is idealized as a single jet
configuration and increased co-flow can be thought of as maintaining a significant density
gradient over a greater streamwise distance of the central jet. However, progressing to even
higher co-flow rates may result in a totally different near field behavior all together, as was
found for homogenous coaxial jets by Dahm, Frieler, and Tryggvason (Dahm, Frieler et al. 1992)
and Ko and Kwan(Ko and Au 1985).
4.2.2 Velocity Field Statistics
4.2.2.1 Mean Streamwise Velocity and Potential Core Length
Mean data is presented to establish average behavior of the jet as a whole, followed by
instantaneous data to shed light on some of the underlying phenomena responsible for the
observed mean trends. Contours of the non-dimensional streamwise velocity, u, are first
- 39 -
presented in Figure 20. The most obvious observation is the presence of high velocities
maintained farther downstream as more co-flow is introduced around the central jet. The extent
of the contour line corresponding to 95% of the exiting velocity moves from 4.5 diameters
downstream with no co-flow to approximately 6.5 diameters downstream at the maximum co-
flow condition. The potential core length, Lp, was approximated for each case where the
centerline velocity was 98% of the exiting velocity, matching closely to the start of velocity
decay. A visual of this location is provided by Figure 21, a plot of the streamwise centerline
velocity distribution. Although the decay of centerline velocity occurs with nearly identical
slopes, the start of the decay (end of the potential core) moves downstream in somewhat regular
increments with the mass flow ratio. Potential core length values are reported in Table 3 and
range from 4.0D to 5.6D. Fitting a linear regression to the data to corresponding velocity ratios
yields a squared correlation coefficient of 0.984 and the relation: ,
where is again the velocity ratio. The empirical values reported by Forstall and
Shapiro(Forstall and Shapiro 1950) are 12 and 4 for the slope and intercept, respectively, but
come from a slightly higher velocity ratio range of 0.2 to 0.5. Nonetheless, the potential core
length from the current study is found to be comparatively more dependent and sensitive to
changes in the velocity ratio. Thus, the non-unity density ratio of the current study confirms
instability growth is density ratio dependent
Again looking at Figure 20, but this time at the low velocity (5%) contours, the width of
the jet and/or shear layer location can be approximated. For increasing co-flow, the intersection
of the 0.05u/Uo contour to the radial location of 1.6r/D occurs farther downstream, moving from
approximately 8.5 to 10.5 diameters downstream. This does not necessarily mean the spreading
rate of the shear layer has decreased, as the location of the virtual origin may also be affected by
- 40 -
varying co-flow ratios. Nonetheless, added co-flow results in a more compact, coherent jet in the
initial region less than ten diameters downstream. The spreading rate of the shear layer and
virtual origin are important jet characteristics for processes dependent on mixing, such as
combustion, because they greatly influence the gas exchange, or entrainment, taking place at the
jet boundary.
4.2.2.2 Mean Transverse Velocity and Entrainment
The shear layer growth characteristics are dependent upon vortex formation and the
pairing process. Consequently, the variation in wave-breaking length and pairing characteristics
seen in the instantaneous schlieren and PIV images has a distinct impact on the mixing of the
present air jet. Figure 22 illustrates the transverse velocity of the jet under all co-flow
conditions. The contours appear noisy because the transverse velocity is a mere fraction (less
than 5% ) of the streamwise exit velocity and closer to the order of magnitude to the resolution of
the velocity measurements. Despite this, trends are still able to be found by comparing the
different cases of mass flow ratio. For the single jet, where wave roll-up occurs almost
immediately, ambient fluid is drawn radially inward at maximum transverse velocities very close
to the jet exit. Likewise, jet fluid near the shear layer is immediately moving radially outward
after exiting the nozzle. The peak magnitudes seen immediately following the exit indicate
entrainment is taking place, corresponding to significant vortex activity. Progressing
downstream, the velocity of ambient fluid decreases, while transverse velocities within the jet
remain at nearly the same magnitude until the shear layer pinches off the end of the potential
core. As increased helium co-flow is added to the system, two trends are observed. First, the
downstream location at which maximum transverse velocities and significant entrainment start to
occur, is noted to shift from about x/D = 1 to x/D = 2. This again corresponds to the increased
- 41 -
wave-breaking length found to occur with the addition of co-flow. The second trend is an
overall decrease in maximum transverse velocities for increased co-flow. This characteristic
likely relates to the suppression of vortex pairing. Liepmann(Liepmann and Gharib 1992) found
that the instantaneous entrainment field, and overall mixing of a jet is highly dependent on the
formation of vortices, particularly streamwise instabilities. He plotted the inward volume flux to
demonstrate the dependence of entrainment on such structures. While the immediate near-field
of the jet under different conditions shows varied behaviors, farther downstream the transverse
velocity fields are similar in appearance. Towards the end of the downstream range considered,
the jet dynamics are no longer dominated by organized vortex structure dynamics, but instead by
fully developed turbulence.
4.2.2.3 Shear Layer Spreading Rate
Hussain and Zedan(Hussain and Zedan 1978) cite that shear layer width, momentum
thickness, and vorticity thickness are all indicators of the relative size of the local shear layer and
they grow linearly in the self-preserving region. As is typical in other studies(Hussain and Zedan
1978; Arakeri, Krothapalli et al. 2003), the shear layer width, B, is used to determine the local
thickness of the shear layer, given by the relation B = R0.95 – R0.10, where R0.95 and R0.10 are the
radial locations where the velocity is 95% and 10% of the local centerline velocity. The linear
region of the shear layer width is plotted in Figure 23 up to the approximate end of the potential
core. For each case, a least squares linear regression was applied and all were found to have a
high correlation, with the worst case having a squared correlation coefficient value of 0.9964.
The slope of the regression fit corresponds to dB/dx, or the shear layer growth rate, and was
found to be 0.2008 for the axisymmetric jet with no co-flow. This growth rate falls within the
range of 0.17 to 0.23, found in previous studies for an axisymmetric jet(Hussain and Zedan
- 42 -
1978). The addition of a low-density co-flow results in a reduction of the shear layer spreading
rate as evidenced by the reported values in Table 3. This data is plotted in Figure 24 and shows
an approximately linear trend between mass flow ratios and spreading rates. For the range of
flow rates examined the shear layer spreading rate decreases by approximately 0.0078 per each
0.5% of helium co-flow, although this trend is not hypothesized to continue for much larger
quantities of co-flow. This behavior of decreased spreading correlates with the trend of vortex
pairing suppression for increased co-flow, observed in schlieren and PIV images.
Table 3: Measured Shear Layer Properties
Mass Flow Ratio (%) 0.0 0.5 1.0 1.5 2.0 2.5 Correlation Coefficient Squared (R2), Linear Regression of Shear Layer Width 0.9988 0.9964 0.9979 0.9973 0.9983 0.9986
Spreading Rate (dB/dx) 0.2008 0.1925 0.1857 0.1764 0.1714 0.1611
Virtual Origin (x0/D) 0.086 0.235 0.569 0.672 0.771 0.678
Potential Core Length (Lp /D) 4.00 4.44 4.78 5.17 5.46 5.64
4.2.2.4 Virtual Origin
The virtual origin is the theoretical streamwise location of a point source of momentum
from which the shear layer originates and self-similar properties scale to. The location of the
virtual origin for each case was approximated by the intersection of the jet axis and a linear
extension of shear layer width data and is provided in Table 3. While reported virtual origin
values in literature range from upstream to downstream locations relative to the jet exit plane for
the axisymmetric jet, values are typically small in value. For this jet configuration and initial
conditions, the virtual origin is always found downstream of the jet exit, with the normal
axisymmetric jet very close to the jet exit plane. The introduction of helium has the overall
effect of shifting the origin farther downstream for increased mass flow rates. This contradicts
- 43 -
the homogenous coaxial jet results of Ko and Kwan(Ko and Kwan 1976), who found larger shifts
of the virtual origin downstream for decreased co-flow values (for velocity ratios also less than
one). In addition, Arakeri(Arakeri, Krothapalli et al. 2003) reported a significant upstream shift
in location for an axisymmetric jet with the addition of homogenous microjets at the jet exit. The
apparent uncharacteristic shift of the virtual origin with the addition of co-flow is attributed to
the density variation. The virtual origin location data, in connection with previously presented
results, suggests an initial suppression in the linear growth of Kelvin-Helmholtz instabilities
from the annular flow. The shift in virtual origin and stability characteristics may stem from
reduced amplification rates as a result of a different density weighted vorticity profile directly
following the jet exit.
4.2.2.5 Turbulence Statistics
Jet mixing is also facilitated by the chaotic fluid motion associated with velocity
fluctuations. For the single axisymmetric jet, the peak streamwise and transverse fluctuating
velocity values are seen within the shear layers (top contour plot in Figure 25 & Figure 26) and
initially within the separating boundary layer (Figure 13). Along the centerline of the jet,
maximum values are reached after the merging of the shear layer, after the end of the potential
core, as demonstrated in Figure 27and Figure 28. The application of a density gradient achieved
with a helium co-flow results in delayed behavior and a shift in peak velocity fluctuations from
the shear layer to downstream of the potential core, and more along the jet axis. This contradicts
the behavior typically demonstrated by homogenous coaxial jets. Ko and Kwan(Ko and Kwan
1976) found greater shifts in the maximum turbulence intensity towards the axis of the central jet
for decreasing co-flow velocity due to a more dominant inner jet drawing the annular jet more
- 44 -
towards the axis. In this study, the shrouding gas is low density and acts to suppress vortex
formation, mixing, and entrainment resulting in a more laminar and inviscid development.
Contour plots in Figure 29 present turbulent kinetic energy production data. Instead of a
gradual shift or trend in behavior, there seems to be a complete jump or change in going from
1.5% to 2% co-flow by mass. In cases 1 through 4, maximum amounts of turbulent kinetic
energy production takes place within the shear layer between one and four diameters
downstream. However, at 2.0% and 2.5% co-flow, production within the shear layer seems to
have been retarded, and instead there is high magnitude production centered on the jet axis
beginning at about eight diameters downstream. Although the very initial region of the
axisymmetric jet has been laminarized by helium co-flow, it would appear that the breakdown to
turbulence became a stronger, more turbulent, more chaotic effect. The reason for this dramatic
shift in behavior is not completely clear. Overall peak velocity fluctuations are seen to be
reduced by up to 50% within the first 2 diameters with only 2% helium co-flow by mass, but
they quickly become and remain similar in magnitude up to 6 x/D. At approximately 8-10
diameters downstream of the nozzle exit, levels for the same 2% helium co-flow are about 20%
greater than the single jet (Figure 30 and Figure 31), accounting partially for the increased
turbulent energy production.
4.2.2.6 Mean and Instantaneous Vorticity
The formation of discrete eddies and vortex roll-ups result from the Kelvin-Helmholtz
instability mechanism and concentrations of vorticity. Vorticity is defined as the curl of the
velocity vector field, and in this instance it is noted that the most dominant component is made
up from gradients of the axial velocity in the radial direction, which is also the most significant
in quasi-parallel shear flows (see Figure 2 and Figure 3). Examination of the mean vorticity
- 45 -
field, given in Figure 32, shows thin, high magnitude bands of vorticity near the jet exit, which
broaden and weaken in the axial direction. Comparison of the cases in Figure 32 and Figure 33
suggests that the higher co-flow cases maintain high levels of vorticity over greater distances,
suggesting that diffusion of vorticity is retarded (in agreement with the reduced growth rates).
Because of the relationship between vorticity and velocity, it comes as no surprise that
the mean vorticity profiles (Figure 32) are elongated to match those of velocity (Figure 20). In
order to gain a better understanding of the flow dynamics, one must look to instantaneous data.
From images, it was previously determined that the wave-breaking length is greater in the
presence of helium co-flow. This is reflected in instantaneous vorticity data in Figure 34, which
shows a coherent band of vorticity being pinched off into discrete pockets farther downstream
for the cases of more helium. The high intensity pockets of vorticity correspond to instabilities
in the shear layer that have grown to an unstable state and have rolled up into coherent vortex
structures. The late appearance of these pockets in the presence of a low density co-flow are an
effect of the corresponding delayed vortex formation and retarded diffusion processes. The
earlier appearance of pockets in the absence of a shear layer density gradient, in turn, results in
the quicker transport and diffusion of energy and mass, and breakdown to a turbulent state.
4.3 Hotwire Power Spectra
Power spectra plots show the distribution of energy of a signal over the frequency domain
at a given location and over a discrete period of time. The convection of energy associated with
turbulent fluctuations within a shear layer is greatly facilitated by the vortex structures that form
from the initial instabilities emanating from the Kelvin-Helmholtz instability mechanism.
Consequently, energy peak(s) within a narrow frequency band in a power spectra plot usually
indicate the most dominantly expressed instability frequency. Hot-wire measurements were
- 46 -
made to survey the power/frequency plane and examine how shear layer instabilities are affected
by a low-density co-flow, as a way to quantitatively compliment the PIV data and schlieren flow
visualization studies. Co-flow mass flow ratios were increased in increments of 0.5%, and the
central jet mean velocity was 18m/s. Lower velocities were utilized such that preferred
frequency modes were within the frequency range sampled (10,000 Hz).
Hot-wire probe locations were selected to be within the potential core such that density
fluctuations would not be sensed by the instrument. As a result, both locations yielded a large
amount of noise in the signals, which may have be due to positioning the probe too far from the
shear layer to feel adequate pressure fluctuations from instabilities. Peaks at low frequencies (on
the order of 10 Hz) at both locations are assumed to be a characteristic of the lab and jet facility.
The first probe location was located at x/D = 0.45 and y/D = 0.45 in order to examine the
initial instability mode with varying amounts of helium co-flow. All cases examined (0.0% to
3.0% co-flow) showed a large broadband peak around 3800 Hz in Figure 35. While this is not
the only peak, the others are assumed to be noise, since calculation of the Strouhal number based
on the initial momentum thickness yields a value of approximately 0.017, matching the value
predicted by Michalke(Michalke 1965) and found experimentally by others(Gutmark and Ho
1983). In addition, the amplitude of this peak was reduced in each case of increasing co-flow,
coinciding with stabilization and mode suppression. The first case of co-flow (0.5%) yielded a
peak decrease of about one half decade, but the reduction in amplitude slowed with increasing
co-flow, as the largest amount (3.0%) yielded a peak approximately 1.5 decades smaller than the
single air jet. Hypothesizing from this spectral plot leads to the conjecture that co-flow has a
stabilizing effect on the initial shear layer instabilities, yet it does not alter the frequency of the
most unstable mode. If this is the case, consideration should be made as to the location of
- 47 -
instability formation compared to the distance required for adequate density gradient formation
from the entrainment and diffusion of helium into the shear layer.
Power spectra were also monitored at downstream locations. The power spectrum at x/D
= 2, and y/D = .25 is presented as Figure 36. This location was contained within the potential
cone and again demonstrated large broadband peaks, with a few dismissed noise peaks. At this
location, the single air jet is dominated by a large spike at approximately 950 Hz with a smaller
harmonic peak of nearly twice the frequency, around 1860 Hz. At 1.0% helium co-flow, the
amplitude of the dominant peak diminished in magnitude and shifted to a higher frequency at
1660 Hz. Upon further increase in co-flow, the amplitude of the peak at 1660 Hz diminished,
and the development of and shift to another peak at a frequency of 3800 Hz is observed. This
frequency matches that of what is hypothesized to be the initial instability previous suggested
and indicates pairing has yet to take place at this location for the higher co-flow rates, matching
the observations in photographs of schlieren and PIV for the particular conditions. Besides
inhibiting vortex pairing in the shear layer, the reduced peak amplitudes of the energy spectrum
also suggest that the low-density co-flow has a stabilizing effect on the jet.
- 48 -
CHAPTER 5: CONCLUSIONS
5.1 Conclusions
The present investigation utilized hot-wire anemometry, particle image velocimetry, and
schlieren flow visualization to study the effects of a low density co-flowing gas on an
axisymmetric air jet in a coaxial jet configuration. Five cases of varying amounts of helium co-
flow up to a maximum mass flow ratio of 2.5% were considered and compared to the case of a
single axisymmetric air jet issuing into ambient air. For all cases, the air jet exited a large
contraction ratio nozzle with a top-hat velocity profile and laminar boundary layer, with a mean
velocity of approximately 50m/s and a Reynolds number of 36,000. Data collection took place
in the jet near-field, up to ten diameters downstream, where transition from a laminar to turbulent
state took place.
Shrouding the turbulent air jet with small flowrates of a low-density gas resulted in
stabilization and laminarization the jet. Over the range of conditions examined, the shear layer
spreading rate was seen to decrease linearly to a maximum of approximately 20% resulting in a
potential core length increase of 41%. The creation of such drastic changes in the entrainment
and mixing in the near-field were a result of stark differences in the vortex structure dynamics.
Instantaneous schlieren and PIV images reveal the growth and roll-up of coherent vortices from
initial instabilities occur over a greater streamwise distance. In addition, the pairing process is
greatly inhibited, resulting in a more coherent jet with a longer transition to turbulence. Hotwire
data indicates the possibility that initial instabilities form at the same frequency, and that co-flow
results in a more stable condition. These results provide further insight into the role of density
gradients in vortex behavior, shear layer development, and mixing processes.
- 49 -
5.2 Future Work
The scope of this project consisted of a single coaxial jet configuration: a central air jet
surrounded by an annular helium jet. Flowrates of the helium co-flow were varied to examine
how the presence of a low-density gas within the shear layer of the air jet altered its properties.
The behavior of the jet with helium co-flow has been documented and could now be used to
predict at other flowrates. Nonetheless, it would be useful, as a continuation of this experiment,
to detail the characteristics of the same air jet for differing co-flow densities and velocities in an
attempt to find a more universal set of parameters for which to describe the behavior of this
generic axisymmetric, weak co-flow configuration. Included in this would be to introduce a
high-density co-flow, for which it is hypothesized that the jet would become more unstable and
transition to turbulence quicker, similar to a low-density jet(Sreenivasan, Raghu et al. 1989).
Utilizing both flow visualization such as schlieren, as well as PIV for mean and instantaneous
flow field measurements is a suggested approach.
Another aspect of the current work that would be important to examine further is the
density field. Mapping out the mean density field for all co-flow conditions would provide more
insight into the mechanism behind the observed results. This initial study is important in its
findings about the effects of introducing a weak low-density co-flow, however, it is not complete
in answering the specifics of exactly how or why the observed trends are taking place. It is not
perfectly clear what the density and density weighted vorticity profiles are. It would be useful to
know how far the helium penetrates into the shear layer radially at any downstream position, or
how far the region of pure helium is maintained downstream for the different co-flows? One of
two techniques is suggested to be used to measure density/concentration for this additional study.
- 50 -
One technique, described by Favre-Marinet and Schettini(Favre-Marinet and Schettini 2001),
utilizes a special hot-wire probe apparatus called an aspirating probe, in which the probe is
insensitive to velocity, and density can instead be sampled. A better approach to obtaining
density measurements would be to use a Rayleigh scattering technique. This technique is a non-
intrusive optical method, which can extract velocity, density, and temperature measurements of a
flow, and is based on frequency shifts in light scattered by gas molecules due to the Doppler
effect(Mielke, Elam et al. 2007).
- 51 -
APPENDIX A: FIGURES
Figure 1: Example free shear layer boundaries and evolving velocity profile.
Figure 2: Velocity profiles at 5 downstream locations for an axisymmetric air jet, Re = 36,000.
- 52 -
Figure 3: Vorticity profiles at 5 downstream locations for an axisymmetric air jet, Re = 36,000.
- 53 -
Figure 4: Axisymmetric jet structure.
Figure 5: Evolution of vortex growth in the free shear layer defined by four regions: (1) Boundary layer separation (2) Exponential growth of flow disturbances (3) Vortex roll-up (4) Vortex pairing and degradation to turbulent state.
Figure 6: Instantaneous PIV image demonstrating two vortices pairing to create a larger vortex; one equal in size to the vortex seen on the right hand side of the image.
- 54 -
Figure 7: Comparison of (a) an air jet with 3% helium by mass and (b) a helium jet at similar Reynolds numbers (Re = 2200).
(a)
(b)
- 55 -
Figure 8: Schlieren photograph of a helium jet exhibiting a side jet.
- 56 -
Figure 9: The scaled contours of the axisymmetric nozzles used in the experiment.
- 57 -
Figure 10: Experimental apparatus setup for PIV.
- 58 -
Figure 11: Cross-sectional view of piping leading up to coaxial nozzle apparatus. *Screens are denoted by dashed lines.
- 59 -
Figure 12: Velocity profile of the central air jet at 0.63 mm above the nozzle exit plane.
- 60 -
Figure 13: Velocity fluctuations profile of the central air jet at 0.63 mm above the nozzle exit plane.
- 61 -
Figure 14: Setup used for PIV.
- 62 -
Figure 15: Sample instantaneous vector fields combined for three camera positions extending 10 diameters downstream for the following cases: (a) No co-flow (b) 2.5% co-flow
Figure 16: Schlieren setup with the following components: (A) Xenon Arc Lamp (B) Concave Mirror (C) Coaxial Nozzles (D) Knife Edge (E) Lens (F) High Speed Camera
(a)
(b)
- 63 -
Figure 17: Sample schlieren images extending 13 diameters downstream for an axisymmetric air jet with a mean velocity of 22m/s and a Reynolds number of 16,000; (a) No co-flow, but 0.5% helium by mass in main
(a)
(b)
(d)
(c)
(e)
- 64 -
flow for adequate density gradients (b) 0.74% co-flow by mass (c) 1.48% co-flow by mass (d) 2.22% co-flow by mass (e) 2.96% co-flow by mass
- 65 -
(a)
(b)
(d)
(c)
- 66 -
Figure 18: Sample PIV images with modified contrast and brightness extending 10 diameters downstream for a central air jet with a 50 m/s mean velocity for the following mass flow ratios as defined in Table 2: (a) 0.0% (b) 0.5% (c) 1.0% (d) 1.5% (e) 2.0% (f) 2.5%
(f)
(e)
- 67 -
(a)
(b)
(c)
(d)
- 68 -
Figure 19: Sample PIV images with modified contrast and brightness extending 10 diameters downstream for a central air jet with a 17 m/s mean velocity for the following mass flow ratios; (a) 0.0% (b) 0.9% (c) 1.3% (d) 1.9% (e) 2.7% (f) 3.3% (g) 3.8%
(f)
(e)
(g)
- 69 -
Figure 20: Streamwise velocity contours.
- 70 -
Figure 21: Streamwise centerline velocities.
- 71 -
Figure 22: Transverse velocity contours.
- 72 -
Figure 23: Linear region of the shear layer width.
Figure 24: Shear layer spreading rate for varying mass flow ratios.
- 73 -
Figure 25: Streamwise velocity fluctuation contours.
- 74 -
Figure 26: Transverse velocity fluctuation contours.
- 75 -
Figure 27: Centerline transverse velocity fluctuations.
Figure 28: Centerline streamwise velocity fluctuations.
- 76 -
Figure 29: Turbulent kinetic energy production contours.
- 77 -
Figure 30: Peak transverse velocity fluctuations.
Figure 31: Peak streamwise velocity fluctuations.
- 78 -
Figure 32: Vorticity contours
- 79 -
Figure 33: Maximum vorticity per streamwise location.
- 80 -
Figure 34: Instantaneous vorticity contours extending 7 diameters downstream for the following co-flow cases (by mass): (a) 0% (b) 0.5% (c) 1.5% (d) 2.5%
(a)
(b)
(c)
(d)
- 81 -
Figure 35: Power spectra at x/D=.45, y/D = .45 for different co-flow rates.
- 82 -
Figure 36: Power spectra at x/D = 2, y/D = .25 for different co-flow rates.
- 83 -
- xi -
REFERENCES Amielh, M., T. Djeridane, et al. (1996). "Velocity near-field of variable density turbulent jets." Int. J. Heat Mass Transfer
39(10): 2149-2164.
Antonia, R. A. and Q. Zhao (2001). "Effect of initial conditions on a circular jet." Experiments in Fluids
31(3): 319-323.
Arakeri, V. H., A. Krothapalli, et al. (2003). "On the use of microjets to suppress turbulence in a Mach 0.9 axisymmetric jet." Journal of Fluid Mechanics
490: 75-98.
Balsa, T. F. and P. R. Gliebe (1977). "Aerodynamics and Noise of Coaxial Jets." AIAA Journal
15(11): 1550-1558.
Becker, H. A. and T. A. Massaro (1968). "Vortex Evolution in a Round Jet." Journal of Fluid Mechanics
31: 435-448.
Bell, J. H. and R. D. Mehta (1988). Contraction design for small low-speed wind tunnels, Joint Institute for Aeronautics and Acoustics. Boguslawski, L. and C. O. Popiel (1979). "Flow Structure of the Free Round Turbulent Jet in the Initial Region." Journal of Fluid Mechanics
90(Feb): 531-539.
Bradshaw, P. (1966). "The effect of initial conditions on the development of a free shear layer." Journal of Fluid Mechanics
26(2): 225-236.
Brown, G. L. and A. Roshko (1974). "On density effects and large structure in turbulent mixing layers." Journal of Fluid Mechanics Digital Archive
64(04): 775-816.
Champagne, F. H. and I. J. Wygnanski (1971). "An Experimental Investigation of Coaxial Turbulent Jets." International Journal of Heat and Mass Transfer
14(9): 1445-1464.
Colucci, P. J. (1993). Linear Stability Analysis of Density Stratified Parallel Shear Flows. Mechanical and Aerospace Engineering
, SUNY Buffalo. M.S.
Crow, S. C. and F. H. Champagne (1971). "Orderly Structure in Jet Turbulence." Journal of Fluid Mechanics
48(Aug16): 547-591.
Dahm, W. J. A., C. E. Frieler, et al. (1992). "Vortex Structure and Dynamics in the near-Field of a Coaxial Jet." Journal of Fluid Mechanics
241: 371-402.
Day, M. J., W. C. Reynolds, et al. (1998). "The structure of the compressible reacting mixing layer: Insights from linear stability analysis." Phys. Fluids
10(4): 993-1007.
Dimotakis, P. E., R. C. Miakelye, et al. (1983). "Structure and Dynamics of Round Turbulent Jets." Physics of Fluids 26(11): 3185-3192.
- xii -
Drazin, P. G. and W. H. Reid (1981). Hydrodynamic stability
. Cambridge [Cambridgeshire] ; New York, Cambridge University Press.
Elliott, G. S., M. Samimy, et al. (1995). "The characteristics and evolution of large-scale structures in compressible mixing layers." Physics of Fluids
7(4): 864.
Falcone, A. M. and J. C. Cataldo (2003). "Entrainment Velocity in an Axisymmetric Turbulent Jet." J. Fluids Eng.
125(4): 620-627.
Favre-Marinet, M., E. B. Camano, et al. (1999). "Near-field of coaxial jets with large density differences." Experiments in Fluids
26(1-2): 97-106.
Favre-Marinet, M. and E. B. C. Schettini (2001). "The density field of coaxial jets with large velocity ratio and large density differences." International Journal of Heat and Mass Transfer
44(10): 1913-1924.
Forliti, D. J., B. A. Tang, et al. (2005). "An experimental investigation of planar countercurrent turbulent shear layers." Journal of Fluid Mechanics
530: 241-264.
Forstall, W. and A. Shapiro (1950). "Momentum and mass transfer in coaxial gas jets." Trans. A.S.M.E. J. appl. Mech.
10: 399-408.
Freund, J. B., S. K. Lele, et al. (2000). "Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate." J. Fluid Mech.
421: 229-267.
Freymuth, P. (1966). "On Transition in a Separated Laminar Boundary Layer." Journal of Fluid Mechanics
25: 683-704.
Furi, M., P. Papas, et al. (2002). "The effect of flame position on the Kelvin-Helmholtz instability in non-premixed jet flames." Proceedings of the Combustion Institute
29: 1653-1661.
Gladnick, P. G., A. C. Enotiadis, et al. (1990). "Near-Field Characteristics of a Turbulent Coflowing Jet." AIAA Journal
28(8): 1405-1414.
Gutmark, E. and C. M. Ho (1983). "Preferred Modes and the Spreading Rates of Jets." Physics of Fluids
26(10): 2932-2938.
Gutmark, E. J., K. C. Schadow, et al. (1995). "Mixing Enhancement in Supersonic Free Shear Flows." Annu. Rev. Fluid Mech.
27: 375-417.
Han, D. and M. G. Mungal (2001). "Direct Measurement of Entrainment in Reacting/Nonreacting Turbulent Jets." Combustion and Flame
124: 370-386.
Hart, D. P. (1998). The elimination of correlation errors in PIV processing. 9th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics. Lisbon, Portugal.
- xiii -
Heeg, R. S., D. Dijkstra, et al. (1999). "The stability of Falkner-Skan flows with several inflection points." Math. Phys.
50: 82-93.
Hinze, J. O. (1959). Turbulence: An Introduction to Its Mechanism and Theory
. New York, McGraw-Hill Book Company, Inc.
Ho, C. and P. Huerre (1984). "Perturbed Free Shear Layers." Ann. Rev. Fluid Mech.
16: 365-424.
Ho, C. M. and L. S. Huang (1982). "Subharmonics and Vortex Merging in Mixing Layers." Journal of Fluid Mechanics
119(Jun): 443-473.
Huerre, P. and P. A. Monkewitz (1985). "Absolute and Convective Instabilities in Free Shear Layers." Journal of Fluid Mechanics
159(Oct): 151-168.
Hussain, A. K. M. F. and M. F. Zedan (1978). "Effects of Initial Condition on Axisymmetric Free Shear-Layer - Effects of Initial Momentum Thickness." Physics of Fluids
21(7): 1100-1112.
Kahler, C. J., B. Sammler, et al. (2002). "Generation and control of tracer particles for optical flow investigations in air." Experiments in Fluids
33: 736-742.
Keane, R. and R. Adrian (1990). "Optimization of particle image velocimeters. Part1: Double pulsed systems." Meas. Sci. Technol.
1: 1202-1215.
Kedia, K. S. and J. Kurian (2005). Supersonic Freejets from Shaped Nozzles. 32nd National Conference on Fluid Mechanics & Fluid Power
. Osmanabad, Maharashtra.
Ko, N. W. M. and H. Au (1985). "Coaxial Jets of Different Mean Velocity Ratios." Journal of Sound and Vibration
100(2): 211-232.
Ko, N. W. M. and P. O. A. L. Davies (1971). "Near Field within Potential Cone of Subsonic Cold Jets." Journal of Fluid Mechanics
50(Nov15): 49-&.
Ko, N. W. M. and A. S. H. Kwan (1976). "Initial Region of Subsonic Coaxial Jets." Journal of Fluid Mechanics
73(Jan27): 305-332.
Krothapalli, A., L. Venkatakrishnan, et al. (2003). "Turbulence and noise suppression of a high-speed jet by water injection." Journal of Fluid Mechanics
491: 131-159.
Kwan, A. S. H. and N. W. M. Ko (1977). "Initial Region of Subsonic Coaxial Jets .2." Journal of Fluid Mechanics
82(Sep7): 273-287.
Kyle, D. M. and K. R. Sreenivasan (1993). "The Instability and Breakdown of a Round Variable-Density Jet." Journal of Fluid Mechanics 249: 619-664.
- xiv -
Laufer, J., Schlinker, R, Kaplan, R.E. (1976). "Experiments on supersonic jet noise." AIAA Journal
14(4): 489-497.
Liepmann, D. and M. Gharib (1992). "The Role of Streamwise Vorticity in the near-Field Entrainment of Round Jets." Journal of Fluid Mechanics
245: 643-668.
Lighthill, M. J. (1952). "On Sound Generated Aerodynamically. I. General Theory." Proc. R. Soc. Lond. A
211(1107): 564-587.
Lugt, H. J. (1983). Vortex flow in nature and technology
. New York, Wiley.
Mathur, P. and C. Messina (2001). "Praxair CoJet™ Technology – Principles and Actual Results from Recent Installations." AISE Steel Technology (USA).
78(5): 21-25.
Mehta, R. D. (1991). "Effect of velocity ratio on plane mixing layer development: Influence of the splitter plate wake." Experiments in Fluids
10: 194-204.
Mehta, R. D. and P. Bradshaw (1979). "Design rules for small low speed wind tunnels." Aero. J.
83: 443-449.
Michalke, A. (1965). "On spatially growing disturbances in an inviscid shear layer." Journal of Fluid Mechanics
23(3): 521-544.
Mielke, A. F., K. A. Elam, et al. (2007). Development of a Rayleigh Scattering Diagnostic for Time-Resolved Gas Flow Velocity, Temperature, and Density Measurements in Aerodynamic Test Facilities. 22nd International Congress on Instrumentation in Aerospace Simulation Facilities
. Pacific Grove, CA.
Monkewitz, P. A., B. Lehmann, et al. (1989). "The Spreading of Self-Excited Hot Jets by Side Jets." Physics of Fluids a-Fluid Dynamics
1(3): 446-448.
Monkewitz, P. A. and K. D. Sohn (1988). "Absolute Instability in Hot Jets." AIAA Journal
26(8): 911-916.
Novopashin, A. and A. Muriel (2002). "Is the Critical Reynolds Number Universal?" Journal of Experimental and Theoretical Physics
95(2): 262-265.
Pantano, C. and S. Sarkar (2002). "A study of compressibility effects in the high-speed turbulent shear layer using direct simulation." J. Fluid Mech.
451: 329-371.
Papamoschou, D. (1991). "Structure of the Compressible Turbulent Shear Layer." AIAA
29(5): 680-.
Papamoschou, D. and A. Roshko (1988). "The compressible turbulent shear layer: an experimental study." J. Fluid Mech. 197: 453-477.
- xv -
Pavithran, S. and L. G. Redekopp (1989). "The Absolute-Convective Transition in Subsonic Mixing Layers." Physics of Fluids a-Fluid Dynamics
1(10): 1736-1739.
Rehab, H., E. Villermaux, et al. (1997). "Flow regimes of large-velocity-ratio coaxial jets." Journal of Fluid Mechanics
345: 357-381.
Rehm, J. E. and N. T. Clemens (1999). "The Large-Scale Turbulent Structure of Nonpremixed Planar Jet Flames." Combustion and Flame
116: 615-626.
Revuelta, A., L. Sanchez, et al. (2002). "The virtual origin as a first-order correction for the far-field description of laminar jets." Physics of Fluids
14(6): 1821-1824.
Russ, S. and P. J. Strykowski (1993). "Turbulent structure and entrainment in heated jets: The effect of initial conditions." Phys. Fluids
5(12): 3216-3225.
Samimy, M., J. H. Kim, et al. (2007). "Active Control of a Mach 0.9 Jet for Noise Mitigation Using Plasma Actuators." AIAA Journal
45(4): 890-901.
Sandham, N. D. and W. C. Reynolds (1990). "Compressible mixing layer: linear theory and direct simulation." AIAA
28(4): 618-624.
Sato, H. and O. Okada (1966). "Stability and Transition of an Axisymmetric Wake." Journal of Fluid Mechanics
26: 237-253.
Savas, O. and S. R. Gollahalli (1986). "Flow Structure in Near-Nozzle Region of Gas Jet Flames." AIAA Journal
24(7): 1137-1140.
Schaffar, M. (1979). "Direct measurements of the correlation between axial in-jet velocity fluctuations and far field noise near the axis of a cold jet." Journal of Sound and Vibration
64(1): 73-83.
Schlichting, H. and K. Gersten (2003). Boundary Layer Theory
, Springer-Verlag.
Settles, G. S. (2001). Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media
, Springer-Verlag.
Sreenivasan, K. R., S. Raghu, et al. (1989). "Absolute Instability in Variable Density Round Jets." Experiments in Fluids
7(5): 309-317.
Srinivasan, V., M. P. Hallberg, et al. (2010). "Viscous linear stability of axisymmetric low-density jets: Parameters influencing absolute instability." Physics of Fluids
22.
Strykowski, P. J. and D. L. Niccum (1991). "The stability of countercurrent mixing layers in circular jets." Journal of Fluid Mechanics
227: 309-343.
- xvi -
Strykowski, P. J. and D. L. Niccum (1992). "The Influence of Velocity and Density Ratio on the Dynamics of Spatially Developing Mixing Layers." Physics of Fluids a-Fluid Dynamics
4(4): 770-781.
Strykowski, P. J. and R. K. Wilcoxon (1993). "Mixing Enhancement Due to Global Oscillations in Jets with Annular Counterflow." AIAA Journal
31(3): 564-570.
Tam, C. K. W., K. Viswanathan, et al. (2008). "The sources of jet noise: experimental evidence." Journal of Fluid Mechanics
615: 253-292.
Thwaites, B. (1960). Imcompressible aerodynamics: an account of the theory and observation of the steady flow of incompressible fluid past aerofoils, wings, and other bodies
, Oxford, Clarendon Press.
Trouve, A., S. M. Candel, et al. (1988). Linear Stability of the Inlet Jet in a Ramjet Dump Combustor. AIAA 26th Aerospace Sciences Meeting
. Reno, NV.
Warda, H. A., S. Z. Kassab, et al. (1999). "An experimental investigation of the near-field region of free turbulent round central and annular jets." Flow Measurement and Instrumentation
10(1): 1-14.
Williams, T. J., M. R. M. Ali, et al. (1969). "Noise and Flow Characteristics of Coaxial Jets." Journal of Mechanical Engineering Science
11(2): 133-142.
Winant, C. D. and F. K. Browand (1974). "Vortex Pairing - Mechanism of Turbulen Mixing Layer Growth at Moderate Reynolds-Number." Journal of Fluid Mechanics
63: 237-255.
Xu, G. and R. A. Antonia (2002). "Effect of different initial conditions on a turbulent round free jet." Experiments in Fluids
33(5): 677-683.
Yule, A. J. (1978). "Large-scale structure in the mixing layer of a round jet." Journal of Fluid Mechanics
89(3): 413-432.