DISINTEGRATION OF SINGLE ORIFICE AND COAXIAL SUPERCRITICAL JETS
By
SHAUN DESOUZA
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2016
4
ACKNOWLEDGMENTS
I would like to thank my advisor, Professor Corin Segal, for this work would not
have been possible without his guidance and expertise. I would also like to thank my
friends and colleagues in the Mechanical and Aerospace Engineering Department for
their technical advice towards my work but also for the great conversations about issues
of the day. I’d like to thank my friend, Matthew Carver, for always inspiring me to push
myself towards higher academic achievement. I would like to thank my family for their
continued love and support throughout my academic career. Finally, I would like to
thank my wife, Danielle, who has been my greatest support during the most difficult
times of my studies. You have brought the joy to the long nights and stressful days.
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TABLE OF CONTENTS page
ACKNOWLEDGMENTS .................................................................................................. 4
LIST OF TABLES ............................................................................................................ 7
LIST OF FIGURES .......................................................................................................... 8
NOMENCLATURE ........................................................................................................ 12
ABSTRACT ................................................................................................................... 14
CHAPTER
1 INTRODUCTION .................................................................................................... 16
1.1 Theoretical Background .................................................................................... 16
1.2 Jet Breakup Theory........................................................................................... 16 1.3 Single Nozzle Subcritical Jet Experiments ........................................................ 22 1.4 Single Nozzle Supercritical Jet Experiments ..................................................... 25
1.4.1 Qualitative Studies of the Jet Surface ...................................................... 26 1.4.2 Spreading Angle Investigations ............................................................... 27
1.4.3 Core Length Measurements .................................................................... 30 1.4.4 Mapping of Jet Thermodynamic Profiles ................................................. 32
1.5 Coaxial Nozzle Subcritical Jet Experiments ...................................................... 33 1.5.1 Qualitative Behavior ................................................................................ 33 1.5.2 Core Length Investigations ...................................................................... 35
1.6 Coaxial Nozzle Supercritical Jet Experiments ................................................... 38 1.6.1 Qualitative Studies of the Jet Surface ...................................................... 39
1.6.2 Core Length Measurements .................................................................... 40 1.6.3 Jet Spreading Angle Investigations ......................................................... 41 1.6.4 Mapping of Jet Thermodynamic Profiles ................................................. 42
2 EXPERIMENTAL SETUP ....................................................................................... 60
2.1 High Pressure Chamber ................................................................................... 60
2.2 Injector Configuration ........................................................................................ 61 2.2.1 Single Injector .......................................................................................... 61
2.2.2 Coaxial Injector ........................................................................................ 62 2.3 Instrumentation, Experimental Control and Data Acquisition ............................ 62
2.3.1 Instrumentation ........................................................................................ 62 2.3.2 Experimental Control and Data Acquisition ............................................. 63
2.4 Working Fluid Photophysics and PLIF implementation ..................................... 64
2.5 Shadowgraphy Implementation ........................................................................ 67
3 SINGLE ORIFICE INJECTION ............................................................................... 75
6
3.1 Experimental Conditions ................................................................................... 75
3.2 Jet Morphology and Flow Visualization Analysis .............................................. 75 3.3 Jet Spreading Angle Analysis ........................................................................... 76
3.4 Droplet Size and Distribution Analysis .............................................................. 78 3.5 Conclusions ...................................................................................................... 79
4 COAXIAL INJECTION ............................................................................................ 85
4.1 Experimental Conditions ................................................................................... 85 4.2 Jet Morphology and Density Map Analysis ....................................................... 85
4.3 Core Length Analysis ........................................................................................ 87 4.4 Inner Jet Spreading Angle Analysis .................................................................. 88 4.5 Conclusions ...................................................................................................... 90
5 RECOMMENDED STUDIES .................................................................................. 99
APPENDIX
A FLUORESCENCE THEORY AND CALIBRATION ............................................... 100
A.1 Gas Phase Calibration .................................................................................... 103 A.2 Liquid Phase Calibration ................................................................................. 105
A.3 Conclusions .................................................................................................... 107
B SHADOWGRAPH EXPERIMENTAL CONDITIONS ............................................. 116
C MATLAB SCRIPTS FOR DATA PROCESSING ................................................... 118
D LABVIEW CODE FOR EXPERIMENTAL CONTROL ........................................... 172
LIST OF REFERENCES ............................................................................................. 180
BIOGRAPHICAL SKETCH .......................................................................................... 187
7
LIST OF TABLES
Table page B-1 Table of experimental conditions for all cases represented in spreading angle
data in Figure 3-5. ............................................................................................ 116
8
LIST OF FIGURES
Figure page 1-1 Criteria of cylindrical liquid jet disintegration regimes ......................................... 44
1-2 Cylindrical jet behavior ....................................................................................... 44
1-3 Classification of disintegration modes at fixed thermodynamic conditions. ........ 45
1-4 Three distinct regimes of a turbulent submerged jet ........................................... 45
1-5 Subcritical jet injected into a subcritical environment .......................................... 46
1-6 Influence of gas composition on jet behavior ...................................................... 46
1-7 Influence of gas temperature on jet behavior. .................................................... 47
1-8 Influence of chamber pressure at a supercritical temperature. ........................... 47
1-9 Back-illuminated images of a single nitrogen jet injected into nitrogen ............... 48
1-10 Software magnified images of the jets in Figure 1-9 ........................................... 48
1-11 Spreading or growth rate of single jets ............................................................... 49
1-12 Jet spreading angle plotted as a function of chamber-to-injectant density ratio. ................................................................................................................... 49
1-13 Theoretical dependence of the spray angle of surface, viscous and aerodynamic forces. ........................................................................................... 50
1-14 Ratio of the dark-core, intact-core, or potential-core length, depending on the case, divided by the density ratio for single jets.................................................. 50
1-15 Core lengths plotted as a function of chamber-to-injectant density ratio ............ 51
1-16 Figure of experimental conditions performed by Roy et al. ................................. 51
1-17 Scaled images of a supercritical jet injected into subcritical chamber conditions ........................................................................................................... 52
1-18 Scaled images of a supercritical jet injected into supercritical chamber conditions ........................................................................................................... 52
1-19 Simultaneous fluorescence, phosphorescence, and superimpose image of both of a liquid acetone jet .................................................................................. 53
1-20 Breakup modes of coaxial jets ............................................................................ 53
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1-21 Air-assisted cylindrical jet atomization regimes .................................................. 54
1-22 Breakup regimes in the parameter space Rel – We for coaxial jets .................... 54
1-23 Correlations for the characteristic length of air-assisted liquid jets ..................... 55
1-24 Images of a coaxial jet at approximately the same inner-jet mass flow rates ..... 56
1-25 Figure shows comparison of the present coaxial- jet dark-core length measurements with all other relevant core length data available ....................... 57
1-26 Spreading rate of the shear layer versus the chamber/injectant or chamber/inner-jet density ratio for single and coaxial jets .................................. 57
1-27 Maximum baseline spread angles as a function of momentum flux ratio ............ 58
1-28 Hydrogen density for a coaxial LN2/H2 injection ................................................ 58
1-29 Radial N2 density profile for single jet. ............................................................... 59
2-1 Schematic of Liquid/Fuel supply system ............................................................. 69
2-2 Section view of the high pressure chamber. ....................................................... 70
2-3 Injector tip with honeycomb structure. ................................................................ 70
2-4 Chamber top assembly depicting the coaxial injector, chamber top thermocouple, and plugged NPT passageways. ................................................ 71
2-5 Coaxial injector schematic with dimensions ....................................................... 71
2-6 Schematic of the data acquisition system. .......................................................... 72
2-7 Schematic of optical and test bench setup ......................................................... 72
2-8 Variation of the number of excited electrons with the number of exciting photons. .............................................................................................................. 73
2-9 The result of correcting for the non-linear fluorescence signal. .......................... 73
2-10 Optical bench Shadowgraphy setup. .................................................................. 74
3-1 Experimental conditions for selected binary single orifice jet disintegration experiments ........................................................................................................ 81
3-2 Shadowgraph images of case 1 from Figure 3-1 ................................................ 81
3-3 Shadowgraph image and PLIF density map of case 2 from Figure 3-1 .............. 82
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3-4 Shadowgraph images for case 3 reported in Figure 3-1 ..................................... 82
3-5 Plot of jet spreading angle versus chamber to injectant density ratio for fluoroketone/nitrogen single orifice jets .............................................................. 83
3-6 Plot of number of particles versus geometric mean of reduced injection and chamber temperature ......................................................................................... 83
3-7 Plot of normalized drop diameter versus the geometric mean of injection and chamber temperature ......................................................................................... 84
4-1 Experimental conditions for binary coaxial jet disintegration experiments .......... 91
4-2 Density and density gradient maps of cases 1 and 2 from Figure 4-1. ............... 92
4-3 Density and density gradient map of cases 3 and 4 from Figure 4-1 .................. 93
4-4 Density and density gradient map of cases 5 and 6 from Figure 4-1 .................. 94
4-5 Density and density gradient map of cases 7 and 8 from Figure 4-1 .................. 95
4-6 Plot of normalized core length as a function of momentum flux ratio of the outer-to-inner jet ................................................................................................. 96
4-7 Theoretical core length correlations .................................................................... 97
4-8 Plot of inner jet spreading angle versus momentum flux ratio for fluoroketone/nitrogen coaxial jets ....................................................................... 98
A-1 Plot of excited molecules versus the number of exciting photons..................... 108
A-2 Plots of fluorescence intensity variation of the laser sheet profile as it passes through the chamber ........................................................................................ 109
A-3 Plot of fluorescence signal intensity versus vapor density. ............................... 110
A-4 Fluorescence intensity as a function of laser power ......................................... 110
A-5 Plots of vertical and horizontal laser sheet intensity variation.. ......................... 111
A-6 Plot of normalized fluorescence intensity versus the length traversed by the laser in pixels.. .................................................................................................. 112
A-7 Calibration line for the absorption coefficient as a function of the fluoroketone vapor density. A linear dependence is noted from the plot. .............................. 112
A-8 Plot of normalized fluorescence intensity versus length traversed by the laser in pixels at 1.25 atm and 17oC. ......................................................................... 113
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A-9 Plot of normalized fluorescence intensity versus length traversed by the laser in pixels at 12.7 atm and 145oC. ....................................................................... 113
A-10 Plot of normalized fluorescence intensity versus length traversed by the laser in pixels at various liquid densities. ................................................................... 114
A-11 Plots comparing the coefficients obtained from the gas curve fit and liquid sum of exponents fits. ....................................................................................... 115
D-1 LabVIEW wiring diagrams for the control of the gas valves and the temperature and pressure monitoring charts. ................................................... 173
D-2 LabVIEW wiring diagram for the gas flow data, shutdown of valves at the end of experiment, and control of the gas heater. ................................................... 174
D-3 LabVIEW wiring diagram for the control of the liquid and chamber heaters. .... 175
D-4 LabVIEW wiring diagrams for the closure of valves at the end of an experiment. ....................................................................................................... 176
D-5 LabVIEW wiring diagram for the closure of valves and bypass solenoid valve control. .............................................................................................................. 177
D-6 LabVIEW wiring diagram for the processing and saving of data....................... 178
D-7 LabVIEW wiring diagram for closing all valves in event of experiment termination. ....................................................................................................... 179
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NOMENCLATURE
Latin Symbols A Nozzle geometric factor
L core length, [mm]
M 𝜌𝑔𝑢𝑔2
𝜌𝑙𝑢𝑙2 , Momentum flux ratio
P Pressure [atm]
Pr Reduced Pressure
T Temperature [K]
Tr Reduced Temperature
ug gas velocity at origin, [m/s]
ul liquid velocity at origin, [m/s]
VR 𝑢𝑔
𝑢𝑙, Velocity Ratio
Y 𝜌𝑙
𝜌𝑐ℎ(
𝑅𝑒𝑙
𝑊𝑒𝑙)2, Non-dimensional Taylor parameter for the jet growth rate
Greek Symbols ν kinematic viscosity (m2/s)
ρ Density (kg/m3)
σ surface tension (N/m)
Dimensionless Numbers Re 𝑢𝑙𝐷𝑙
𝜈, Reynolds number
We 𝜌𝑔𝑢𝑔𝐷𝑙
𝜎, Weber number
Subscripts
ch chamber gas properties
FK fluoroketone properties
g gas properties, annulus flow for coaxial injection
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l liquid properties, central flow for coaxial injection
N2 nitrogen properties
r reduced properties
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
DISINTEGRATION OF SINGLE ORIFICE AND COAXIAL SUPERCRITICAL JETS
By
Shaun DeSouza
December 2016
Chair: Corin Segal Major: Aerospace Engineering
Two separate experimental studies were undertaken to characterize the behavior
of single orifice and coaxial supercritical jets injected into environments varying from
sub-to supercritical conditions. It was determined that the chamber-to-injectant density
ratio had a dominant effect on the visual breakdown of the jet as well as the mixing
behavior. The outer-to-inner momentum flux ratio was found to be the dominant factor in
the case of coaxial injection.
The study of single orifice jets covered a broad range of density ratios. The data
was compared to previous single orifice injection studies performed in the same facility
under similar conditions. The jet disintegration process was observed from
shadowgraph images and the jet lateral spreading angle was measured. An agreement
was found between the shadowgraph data and previous shadowgraph studies and the
differed from the PLIF quantitative results. The results show a square root dependence
of the jet spreading angle with respect to the density ratio. The study further evaluated
the effect of thermodynamic conditions on droplet production and quantified droplet size
and distribution. The results indicate an increase in normalized drop diameter and a
15
decrease in droplet population with increasing chamber temperatures. Droplet size and
distribution were found to be independent of chamber pressure.
Density distribution was quantified for coaxial jets injected in an inert gaseous
atmosphere under a range of subcritical and supercritical conditions. Density gradient
profiles were inferred from the experimental data. A novel method was applied for the
detection of detailed structures throughout the entire jet center plane. Core lengths were
measured for each of the cases and correlated with previous visualization results. An
eigenvalue approach was taken to determine the location of maximum gradient, hence,
systematically determining the core length. The results show a significant influence of
the outer-to-inner momentum flux ratio on the core length. Furthermore, the inner jet
spreading angle was calculated by detecting the jet boundary and applying a linear fit
through the contour. The jet spreading angle was found to increase to a maximum and
then decay with increasing momentum flux ratio.
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CHAPTER 1 INTRODUCTION
1.1 Theoretical Background
Practical application when fluids in a supercritical state are injected in an
environment of various thermodynamic conditions and chemical composition are
numerous, ranging from propulsion applications to manufacturing industry and drug
delivery. There is a need to expand the current understanding of species transport in
shear layers under supercritical conditions as well as the bulk mass transfer at a
macroscopic scale when fluids of supercritical and/or subcritical state participate in the
mixing process. For this purpose, in this work coaxial jets are injected in a quiescent
atmosphere and their disintegration and mixing are observed.
In what follows, a background of current state of knowledge is presented;
beginning with single jets of subcritical and supercritical states followed by coaxial jets
studied both experimentally and theoretically. The experimental method used here
provides information of quantitative data previously not available, and thus, it
complements results obtained elsewhere.
1.2 Jet Breakup Theory
The early theoretical work by Plateau [1] and Rayleigh [2] laid the foundation for
the understanding of the jet breakup process. Plateau suggested that the surface
energy of a cylindrical column of fluid was not minimized for its given volume and hence
it must breakup into droplets. Rayleigh approached the problem by neglecting gravity,
viscosity of the jet, and the effects of the ambient fluid to conclude that disturbances
greater than the circumference of the jet are the cause of instability. Once the
wavelength of the surface disturbance has grown to the radius of the jet, a pinch point
17
appears and droplet formation occurs. His conclusion was that hydrodynamic instability
was the cause of jet breakup. Further work was conducted to expand upon these
theories by accounting for effects that were once neglected. Viscosity and density
effects were evaluated by Chandrasekhar [3]; it was found that droplet size was
increased and breakup rate was reduced by viscosity.
The effect of the ambient fluid on the jet breakup process was first considered by
Weber [4] and tested experimentally by Sterling & Sleicher [5]. Weber concluded that
ambient environment assisted in the growth of disturbances on the surface of the fluid
column. The presence of the ambient fluid provided a resistance to the jet and the result
is the growth and amplification of disturbances on the surface of the fluid column. The
experimental results of Sterling & Sleicher did not confirm Weber’s theory but a modified
semi-empirical relationship was proposed and reported in Figure 1-1. Taylor further
developed the hydrodynamic instability theory by accounting for the density effects of
the ambient fluid. It was suggested that droplets much smaller than jet diameter were
able to form at the liquid-gas interface if the force of the gas inertia was sufficiently high
[6]. This mode of breakup is known as atomization.
The works of Rayleigh, Weber, and Taylor have contributed to the theoretical
understanding and prediction of the jet breakup phenomenon. The breakup of a round
liquid jet is further influenced by internal nozzle effects, surface tension, inertia,
aerodynamic forces, and the thermodynamic state of the liquid and gas. The
development of the linear stability theory has allowed researchers to deduce the
qualitative behavior of the breakup phenomena and predict the existence of the five
currently accepted jet breakup regimes, illustrated in Figure 1-2, as follows:
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Dripping. The dripping regime exists at low jet velocity. Liquid droplets are
pinched off at the nozzle exit. The undisturbed liquid core length is one of the main
features of interest for a jet and has been referred to as the dark cork, potential core,
and intact core among others. The common characteristics are the uniform centerline
flow properties such as temperature, velocity and density. Often, measurement of the
core length is taken as the unbroken length before any separation occurs. The
application of this definition is different among researchers due to limits imaging
techniques. The linear stability curve relates the core length to the jet velocity and
defines the breakup regimes. As jet velocity increases, the Rayleigh breakup mode
dominates.
Rayleigh breakup. The Rayleigh breakup takes place many jet diameters
downstream of the nozzle exit due to long wavelength, small amplitude disturbances on
the surface of the liquid jet. Droplet diameters are larger or of the order of the nozzle
diameter. The breakup mechanism, identified by Rayleigh, is capillary pinching. This
behavior is characterized by axisymmetric disturbances on the jet surface that
propagate downstream of the nozzle and grow in amplitude until the amplitude of the
disturbance is equal to the jet radius and a droplet is pinched off from the liquid column.
Liquid core length through the Rayleigh regime increases linearly with velocity, reaches
a maximum and then decreases as seen in Figure 1-2.
First wind induced. The first wind induced regime occurs at higher jet velocities
just after the first maximum of the jet stability curve (Figure 1-2). As the jet velocity
increases, the effect of the ambient environment becomes more pronounced. The effect
has been identified in the theoretical work of Weber [4] with modifications proposed by
19
various researchers based on experimental results. The mechanism is similar to the
Rayleigh regime but droplet production is now on the order of the jet diameter. The
difference lies in the relative effect of the ambient environment with the first wind
induced regime characterized by the magnitude of the inertia force being a significant
percent of the surface tension force.
Second wind induced. Continuing to increase the jet velocity results in a
transition to the second wind induced breakup regime where capillary pinching is no
longer the main breakup mechanism. Short wavelength disturbances grow on the jet
surface causing the instability and resulting jet breakup a short distance downstream of
the nozzle after an initially smooth profile. At this point along the jet stability curve, the
breakup length is not well defined as theories by researchers are often contradictory as
will be reported in Section 3.
Atomization. Finally, with sufficiently high jet velocity, the jet begins to atomize
at the injector exit. Tiny droplets, much smaller than the jet diameter, form a dense
spray such that a core does not exist, or it is difficult to characterize. Hence, spray
characteristics are often evaluated such as the mean droplet diameters, droplet
trajectories, and spreading angles.
Ohnesorge [7] attempted to categorize the breakup regimes based on
nondimensional numbers to resolve the effects of the competing fluid dynamic forces.
The Reynolds (Re), Weber (We), and Ohnesorge (Oh) numbers have been used to
segregate, numerically, the breakup regimes. They are defined as follows:
𝑅𝑒 = 𝜌𝑢𝐷
𝜇 𝑊𝑒 =
𝜌𝑢2𝐿
𝜎 𝑂ℎ =
𝜇
√𝜌𝜎𝐿
20
The Reynolds number is a balance between the viscous and inertial forces and is
indicative of the level of turbulence present in the flow. The Weber number is a measure
of the inertial force relative to the surface tension at the interface between two fluids.
The Ohnesorge number combines the Reynolds and Weber numbers to weigh the
dominance of the inertia, viscous, and surface tension forces present in the flow. Figure
1-3 shows a plot of Ohnesorge number versus Reynolds number.
Figure 1-1 shows the results of several studies on the jet disintegration regimes
as compiled by Dumouchel [8]. Ranz [9] performed a theoretical analysis to quantify the
point at which the effect of the ambient fluid had a dominating effect on the jet breakup
process. The first condition at which the surface tension force is great enough to sustain
a fluid column corresponds to the end of the dripping regime. Considering the
interaction between the ambient fluid and the jet surface tension, Ranz [9] further
proposed that effect the of the surrounding fluid (WeG) was no longer negligible when
the inertia force of the surrounding fluid reached 10% of the surface tension force of the
liquid column.
Sterling and Schleicher [5] sought to define the maximum in the jet breakup
length as a point of dominance for the aerodynamic forces imposed on the jet. Their
result is reported in Figure 1-1 in the transition from the Rayleigh to first wind induced
regimes. Ranz [9] also sought to determine the point at which the aerodynamic forces of
the surrounding fluid were the same order of magnitude as the jet surface tension force,
marking the transition from first wind to second wind induced breakup modes. The
transition to the atomization breakup mode was considered by Miesse [10] as the point
at which breakup occurred directly at the nozzle exit. A modification of the previous
21
correlations was proposed by Reitz [11], seeking to quantify the nozzle effects on the
atomization process. The proposed empirical model accounts for the effects of
turbulence, cavitation, and other nozzle internal flow phenomena that affect the breakup
process. Taylor [6] considered the effects of the density ratio between the liquid and gas
interface by analyzing high speed images of jets. A mass balance was performed to
quantify the rate of droplet production, and hence mass loss from the liquid column. His
results are reported in Figure 1-1 with the numerical evaluation of the function f(T)
performed by Dan et al. [12].
The understanding of the transition from one breakup mode to next becomes
more complex when considering the thermodynamic state of the injected fluid.
Atomization can be considered a purely subcritical process dependent on the breakup
of a fluid surface. Jet disintegration, conversely, occurs when there exists is no fluid
surface tension forces to overcome. An example of such behavior is the turbulent
submerged jet.
The turbulent submerged jet structure, as described by Abramovich [13], consists
of three main regions as depicted in Figure 1-4. The potential core exists just after
injection where centerline properties such as temperature, density, and velocity are all
constant. Immediately following the potential core is the transition region where
turbulent mixing and entrainment occur. This relatively short-lived region quickly
develops into a fully turbulent self-similar profile. It has been shown that the turbulent
submerged jet behavior is analogous to that of a supercritical jet [14].
There has been a large scale effort to experimentally validate and improve the
theoretical understanding of the jet breakup process. The work of Lefebvre [15]
22
documents the experimental and theoretical development of theories on atomization
and sprays. The spray characteristics such as the core length, spray angle, and droplet
size distribution have been measured experimentally to validate and improve the
theoretical understanding of the liquid jet breakup process. The following is a review of
those efforts as they pertain to high pressure flows in the subcritical to supercritical
regime.
1.3 Single Nozzle Subcritical Jet Experiments
The study of a single round jet ejecting into a quiescent environment has relevant
combustion applications for diesel sprays in the high We number range (We > 13) and
hence experimental efforts on high speed jets are considered.
The work of Reitz and Bracco [16] sought to determine the mechanism causing
atomization and quantifying these effects in a theoretical model. Proposed mechanisms
of atomization include liquid turbulence, liquid/gas aerodynamic interaction effects, jet
velocity profile rearrangement effects, and oscillations in the supply pressure. Fourteen
L/D nozzle geometries were tested with a constant exit diameter. Surface finishes and
different nozzle contours were also considered to fully explore internal nozzle effects.
The working fluid was a mixture of water and glycerol while the chamber gas was varied
between helium, nitrogen, and xenon. Experiments were performed at room
temperature and three subcritical pressures. The vast experimental results reported by
this study concluded that spray angle increased with increased chamber pressure,
increased viscosity results in an increase in the core length of the jet, divergence angle
is decreased as L/D is increased, and noted stabilizing effects of rounding and
lengthening nozzles.
23
Experimental studies exploring nozzle geometric effects were also conducted by
Ohrn et al. [17] who also varied nozzle L/D while maintaining a constant nozzle
diameter. Surface finishes and inlet geometries were also varied with the conclusion the
sharp-edged inlets were most sensitive to perturbations. The discharge coefficient was
measured and found to increase with an increase in the inlet radius. Nozzle L/D ratio
was found to a have a weak effect in comparison to the nozzle inlet condition.
Further studies exploring nozzle effects were performed by Karasawa et al. [18]
who sought to relate the droplet sizes with the nozzle L/D ratio, nozzle inlet shape, and
nozzle diameter. The influence of the nozzle L/D ratio and inlet shape were negligible
and it was determined that the nozzle diameter had the most dominating influence on
droplet diameter.
Wu et. al [19] utilized shadowgraphy and holography to perform an experimental
study of turbulent gas/liquid mixing layers. Water, glycerol, and n-heptane jets with
nozzle diameters between 3.6-9.5 mm were injected into still air at one atm. The Sauter
mean diameter (SMD) of the droplets were calculated and agreed well with the
universal root normal distribution proposed by Simmons [20]. Wu and Faeth [21] also
performed a study to characterize the aerodynamic effects on the jet breakup process. It
was determined that aerodynamic effects were less pronounced for liquid-to-gas density
ratios less than 500. Experimental images were used to deduce the location of primary
breakup as well as droplet size as a function of downstream location of the injector. It
was found that the aerodynamic effects assisted in primary breakup and merged the
primary and secondary breakup locations when Rayleigh breakup times of ligaments
were longer than secondary breakup times of droplets. Faeth et al. [22] continued to
24
explore the multiphase mixing layer and determined that secondary breakup must occur
because the downstream region of the dense liquid spray was still dilute.
Smallwood and Gulder [23] performed an extensive review of jets where they
document the development of the diagnostic techniques used to study the dense core
structure of jets. In that regard, they detail the usefulness of each technique in
extracting the desired information. The consideration of the various breakup
mechanisms and their application to diesel sprays is reported.
High temporal resolution x-ray absorption images were used to determine the
mass distribution profile of diesel sprays by Yue et al. [24] A Gaussian radial distribution
was observed in the near nozzle region. Furthermore, it was found that a dense liquid
core was not detected over a pressure range of 20-80 MPa. Insead, a liquid/vapor
mixture with a volume fraction not exceeding 50% was observed in the vicinity of the
nozzle.
A jet disintegration study was performed by Sallam et al. [25] where three
breakup modes were observed for non-cavitating jets. Mean and fluctuating breakup
lengths were reported over a Reynolds number range of 5,000-200,000 for water and
ethanol jets injected into air at STP. The Rayleigh, primary, and bag-shear breakup
modes were observed under low, moderate and high We numbers, respectively. Droplet
size distribution and breakup length trends were in agreement with existing theoretical
models for both modes of disintegration.
Paciaroni et al. [26] developed an imaging technique that allowed the detection of
small scale features near the jet surface in very short exposure times. Ballistic imaging
was used to obtain high spatial resolution images at six different downstream locations
25
of the nozzle. The analysis of these images report droplet formation and spatially
periodic behavior.
Roy [27] utilized the planar laser induced fluorescence diagnostic technique to
image subcritical jets injected into subcritical environments. The analysis of these
resulted in detailed density and density gradient maps as seen in Figure 1-5.
Experiments performed in the subcritical regimes are only an extension of PLIF based
work done by Roy. The focus of Roy’s work was primarily in the supercritical regime.
The application of this technique to the supercritical regime will be discussed in the next
section.
1.4 Single Nozzle Supercritical Jet Experiments
The wide array of industrial applications makes the study of liquid injections into
supercritical environments of great importance. The coating of pharmaceuticals,
extraction of plant based oils, and power production all utilize supercritical fluid
technology all with the goal of efficiently dispersing a liquid into an extreme environment
relative to the critical point. The thermodynamic conditions in modern thrust chambers
have been increasing with higher chamber pressures driving liquid rocket engines to
gain higher specific impulse. Similarly, gas turbines and diesel engines have seen an
increase in efficiency and power output as a result of operating at exceedingly high
chamber pressures. This has motivated experimental efforts to understand liquid jet
injection into supercritical environments.
A supercritical fluid exhibits several interesting features that influence the way a
liquid jet will breakup and disintegrate. Supercritical fluids have no surface tension to
assist in droplet formation or cohesion of the liquid column. It also experiences a large
fluctuation in density at the critical point, has no latent heat, specific heat becomes very
26
large, and there is no longer a distinction between a liquid and gas. This study is further
complicated by the issue of solubility of liquids and gases at high chamber pressures
[28]. With the fuel and oxidizer mixing and dissolving at elevated pressures, the critical
point begins to shift dynamically. The critical mixing temperature must be exceeded for
a supercritical state to be realized under these conditions [29].
Newman and Bruzstowski reported the first experimental efforts on injection of
CO2 into an N2 environment at supercritical pressures [28]. The result of their work
determined that an increase in CO2 concentration and the resulting density increase in
the N2 filled chamber formed a fine atomized spray at supercritical pressure (Figure 1-
6). This increase in chamber-to-injectant density ratio caused a widening of the jet
profile. Furthermore, an increase in chamber temperature at fixed concentration and
pressure results in gas density to decrease, surface tension becomes nonexistent as
critical point is approached, and evaporation rates increase with constant injection
temperature (Figure 1-7 and 1-8). The visual length scale decreased as a consequence
of decrease in both radial and axial profiles. With the decrease in surface tension comes
a decrease in droplet formation and the atomization behavior the jet may have exhibited
under subcritical conditions now begins to behave like a turbulent variable density
gaseous jet. The confirmation of these findings and expansion on the available theories
will be presented further.
1.4.1 Qualitative Studies of the Jet Surface
Chehroudi et al. [30] studied LN2 jets injected into a gaseous N2 environment and
phenomenological effects of varying the chamber pressure from subcritical to
supercritical values while maintaining a supercritical injection temperature. The
27
experimental results are shown in Figure 1-9. The back-illuminated images confirm the
trends reported by Reitz and Bracco [31].
Classical liquid breakup behavior can be seen at subcritical chamber pressures
in frames 1-4 of Figure 1-9. Second wind induced breakup trends are apparent with
droplet and ligament formation downstream of the injector. The first magnified image in
Figure 1-10 further illustrates the subcritical jet breakup behavior. Frame 5 in Figure 1-9
and the central image in Figure 1-10 are classified as the transcritical regime by
Chehroudi who reported the formation of “finger-like” entities at the jet interface. Droplet
formation no longer occurs above a reduced pressure of 1.03 with surface tension and
enthalpy of vaporization diminishing. The jet interface begins to smoothen as the liquid
column dissolves before droplet formation occurs. Finally, when the chamber pressure
far exceeds the critical pressure of the working fluid, all classical jet breakup behavior is
subdued and the jet behaves as a turbulent gaseous jet. Confirmation of this behavior
was provided by Chehroudi in his fractal analysis of the jet boundary. It was found that
the fractal dimension of the jet resembled that of a turbulent gas jet for supercritical
pressures and liquid sprays for subcritical pressures [32].
1.4.2 Spreading Angle Investigations
The development of sophisticated image diagnostic techniques has played a
major role in making quantitative measurements of spray characteristics. The jet
spreading angle is an indicator of how well the jet has mixed with the surroundings.
Determination of the spreading angle first requires identification of the jet boundaries.
The various optical diagnostic techniques and results of their analysis are considered.
Chehroudi was the first to make quantitative measurements of jet spreading
angles and determined the criteria necessary for such a measurement [30]. Once it was
28
confirmed that the jet was inertially dominated, measurements of the spreading angle
were taken near the injector ensuring that a classical two dimensional mixing layer
existed. Chehroudi utilized the images taken by back-light illumination and the
calculated angles were compared with theories of liquid jets emanating into gaseous
environments and gaseous jets into gaseous environments due the existence of both
behaviors when varying the thermodynamic conditions about the critical point. Figure 1-
11 is the plot generated by Chehroudi with various theories plotted alongside the data.
Chehroudi’s findings were in agreement with Dimotakis’ theory [33] and found decent
agreement with the experimental trends reported by Papamoschou & Roshko [34] as
well as Brown & Roshko [35]. The work reported by Chehroudi [36] was the first
qualitative evidence of the behavioral similarities of supercritical jets and turbulent
submerged jets beyond physical appearance.
The work of Chehroudi continued with the application of the Raman scattering
diagnostic technique for characterization of the jet behavior. Although the goal of
applying this technique was to quantify the density distribution within the jet, spreading
angles were also inferred from the data set and compared to the back-illuminated
images originally analyzed. It was concluded that different definitions of mixing layer
thickness exist as reported by Brown and Roshko [35]and that the same criteria used
for the back-illuminated images did not yield the same results as the two-dimensional
Raman images. It was determined that twice the full-width half-maximum Raman
intensity profile yielded results in agreement with the diffuse lighting technique [37] and
was later confirmed by Oschwald and Micci [38] for 15 < x/D < 32. Oschwald and Micci
also reported that little agreement was found outside of this range and therefore not a
29
universal trend [38]. To justify their findings, they considered that Raman scattering
correlated to the density profile and shadowgraphy measured gradients in the density
distribution and hence, the two techniques were not directly comparable but some
correlation can be made.
The Planar Laser Induced Fluorescence (PLIF) technique was the next major
development in quantifying jet density profiles but is once again used to assess jet
spreading angles as well. Segal and Polikov [39] as well as Roy and Segal [40] utilized
a perfluoronated ketone injected into a gaseous nitrogen environment while varying the
chamber conditions about the critical point. The application of this diagnostic technique
required extensive calibration to account for the nonlinear fluorescence signal and
determination of the absorption coefficient [41]. The result of this calibration is a
corrected image that properly identifies the boundaries on both sides of the jet as the
laser is absorbed in the direction of propagation. The jet growth rate correlation
determined by Roy for single and binary species systems lies directly between the Reitz
and Bracco correlation for liquid sprays and Chehroudi’s correlation for supercritical jets
[40] as seen in Figure 1-12.
Mie scattering is utilized simultaneously with shadowgraphy by Lamanna et al.
[42] to classify the behavior of three different disintegration regimes for n-hexane jets
injected into argon. Detection of a liquid core is possible by the presence of a strong Mie
signal which allows for confirmation of the thermodynamic state of in the near nozzle
region. Liquid-gas aerodynamic interactions and nozzle geometry effects were
accounted for in a model based off of the linear stability analysis of Taylor [6] and the
correlation proposed by Reitz and Bracco [16]. The correlation included parameter, Y,
30
which accounts for surface tension, viscous, and aerodynamic forces and is plotted
along the abscissa of Figure 1-13. The function f(Y), represented on the ordinate axis,
accounts for the influence of dominant forces on the lateral growth rate. The constant,
A, was determined from experiment and accounts for the effects of the nozzle
geometry. Experimental data as well as the growth rate model are illustrated in Figure
1-13. The findings show that the thermodynamic state of the fluid has a direct influence
on the lateral spreading rate of the jet and the inclusion of the Y parameter provides an
accurate description of the jet growth rate. The analysis shows that the model proposed
by Reitz and Bracco [16] can accurately predict the growth rate of near critical jets. The
discrepancy in model in predicting the spreading angle for jets at T=505 K in Figure 1-
13 was determined in the thermodynamic analysis of the jets. The nozzle outflow
conditions for these tests were sonic, thus no longer obeying classical atomization
theory [42].
1.4.3 Core Length Measurements
The varying definitions of the physical characteristics of jets such as potential
core length, intact core length, unbroken length, and dark core length create a
discrepancy in the way this feature is measured and once again it is the development of
diagnostic imaging techniques that lead to improvement in the quantification of this
property of jets. Chehroudi’s analyzed back illuminated images by considering the dark
region near the injector as being representative of the potential core region of the jet
[30], [36]. Branam and Mayer [43] applied the Raman scattering technique and used the
centerline intensity profile to quantify the potential core length. This lead to reasonable
agreement with a model proposed by Chehroudi as well as a correlation developed by
Branam and Mayer as seen in Figure 1-14.
31
Roy’s [40] analysis of PLIF data lead to a new method of quantifying the potential
core length. With a detailed view of the jet core structure provided by the PLIF images,
Roy developed an algorithm that systematically analyzed the core. The image was
scaled by the most intense pixel and correlated to density measurement. The jet was
then sectioned into blocks equal to its diameter for which a corresponding density matrix
is also formed. The density fluctuations were analyzed by comparing the determinants
of the eigenvalue matrices of the gridded sections. It should be noted that this technique
is sensitive to separation of core structures. Measurements were taken before any
separation to negate this issue and also verified visually to be sure that the true core
length was recorded [40]. Cases have been discarded where the core length was
overestimated by an error in approximating the inflexion points of the polynomial curve
fit. A comparison of Roy’s data with the predictions of Abramovich [13] and Chehroudi is
represented in Figure 1-15. Abramovich reported core lengths between 6 and 10 for
cold turbulent submerged gas jets. Roy reported a constant core length of 11.5 across
an order of magnitude range of density ratios. His findings are in agreement with the
theoretical analysis of Abramovich and conclude that a jet injected at supercritical
conditions behaves like a gas jet injected into a gaseous environment. The core length
measurement is independent of the initial state of the jet as there is no variation in core
length with density ratio. It is worth noting that the findings presented on subcritical
diesel sprays by Chehroudi do not show agreement with the data presented by Roy.
Chehroudi’s correlation shows a dependence on the density ratio and the jet diameter
while no such dependence is supported by Roy’s findings.
32
1.4.4 Mapping of Jet Thermodynamic Profiles
The use of high powered lasers to apply Raman scattering, Mie Scattering,
Planar Laser Induced Fluorescence and Phosphorescence techniques as well as the
development of sophisticated image processing techniques has allowed researchers to
map the density and temperature distribution through a planar section of a jet.
Oschwald and Schik first reported radial density profiles by means of Raman scattering
[44]. Temperature fields were then calculated using an appropriate equation of state.
Oschwald and Schik reported normalized radial density and temperature profiles. Their
findings suggest that the behavior of the temperature profile represents the
thermophysical properties of the fluid. Behavior similar to liquid boiling is reported when
the fluid reaches a maximum in specific heat causing an expansion of the fluid without
an increase in temperature.
Chehroudi explored the self-similarity of turbulent jet density profiles in his
Raman scattering investigations. Success was found in the near and supercritical
regimes with a breakdown of the model as subcritical pressures are approached. In
addition, Chehroudi measured the FWHM of the radial density profiles and compared
them with the results of other researchers [37]. The nozzle configurations and Reynolds
numbers varied between researchers with So et al [45] and Richards and Pitts [46]
reporting results for subcritical pressures only.
Segal and Polikov [39] as well as Roy and Segal [47] measured the density
distribution and calculated density gradients of fluoroketone jets in single and binary
species systems. The intensity of the fluorescence signal is correlated to the density of
the working fluid by means of the PRSV equation of state and principles of fluorescence
photophysics. This allows for calculation of the density within two percent uncertainty.
33
The detailed correction procedure for the absorption coefficient and nonlinear
fluorescence signal showed positive results with a uniform density profile and no
preferential weighting that should be seen in the direction of propagation of the laser
due to absorption effects. Figure 1-16 reports test cases performed by Roy et al. [48].
Figure 1-17 and Figure 1-18 shows density and density gradient profiles obtained
by the PLIF diagnostic technique. The detection of droplets, bulges, and ligaments are
observed in the magnified density gradient images of the jet interface.
Further expansion of the available image diagnostic techniques is reported by
Tran who developed acetone Planar Laser Induced Fluorescence and
Phosphorescence (PLIFP) imaging to study jet mixing behavior. This technique requires
acquiring the fluorescence and phosphorescence signals simultaneously and
accounting for the shift in emission wavelength and lifetime. Acetone jets were injected
into air at subcritical and supercritical conditions. Phosphorescence was used to
determine if the location of the shear layer was detectable as the jet moved from less
diffusive to highly diffusive. Acetone density and mixture fraction are reported in Figure
1-19 from [49].
1.5 Coaxial Nozzle Subcritical Jet Experiments
1.5.1 Qualitative Behavior
The study of jet disintegration under the influence of a coaxial gas stream has
been considered due to the provided increase in atomization quality. The ability to
maintain this mode of operation is ideal for airblast atomizers and coaxial fuel injectors.
The influence of the co-flowing stream assists in peeling droplets from the central jet
interface, thus increasing the rate at which the fuel can evaporate, mix with the
surroundings, and combust. The characterization of coaxial jet disintegration was a
34
result of the work of Farago and Chigier [50] who were able to classify three atomization
regimes based on the gaseous Weber as reported in Figure 1-20 and illustrated in
Figure 1-21. The influence of the coaxial flow varies with the velocity of the gas. The
first mechanism is classified by droplet production on the order of the central jet
diameter. This occurs with no ligament and bulge formation on the jet surface. The
Rayleigh regime is associated with both axisymmetric and non-axisymmetric
disturbances on the jet surface. The former occurs at WeR below 15 and the latter in the
range of 15 < WeR < 25. An increase in the gaseous Weber number imposes increased
shear on the liquid/gas interface with the disturbances now becoming non-axisymmetric.
Figure 18a illustrates the behavior of non-axisymmetric Rayleigh behavior resulting in a
hook shaped appearance.
The membrane type breakup mechanism shown in Figure 18b indicates
increased droplet production that is much smaller than the central jet diameter. The
droplet formation is the result of Kelvin-Helmholtz instabilities on the surface of the jet
which now similar in appearance to a thin liquid sheet.
As the gaseous Weber number exceeds 100, fiber type ligament mode
dominates and air assisted atomization ensues. The fiber type breakup mode is further
categorized in pulsating and super pulsating modes. The pulsating mode has
characteristics typical of atomization such as the peeling of tiny droplets and bulges
from the jet interface. The super pulsating mode exhibits similar characteristics but a
highly periodic density fluctuation in different regions of the spray is observed.
Figure 1-22 is a plot of Reynolds versus Weber number identifying regimes of
different breakup modes for coaxial jets produced by Lasheras and Hopfinger [51]. The
35
fiber type atomization mechanism characteristic of coaxial jet disintegration exists at
exceedingly high Weber and Reynolds numbers. A range of momentum flux ratios are
reported for water-air coaxial jets as well as the operating regimes of rocket engines
denoted by the hash lines in the regime 104-105 for both the Reynolds and Weber
numbers. The identification of such regimes, although qualitative in nature, assists in
the classification and verification of breakup modes of visual data. The fiber type
breakup regime is most common in rocket engines exhibits features similar to second
wind and atomization breakup modes, i.e. short wavelength disturbances. The jet
atomization characteristics include the shedding of fibers and their subsequent breakup
into droplets much smaller than the nozzle diameter in near nozzle region. Ligament
formation is see further downstream as the jet begins to take on a wavy appearance.
These ligaments eventually breakup into droplets larger than the droplets observed in
the near nozzle region [52]. The identification of qualitative breakup behavior is an
important first step in characterizing the qualitative and geometric features of the jet.
1.5.2 Core Length Investigations
A great deal of experimental effort has been made to develop models of the core
lengths of single phase and two phase coaxial jets. Figure 1-23 has been compiled by
Dumouchel [8] which documents different core length correlations developed by various
researchers.
The work done by Eroglu et al. sought to measure the core length of coaxial jets
and develop a correlation as reported in Figure 1-23. Over 1500 shadowgraph images
were analyzed with membrane and fiber type breakup modes observed for water/air
coaxial jets.
36
Woodward et al. implemented x-ray radiography to quantify the liquid core length
of coaxial jets consisting of water and either helium or nitrogen. The effects of liquid and
gas velocities as well as ambient pressure and gas density all influenced the liquid core
length. The Z parameter in the correlation account for the effects velocity ratio between
the liquid and gas streams.
Engelbert et al. [53] sought to quantify the effects of momentum flux ratio and
velocity and reported that the relation between momentum flux ratio and potential core
length is inversely proportional. Rehab et al. [54] utilized fluorescence imaging to
classify two regimes of coaxial flow with respect to the velocity ratio. They argued that a
critical velocity ratio existed that defined two regimes of flow behavior. This theory
confirmed the behavior of inverse proportionality proposed by Engelbert for velocity
ratios below the critical value. For values exceeding the critical velocity ratio, the
potential core of the central jet is reduced and followed by a recirculation bubble with
low frequency oscillation [54].
The near-field and far-field breakup mechanisms were investigated for water/air
coaxial jets by Lasheras [55]. Models were developed to quantify the behavior of the
driving mechanisms at each location. Entrainment was determined to be the driving
force in the shedding droplets, masses, and ligaments from the liquid surface and the
model developed quantified the shedding frequency as a function of momentum ratio.
The secondary breakup mechanism in the far field assists in the breakup and
coalescence of droplets. The model developed for the secondary breakup mechanism
considers the local turbulent dissipation rate of the gas since the kinetic energy of the
gas stream was found to be the primary driver of secondary atomization.
37
Pocheron et al. considered the coaxial gas density effects on the core length.
Studies of water/air and LOX/inert gas were performed at atmospheric pressure. A
probe was used to detect whether a liquid or gas was present on the tip. Using the
probe to scan the length of the jet, the location where there was a 100% probability of
the jet existing was determined. The liquid core length was then defined as the distance
at which there was only a 50% chance of detecting the jet.
Leroux et al. explored the nozzle effects on the breakup lengths of coaxial jets.
Five working fluids were used in conjunction with air in the annular passage providing a
wide range of operating conditions. Shadowgraph images were collected and analyzed.
The map of momentum ratio versus Reynolds number was explored to determine the
momentum ratio limits of the different breakup regimes. The Rayleigh and super
pulsating regimes were isolated and it was assumed that the membrane and fiber type
breakup behavior existed between the range of 7 x 106/ReG1.9 < M < 2 x 105/ReG
1.1. The
Rayleigh and super pulsating regime exist below and above those limits respectively.
The map of M vs Re was successful in delineating the Rayleigh and super pulsating
modes but not appropriate for dissociating the membrane and fiber behavior.
The effect of momentum flux ratio was further explored by Villermaux [56] who
demonstrated that surface tension and viscosity played no role in the breakup process
above a momentum ratio of 35. Therefore, the breakup length was independent of any
such effects. Additionally, the vorticity thickness of the gas stream at the nozzle exit
was shown to be proportional to the initial wavelength of the disturbance at the onset of
instability.
38
The effect of large area ratios (100-1000) was considered by Varga [57]. For
comparison, the area ratio of the SSME preburner injector is 2.81. The jet breakup
process was accelerated by the large aerodynamic forces provided by the gas stream
with primary breakup occurring in the first few gas-jet diameters. The Kelvin-Helmholtz
instability has been shown to be the dominant cause of primary breakup with the
Rayleigh-Taylor instability driving the secondary breakup process. The droplet sizes at
the onset of secondary atomization have been shown to correlate with the wavelength
of the most unstable Rayleigh-Taylor wave.
1.6 Coaxial Nozzle Supercritical Jet Experiments
The coaxial fuel injector can be found in the Space Shuttle Main Engine (SSME)
as well as many other liquid rocket engines as it is an ideal design for delivering the fuel
and oxidizer to the thrust chamber. The central post is supplied with liquid oxidizer and
the annular flow is gaseous fuel. The central jet disintegration is assisted by the shear
gas flow and mixing of the fuel and oxidizer is accelerated in the shear layer before
eventual combustion. The outer-to-inner jet velocity and momentum flux ratio are
common operating parameters considered in the design of shear coaxial injectors. The
operating conditions of the Space Shuttle Main Engine is roughly 1.2 <M<3.4, and 10
<Vr<11.5 as reported by Vivek [58]. Velocity ratios above 10 are reported to improve
combustion stability for LOX/GH2 injector configurations [59]. The conditions that exist in
the thrust chamber of liquid rocket engines are commonly above the thermodynamic
critical point of the fuel and hence the atomization phenomena that would have existed
at subcritical conditions no longer exist.
The study of shear coaxial jets is categorized into two types of injection
conditions: single phase and two phase. Single phase coaxial injection involves
39
gas/gas, liquid/liquid, and supercritical/supercritical injections into the same respective
environment. Two phase injections involve a liquid central flow with a gaseous annulus
flow and chamber. Widespread experimental effort has supported the development of
fuel injector design for liquid rocket engines with the efforts in the single and two phase
regimes necessary for a full understanding of the nature of coaxial injection from
subcritical to supercritical conditions.
1.6.1 Qualitative Studies of the Jet Surface
The experimental effort toward classifying the behavior of coaxial jets begins with
Telaar who conducted experiments with LN2 and gaseous He coaxial jets [60]. Telaar
sought to determine the effect of ambient pressure on the jet breakup process for sub-to
supercritical conditions. Shadowgraphy was used as the flow visualization technique to
image the jet boundary and qualitatively discern the jet behavior. The core flow
experienced the expected behavior in its transition from subcritical to supercritical
pressure, namely, a reduction in surface tension. The influence of the coaxial flow, as
discussed by Davis and Chehroudi [61], is to accelerate the liquid breakup process for
subcritical jets and to enhance mixing for supercritical turbulent jets.
The typical fuel and oxidizer delivery system for a liquid rocket engine generally
utilizes the fuel as a coolant for the nozzle prior to injection into the combustion
chamber. This leads to a significant temperature differential between the fuel and
oxidizer and hence the annular flow provides heat transfer to assist in the evaporation of
the liquid oxidizer inside the nozzle and the along the shear layer. Figure 1-24 illustrates
the effect of annulus mass flow rate at constant central flow rate. These images confirm
the trend of accelerated breakup and enhanced mixing in the subcritical and
supercritical regimes, respectively.
40
The images reported in Figure 1-24 illustrate the effect of outer jet mass flow rate
and pressure. The effect of increasing the annular mass flow rate is apparent from
frame 1 to 9. A noted decrease in core length and droplet size along with an increase in
droplet production is apparent. The near critical and supercritical regime in Figure 1-24
in frames 9-15 exhibit the same core length trend as annular mass flow rate in
increased. The turbulent gas jet behavior is still apparent at supercritical conditions with
the annular flow serving to accelerate the mixing process instead of being the source of
droplet production.
1.6.2 Core Length Measurements
The core length plays a major role in determining the degree to which the jet has
mixed with its surroundings. The coaxial jet, like the single round jet, exhibits many of
the same features when it comes to core length measurements but the core length is
now dependent on the outer-to-inner jet momentum flux ratio, velocity ratio, density
ratio, Reynolds number, and Weber number.
Woodward [62] sought the measure the potential core length of a LOX stimulant
over a broad range of Reynolds number, Weber number, and density ratios via x-ray
radiography and flow visualization. Two techniques were used to analyze the data with
no quantification of the uncertainty in the measurement. A correlation was developed for
the potential core breakup length as a function of Reynolds number, Weber number,
and density ratio.
Chehroudi and Davis [61] performed studies on subcritical to supercritical coaxial
LN2/GN2 jets into supercritical chamber pressures. They reported the core lengths as a
function of momentum flux ratio due to the difficulty in defining the Weber number when
surface tension reduced to zero at supercritical conditions. Core lengths were reported
41
as being small or nonexistent at supercritical conditions. The definition of core length,
dark core length, and potential core length continue to create confusion in the study of
coaxial jets as seen in the single jet case. Davis and Chehroudi [63] defined the core
length of coaxial jets as the connected dark fluid region before the first break in the
core. They employed an adaptive thresholding technique to make their measurements.
Chehroudi and Davis further concluded that supercritical coaxial jets behaved as single
phase variable density turbulent gaseous jets and subcritical coaxial jets behaved like
two phase mixing layers. The data obtained by Davis and Chehroudi is illustrated in
Figure 1-25 along with data from other researchers. A correlation is drawn through the
subcritical data while the near and supercritical data are grouped together. The behavior
of gas/gas and liquid/liquid coaxial jets confirms the single phase behavior. Subcritical
jets follow the two phase mixing layer trends as will be more apparent in the spreading
angle analysis. The range of experimental data covers three orders of magnitude with
the behavior of coaxial and single jets converging as M approaches zero. The trends for
single phase and two phase behavior are consistent among researchers.
1.6.3 Jet Spreading Angle Investigations
Jet spreading angles for coaxial injection allow for determination of the mixing
efficiency just like the single injection case. The jet growth rate for a coaxial jet is
defined as the spreading angle of the inner and outer jet combined. The spreading
angle is plotted against the chamber to inner jet density ratio along with correlations and
single jet investigations as reported by Davis and Chehroudi [64]. The plot along with
the data obtained by Chehroudi and Davis further support the trend of subcritical jets
behaving like two phase mixing layers and supercritical jets to behave like turbulent
variable density gaseous jets (Figure 1-26).
42
Gautam and Gupta [65] explored the effects of annular gas flow rate on the
spreading angle of coaxial liquid nitrogen and helium jets. They reported a decrease in
lateral spreading angle with an increase in gas flow rate. The increase in helium in the
surrounding air decreased the local density and hence a decrease in the spreading
angle should be expected. Their data was compared with correlations by Chehroudi et
al. [30] and Reitz and Bracco [16].
Rodriguez et al. [66] sought to classify the inner jet spreading angle of non-
reacting LN2/GN2 coaxial jets. Back-lit images were acquired in the sub-, near-, and
supercritical regimes in the velocity and momentum flux ratio ranges: 0.25 < VR < 23,
0.02 < M < 23, respectively. The use of a single species allowed for the existence of a
single critical point. Measurements of the inner jet spreading angle were made on the
basis of the inner jet core length since the inner jet density is much high than the
surrounding gas, therefore, producing a much darker signal in the experimental images.
The contour of the inner jet was detected and the spreading angle measurement was
made for the right and left boundaries of the jet. The jet spreading angle was defined as
the sum of both angle measurements. The spreading angle of the subcritical jets
showed a relatively constant value over a wide range of momentum flux ratios. Data for
the near-critical and supercritical exhibited a similar trend with the spreading angle
increasing to a maximum value and subsequently decaying at increased momentum
flux ratios as seen in Figure 1-27.
1.6.4 Mapping of Jet Thermodynamic Profiles
LN2 and GH2 coaxial injection under sub-to supercritical conditions was
investigated experimentally by Oschwald et al. [44] with the goal of mapping density
profiles of both streams. Density profiles have been generated by two dimensional
43
Raman scattering and utilizing a filtering technique to isolate the individual Raman
signals of the LN2 and H2. Difficulties arise at the shear layer interface where a large
density gradient, and hence gradient in index of refraction, was a source of
experimental error. Two dimensional species distribution images were reconstructed
from the individual radial density profiles and are represented in Figure 1-28. Radial
density profiles are reported in Figure 1-29. Oschwald [67] sought to classify the
evolution of the mixing process by tracking the maximum in the radial density profile in
the axial direction. The study of this behavior showed that there was a plateau in the
density profile that was associated with the far field density.
Coupling the radial density profile information with the far field plateau density
made it possible to compare the single injection and coaxial flow case. It was
determined that the co-flowing gas forced the evolution of the jet towards the plateau in
the density profile much quicker than the single injection case, confirming the enhanced
mixing behavior of the annular flow. Finally, the effect of the thermodynamic state was
explored by varying the temperature of the central jet to values above and below the
pseudo-boiling point, the temperature and pressure at which the specific heat is a
maximum and thermal diffusivity is at a minimum. Injection above the pseudoboiling
temperature led to densities similar to the gaseous phase while injection below the
pseudoboiling temperature exhibited liquid-like densities. In either case, it was found
that the coaxial gas velocity had a weak effect on the jet breakup process compared to
the thermodynamic state.
Schumaker and Driscoll [68] utilized acetone PLIF to produce instantaneous and
averaged images of mixture fraction fields. They injected acetone seeded air through
44
the central jet and helium or hydrogen through the annulus but report results based on
using pure oxygen as the working fluid in the central jet in an effort to directly compare
the results with reacting O2/H2 systems. Mixing lengths were inferred from the
experimental data by spanning a range of velocity ratios, density ratios, injector
diameters, and Reynolds numbers. A dependence on the outer-to-inner momentum flux
ratio was reported.
Figure 1-1. Criteria of cylindrical liquid jet disintegration regimes. aRanz [9], bSterling and Sleicher [5], cMiesse [10], dReitz [11], eDan et al. [12], f Taylor [6]
Figure 1-2. Cylindrical jet behavior. Left – jet stability curve, Right – example of visualizations (from left to right): Rayleigh regime (region B) ReL = 790, WeG = 0.06; first wind induced regime (region C) ReL = 5,500, WeG = 2.7; second wind induced regime (region D) ReL=16,500, WeG = 24; atomization regime (region E) ReL = 28,000, WeG = 70 (Images from Leroux [69])
45
Figure 1-3. Classification of disintegration modes at fixed thermodynamic conditions. The disintegration modes are highly dependent on jet velocity and thermodynamic conditions. Increasing the ambient gas density or increasing the jet velocity leads to increased droplet production and transition to the atomization regime. Baumgarten [70]
Figure 1-4. Three distinct regimes of a turbulent submerged jet
46
Figure 1-5. Subcritical jet injected into a subcritical environment. A) Density map of subcritical jet. Droplet formation is apparent around 20 jet diameters. B) Density gradient map.
Figure 1-6. Influence of gas composition on jet behavior. The jet is initially at Tr =0.97 is injected into the chamber at Tr =0.97, Pr =1.04 with injection velocity = 3.7 m/sec. Partial pressure ratio of CO2 is 0, 0.5 atm, and saturation value respectively.
47
Figure 1-7. Influence of gas temperature on jet behavior. The jet is initially at Tr =0.97 is injected into the chamber at Pr =1.228 and Tr = 0.97, 1.05 and 1.10 respectively with injection velocity = 2 m/sec. Initial CO2 partial pressure = 0 atm.
Figure 1-8. Influence of chamber pressure at a supercritical temperature. The jet is initially at Tr =0.97 is injected into the chamber at Tr=1.05 and Pr = 0.85, 1.04 and 1.228 respectively with injection velocity = 3.35 m/sec.
48
Figure 1-9. Back-illuminated images of a single nitrogen jet injected into nitrogen at a fixed supercritical temperature of 300K but varying sub- to supercritical pressures (For N2: Pcritical = 3.39MPa; Tc = 126.2K). From lower right to upper left: Pch/Pcritical (frame no.) = 0.23 (1), 0.43 (2), 0.62 (3), 0.83 (4), 1.03 (5), 1.22 (6), 1.62 (7), 2.44 (8), 2.74 (9). Reynolds’ number (Re) was from 25,000 to 75,000. Injection’ velocity: 10–15 m/s. Froude’ number: 40,000 to 110,000. Injectant temperature: 99 to 120 K. Chehroudi et al. [30].
Figure 1-10. Software magnified images of the jets in Figure 1-9 at their outer boundaries showing transition to the gas-jet-like appearance starting at just below the critical pressure of the injectant. Images are at fixed supercritical chamber temperature of 300 K. Chehroudi et al. [30].
49
Figure 1-11. Spreading or growth rate of single jets as a tangent of the visual spreading angle versus the chamber-to-injectant density ratio. Data taken by Chehroudi
are indicated by an asterisk (∗) in the legend. Chehroudi et al. [30].
Figure 1-12. Jet spreading angle plotted as a function of chamber-to-injectant density ratio. Roy’s data points and proposed model lie between those proposed by Reitz and Bracco for diesel sprays (L/D = 85) and Chehroudi’s model for N2 injected into supercritical N2 environment. The single species mixing cases produce higher spreading angles than the binary species cases. Both have been indicated.
50
Figure 1-13. Theoretical dependence of the spray angle of surface, viscous and aerodynamic forces, while the on the parameter Y and comparison with experimental function f(Y) reflects their impact on the growth data.
Figure 1-14. Ratio of the dark-core, intact-core, or potential-core length, depending on the case, divided by the density ratio for single jets. Chehroudi et al. [36], determined by analysis of shadowgraphs, for an injector L/D = 200.
51
Figure 1-15. Core lengths plotted as a function of chamber-to-injectant density ratio. Our data points and proposed model lie slightly above the theory of Abramovich for turbulent submerged cold gas jets but follow a similar trend. The core length stays relatively constant at about 11.5 jet diameters.
Figure 1-16. Figure of experimental conditions performed by Roy et al. [48]. Reduced temperatures and pressures are reported for Novec 649. Critical Temperature: 441K, Critical Pressure: 18.4 atm.
52
Figure 1-17. Scaled images of a supercritical jet injected into subcritical chamber conditions. Test conditions correspond to cases 1-4 in Figure 1-16. (a–d) density images; (e–h) magnified density gradient images. [48]
Figure 1-18. Scaled images of a supercritical jet injected into supercritical chamber conditions. Test conditions correspond to cases 5–8 in Figure 1-16: (a–d) density images; (e–h) magnified density gradient images. [48]
53
Figure 1-19. Simultaneous fluorescence, phosphorescence, and superimpose image of both of a liquid acetone jet at 450 K and 59 atm in 575 K air. 0 mm is at jet center. Mass flow rate – 8.34 g/s. Vjet – 13.45 m/s. Vgas ~ 1.0 m/s.
Figure 1-20. Breakup modes of coaxial jets
54
Figure 1-21. Air-assisted cylindrical jet atomization regimes. A) Non-axisymmetric Rayleigh regime, B) membrane-type regime, C) fiber-type regime, D) superpulsating submode, Farago and Chigier [50].
Figure 1-22. Breakup regimes in the parameter space Rel – We for coaxial jets. Lines of constant M are calculated for water/air coaxial jets by Lasheras and Hopfinger [51]. Here, Rel = (UlDl/νl), We = (ρgUg
2Dl/ σ) ; M = ρgUg2 / ρlUl
2.
56
Figure 1-24. Images of a coaxial jet at approximately the same inner-jet mass flow
rates (∼275 mg/s). Columns are at about the same outer- annular-jet mass flow rates. For each row, the annular mass flow rate starts at a zero value to 2800 mg/s and increases from the left column to the right. The chamber
pressure levels for images 1–5 are subcritical (∼1.41MPa), for 6–10 are near-critical (∼3.46MPa), and for 11–15 are supercritical (∼4.77MPa). Inner-and outer-tube flow average temperatures at injector exit are 170K and 112 K, respectively. Davis and Chehroudi [63]
57
Figure 1-25. Figure shows comparison of the present coaxial- jet dark-core length measurements with all other relevant core length data available in the literature versus momentum flux ratio. Data reported by Eroglu et al. [71], Englebert et al. [53], and Woodward [72]are two-phase flows and the rest are single phase. The range of core length for cryogenic single jet (LN2/GN2) is also shown at the left margin. This figure was compiled by Davis and Chehroudi [63], [64].
Figure 1-26. Spreading rate of the shear layer versus the chamber/injectant or chamber/inner-jet density ratio for single and coaxial jets compared with different predictions for planar shear layers. For the coaxial data, the chamber pressure increases from sub- to near- and to supercritical conditions in the direction of the arrow.
58
Figure 1-27. Maximum baseline spread angles as a function of momentum flux ratio for sub-, near-, and supercritical conditions as reported by Rodriguez et al. [66] for coaxial without an external acoustic excitation source.
Figure 1-28. Hydrogen density for a coaxial LN2/H2 injection (TN2 = 140 K, TH2 = 270 K). Oschwald et al. [67]
59
Figure 1-29. Radial N2 density profile for single jet (VN2 = 5 m/s, TN2 = 140 K), 2mm (x/D = 1.05) downstream of the coaxial injector exit. (b) Radial N2 and H2 density profiles for coaxial LN2/H2 injection for a coaxial jet (VN2 = 5 m/s, TN2 = 140K, VH2 = 60 m/s, TH2 = 270 K), 2mm (x/D = 1.05) downstream the injector exit. Laser beam direction is from left to right. Oschwald et al. [67].
60
CHAPTER 2 EXPERIMENTAL SETUP
A detailed summary of the experimental setup can be found in Polikov [73] and
Roy [27]. Therefore, only a brief description of important features is included with details
on any major changes included for completeness. Figure 2-1 shows a schematic of the
experimental facility as described by Polikov [73]. Nitrogen is supplied via an industrial
supply tank to the high pressure chamber and the annulus of the coaxial injector after
being electrically heated. Fuel is pressurized in a stainless steel storage tank with an
additional nitrogen supply. The fuel supply utilizes a smaller version of the electric heat
exchanger used in the gas supply system to preheat the fuel prior to injection.
2.1 High Pressure Chamber
The design of the high pressure chamber must allow for safe operation above the
critical point of the working fluid while allowing optical access for image acquisition. The
high pressure chamber can be safely operated at pressures up to 70 atm (1000psi) and
300 oC (572 oF) with a maximum operating limit of 150 atm (2200 psi) and 350 oC (662
oF). Figure 2-2 depicts a section view of the high pressure chamber. Visible in the
diagram are the coaxial injector, thermocouples at the top and bottom of the chamber,
and quartz windows for optical access.
The chamber was constructed of brass due to its ability to operate at elevated
pressures while providing fast enough heat transfer to provide uniform temperature
distribution from the injection plane to the exhaust at the bottom of the chamber. The
chamber temperature is controlled by four cartridge heaters inserted into slots drilled
into the corner of the chamber body. Omega CIR-1060 cartridge heaters are used with
an effective total power output of 0.4 kW. The chamber pressure is monitored using
61
Omega PX303-1KG10V pressure transducers while the chamber temperature is read
using Omega K-type thermocouples at the top and bottom of the chamber.
Internal chamber dimensions are 1.8”x1.8”x9” to prevent liquid deposition on the
window caused by splashing from the bottom of the chamber and flapping of the liquid
jet. In addition, the windows on the chamber must provide maximum field of view to
allow for near injector studies as well as late stage breakup studies. Quartz windows
were selected for their high transmittance and ability to operate at temperatures up to
1000 oC and pressures up to 70 atm with a safety factor of seven. The windows are
flush mounted onto flanges and sealed using high temperature RTV and a silicon o-ring.
The effective field of view is 3.3” x0.84”; which allows studies between 0 and 40 jet
diameters for a 2 mm injector. To simplify facility maintenance, dummy flanges were
fabricated and used where optical access wasn’t necessary. The windowed flanges and
dummy flanges are sealed using a graphite gasket between the chamber body and the
flange.
2.2 Injector Configuration
2.2.1 Single Injector
The single injector configuration (Figure 2-38) utilizes a 2 mm diameter injector
which allows for near field and late stage breakup studies given the effective field of
view. Laminar flow exiting the injector is achieved by keeping the length to diameter
ratio of the injector at 2.5. A honeycomb structure is welded to the injector near the tip to
reduce post vibration and straighten the gas flow during coaxial injection. The coaxial
passageway is closed off during single injection studies by replacing the NPT plug on
the bottom of the chamber lid assembly to an NPT plug matching the outer dimensions
of the 2mm injector. The chamber is pressurized via four holes drilled in the body of the
62
chamber lid. The holes are in the direct vicinity of the windows which prevents liquid/gas
interaction and helps protect the windows from splashing.
2.2.2. Coaxial Injector
Coaxial injection is achieved by replacing the NPT plug on the bottom of the
chamber lid assembly with a new plug. The injector selected for this experimental
campaign was designed to the SSME pre-burner dimensions to simulate the area ratio
of a rocket engine coaxial injector. The passageways used to pressurize the chamber
during single injection are now sealed using four ¼ NPT pipe plugs as seen in Figure 2-
4. A detailed view of the coaxial injector is presented in Figure 2-5.
2.3 Instrumentation, Experimental Control and Data Acquisition
2.3.1 Instrumentation
The instrumentation on the test facility consists four main pieces of hardware: six
thermocouples, three pressure transducers, two flow meters, and two electric heaters.
The precise location of each piece of hardware can be located in Figure 2-1.
The six Omega K-type thermocouples monitor the fuel and gas supply
temperatures, the electric heater cores, and the chamber top and bottom. Omega
PX303-1KG10V pressure transducers are used to monitor pressure in the chamber as
well as the fuel and gas lines. The operational range is 0-1000 psi with a linear output
voltage in the range of 0-10 volts. The flow rate in the gas line is measured via an
Omega FLMG 12050SS-MA flow meter. Operational limits are 1-100 atm and 0-50
SCFM with a voltage output of 0-5 V. Pressure is monitored downstream of the flow
meter to assist in calibration and correction of gas flow rate from SCFM to ACFM. The
liquid flow rate is measure with a Sponslor Lo-Flo precision flow meter. The operational
range is 5-100 cc/s with +/- 0.25% linearity.
63
Two heating elements were constructed to regulate the temperature in the fuel
and gas lines. The gas heat exchanger was constructed using six Omega CIR-2121/240
cartridge heaters with an effective power output of 6kW. The nitrogen gas passes
through a threaded passageway within the heating element providing temperature
control of the gas flow prior to injection. Omega K-type thermocouples monitor the
temperature of the heater core and the temperature of the liquid after heating.
Temperature control of the fuel is provided by a similar cartridge heater element used in
the gas supply system with the exception of a 3kW power output. This ensures a
constant injection temperature for 30s at 50cc/s. The temperature of the heater core
and temperature of the liquid prior to injection as also monitored.
2.1.2 Experimental Control and Data Acquisition
The experimental control and data acquisition is best summarized in Figure 2-6.
A computer equipped with a National Instruments AT-MIO-64E-3 data acquisition board
and LabVIEW is utilized for controlling the experiment and acquiring data. The various
sensors and solenoid vales are wired into their respective terminal blocks, multiplexers,
signal conditioners, and the NI SCXI-1000 chassis connected to the computers onboard
DAQ.
Control of the experimental parameters is performed through the LabVIEW GUI.
The temperature of the chamber and heaters are set and allowed to reach their
operating points. The control of the gas and liquid flow are achieved through the use of
Omega SV-128 solenoid valves. Once the desired experimental parameters are
achieved, the LabVIEW program can begin to acquire the sensor data and write it to an
output file. The acquisition of all sensor channels is unnecessary and therefore limited
to the liquid and gas temperature, pressure, and flow rate as well as the chamber
64
temperature and pressure. The voltage output from the image acquisition system is also
recorded to facilitate synchronizing the sensor and image data.
2.4 Working Fluid Photophysics and PLIF implementation
The working fluid utilized in all studies is a perfluorinated ketone commonly
referred to as fluoroketone with the technical name, 2-trifluoromethyl-1,1,1,2,4,4,5,5,5-
nonafluoro-3-pentanone, or also simplified as FK-5-1-12. It is ideal for use in studies of
jet disintegration and mixing in the supercritical regime due to its low critical temperature
and pressure of 168 oC and 18.4 atm, respectively. Comparatively. water (374 oC, 218
atm) and acetone (235oC, 47.4 atm) which are common working fluids used in
supercritical experiments, require stricter design standards due to increased pressure
requirements and the potential for volatile reactions, respectively. With fluoroketone, the
facilities can be designed with cheaper materials due to lower thermodynamic
requirements with no risk of volatile behavior experienced with acetone. Fluoroketone is
also inert making it compatible with common construction materials and safe to use in
large quantities. In addition, it has low toxicity, is environmentally acceptable, and
experiences no thermal decomposition in air below 500 oC [27].
Further utilizing the material properties of the working fluid, it produces a strong
fluorescence signal with broadband excitation that can be achieved with many common
high power lasers. Fluoroketone experiences a strong absorption in the near ultraviolet
range with peak absorption at 307 nm. The laser selected is a Continuum Surelite
Nd:YAG laser tuned to its third harmonic with a wavelength of 355 nm. The average
energy per pulse is 150 mJ with pulse duration of 10 ns and frequency of 10 Hz. The
absorption cross section is 3.81 x10-19 cm2/molecule as determined by Roy [27].
65
Figure 2-7 is a schematic of the optical bench and test facility setup. The laser
beam is steered through three dichroic mirrors to remove any residual 532nm light
which results in a beam that is 99.998% pure 355 nm light. A laser sheet must then be
formed by passing the beam through three cylindrical lenses. The laser sheet is 25mm
wide and 0.1 mm thick. The beam is directed through the center of the jet and a PI MAX
II ICCD (Intensified Charge Coupled Device) camera is placed perpendicular to the
propagation direction of the laser sheet to capture the fluorescence signal. A bandpass
filter centered at 420 nm +/- 10 nm FWHM is mounted after the camera lens to eliminate
any elastic light scattering and isolate the fluorescence signal. Camera spatial resolution
is 44μm/pixel on 1024x1024 chip that has been cropped to 381x1024. Cropping of the
CCD chip increases the camera frame rate from 7 Hz to 10 Hz to match the laser
frequency. The camera, laser, and data acquisition system are all synchronized using a
Stanford Instruments DG-535 delay generator.
The Planar Laser Induced Fluorescence (PLIF) diagnostic technique utilizing
Fluoroketone as the working fluid has been well documented by Roy et al. [41]. A brief
discussion is included in this chapter with a more detailed analysis included in Appendix
A. The technique corrects for the nonlinear fluorescence signal caused by the high
power laser and the dense absorbing medium. Temperature and pressure effects have
been found to be negligible on the fluorescence signal [73].
Figure 2-8 is a plot of the excitation of electrons by photons which indicates that
a threshold of electron output exists for a given photon input. A linear regime can be
approximated but all experiments performed are in the nonlinear regime. The
66
fluorescence theory as derived by Roy [27] yields an equation for the electron output
versus photon input as indicated by Figure 2-8.
𝑁𝑒 = 𝑁𝜎𝑔
𝜎𝑔 + 𝜎𝑒[1 − 𝑒
−𝑁𝑝ℎ(𝜎𝑔+𝜎𝑒)
𝐴 ] (2-1)
The terms in this equation 1 are as follows:
N: total number of molecules
Ne: number of excited molecules
Nph: number of photons
σg, σe: absorption cross section of ground state and excited state
molecules
A:laser sheet area
The electron output is related to the signal intensity measured on the CCD chip
by considering the fluorescence yield (φ), as well as the optics efficiency and solid angle
of collection which have been grouped into a single term, F, in equation 2.
𝑆(𝑝𝑥, 𝑝𝑦) = 𝐹𝜌(𝑥, 𝑦)𝜑[1 − 𝑒−𝐼(
𝜆ℎ𝑐
)𝜎] (2-2)
The number density of the total electron output is directly proportional to the local
density in the flow field and thus the spatial pixel intensity is a function of the spatial
density distribution. In addition, the laser intensity drop through the absorbing medium is
accounted for by applying the Beer-Lambert law. All resulting constants have been
grouped into a single term, k.
𝑆(𝑝𝑥, 𝑝𝑦) = 𝐹𝜌(𝑥, 𝑦)𝜑[1 − 𝑒−𝑘𝑒−𝜎𝑛𝑥] (2-3)
Finally, the fluorescence intensity can be directly correlated to the local density
using the PRSV equation of state and the experimental sensor data.
67
𝑝 = 𝑅𝑇(𝑉 − 𝑏) − 𝑎𝛼(𝑉(𝑉 + 𝑏) + 𝑏(𝑏 − 𝑉)) (2-4)
The well documented thermodynamic properties can be predicted within 2%
uncertainty within the range of 0.1-100 atm and 150-600K. The coefficients a, b, and α
have been reported for Novec 649 (fluoroketone) by Polikov and Segal [74]. A
background image, laser sheet intensity profile, and experimental image of the jet are all
required to accurately map the density and gradient distributions. Core lengths and
spreading angles can also be inferred and measured. Figure 2-9 shows the result of
weighting the image by the laser sheet profile and removing the background signal. The
image on the left shows preferential weighting of the vapor density in the direction of
propagation of the laser (left to right). The image on the right shows an evenly weighted
density distribution as well as a more symmetric density profile. This technique was
implemented by Roy [48] and is the basis of the image processing method that will be
utilized in this study.
2.5 Shadowgraphy Implementation
Figure 2-10 depicts the optical bench setup for the parallel light shadowgraphy
technique. Flow visualization was accomplished using a 1,000W halogen lamp source,
providing 2,700 lumens with a color temperature of 3,200 K. The diffuse light was
focused and collimated through a bi-convex lens with a focal length of 20 cm. The
parallel light was then directed through the high pressure chamber using a mirror and
the light was captured with a PCO 1200s high speed CMOS camera. An effective
spatial resolution of 28 μm/pixel and frame rate of 1000 Hz was achieved by cropping
the chip to 511x1130. This simple flow visualization technique was used to measure
spreading angles for comparison with PLIF results.
68
The image processing technique is much simpler for the processing of the
shadowgraphy data. Two images are required: a background and the experimental
image. Seven hundred frames are acquired per test run and one hundred background
images. The background image is averaged and subtracted from each individual
experimental image. The processed image can now be averaged or used for further
processing.
The goal of image processing is to increase the signal to noise ratio. Dark noise
and background noise are sources of noise introduced into the experimental image. By
removing these through background subtraction, we obtain a much better signal to
noise ratio. The following two sections report the results of the single orifice
shadowgraphy experimental campaign as well as the coaxial jet PLIF study.
69
Figure 2-1. Schematic of Liquid/Fuel supply system. Gas supply line: 1 = gas bottle, 2 = pressure regulator, 3 = solenoid valve, 4 = needle valve, 5 = shop air supply check valve, 6 = gas flow=meter, 7 = pressure transducer, 8 = heater, 9 = heater core thermocouple, 10 = gas temperature thermocouple. Liquid supply line: 12 = gas bottle, 13 = pressure regulator, 14 = ball valve, 15 = fuel tank, 16 = ball valve, 17 = needle valve, 18 = liquid flow-meter, 19 = shop air supply check valve 20 = main liquid line solenoid valve, 21 = bypass liquid line solenoid valve, 22 = main line needle valve, 23 = bypass line needle valve, 24 = liquid line pressure transducer, 25 = liquid line heater, 26 = liquid line heater core thermocouple, 27 = liquid recuperation tank, 28 = ball valve, 30 = liquid temperature thermocouple. Chamber: 11 = chamber, 31 = chamber upper temperature thermocouple, 32 = chamber bottom thermocouple, 33 = pressure relief valve, 29 = exhaust needle valve, 34 = chamber pressure transducer. [73]
70
Figure 2-2. Section view of the high pressure chamber.
Figure 2-3. Injector tip with honeycomb structure.
71
Figure 2-4. Chamber top assembly depicting the coaxial injector, chamber top thermocouple, and plugged NPT passageways.
Figure 2-5. Coaxial injector schematic with dimensions. The image on the left depicts the NPT plug with the coaxial passage as well as the central post injector with the honeycomb structure for straightening the gas flow. The injector has been fabricated to the dimensions of the SSME preburner injector.
72
Figure 2-6. Schematic of the data acquisition system.
Figure 2-7. Schematic of optical and test bench setup
73
Figure 2-8. Variation of the number of excited electrons with the number of exciting photons.
Figure 2-9. The result of correcting for the non-linear fluorescence signal. The image on the left shows preferential weighing of the density distribution in the direction of propagation of the laser (left to right). The image on the right shows a more uniform density distribution on the left and right hand side of the jet. In addition, the jet appears slightly more symmetric.
75
CHAPTER 3 SINGLE ORIFICE INJECTION
3.1 Experimental Conditions
The current study of single orifice jets injected into a chamber of sub-to
supercritical temperatures and pressures was focused on the effect of the chamber-to-
injectant density ratio on the jet disintegration process. Forty-eight tests were run in the
density ratio range of 0.0035-0.1280 with the all experimental conditions reported in the
appendix. Spreading angles were measured from the visualization data and reported in
the section to follow.
The experimental conditions for the selected images are presented in Figure 3-1.
The cases have been selected to correspond with similar injection conditions from the
previous PLIF studies. These cases are used for comparison between the PLIF and
shadowgraph data. The first case represents subcritical injection into a subcritical
environment, the second is supercritical injection into an environment of supercritical
pressure while chamber temperatures are subcritical and all conditions are supercritical
in the final case.
3.2 Jet Morphology and Flow Visualization Analysis
The images for case 1 represented in Figure 3-1 are reported in Figure 3-2. All
thermodynamic conditions are subcritical and the injection velocity is low compared to
the supercritical cases. A dense liquid jet is observed with low amplitude disturbances
apparent on the surface of the jet. The breakup mode is in the Rayleigh regime. The
high density region of the jet persists beyond 10 jet diameters as determined from the
PLIF image.
76
Case 2 represented in Figure 3-3 exhibits the effect of increasing the chamber
pressure and injection temperature beyond the critical point with the chamber
temperature held at a subcritical value. Droplets and ligaments are seen forming on the
jet surface. With the injection temperature supercritical and the chamber temperature
subcritical, there exists local subcritical conditions resulting in the reassertion of surface
tension and condensation of the supercritical phase. Droplet formation is seen at
downstream locations of x/D > 10. Droplet sizes appear to increase with increasing
downstream location. The high density region in the PLIF images are roughly the same
in magnitude as the fully subcritical case.
The effect of elevating both the temperature and pressure beyond the critical
point produces the behavior reported in Figure 3-4. Droplet production has ceased and
surface tension has become non-existent with the appearance of gas/gas-like mixing
behavior present in the images. Finger-like threads are still apparent on the jet surface.
There is a reduction in the jet penetration length as determined from the PLIF density
map. The lateral spreading rate has increased as expected with an increase in
chamber-to-injectant density ratio. The findings of the spreading analysis are reported in
the following section.
3.3 Jet Spreading Angle Analysis
The results of the jet spreading angle analysis are presented in Figure 3-5. The
result of an increase in chamber-to-injectant density ratio is an increase in the lateral jet
spreading angle. A wide spreading angle is indicative of increased mixing. In addition,
the need for evaporation and break down of surface tension is no longer necessary in
the supercritical regime. The correlation for the presented data follows the trends of the
flow visualization study by Reitz & Bracco [31] closely. According to the data, the
77
spreading angle of a fluoroketone jet injected into a N2 environment in subcritical and
supercritical conditions follows the trend:
𝜃 = 0.3(𝜌𝑁2
𝜌𝐹𝐾)
12
(3-1)
The above equation was obtained using a power curve fit through all of the data
points extending from subcritical to supercritical test conditions in the density ratio range
of 0.0035- 0.1280. The correlation found in the present dataset differ from the findings
of Roy [27] and Reitz and Bracco [31] by a small difference in the coefficient. Otherwise,
all datasets show a square root dependence on the chamber-to-injectant density ratio.
The variation between the data presented in this study and the findings of Roy which
were obtained in the same facility can be justified by the different imaging techniques
employed in each study. The integrative nature of the shadowgraph flow visualization
technique captures an average throughout the jet unlike the PLIF technique which
images a single plane through the center of the jet. The data from the back-lighting
technique employed in this study and the work by Reitz and Bracco [31] show
agreement. The method of finding the jet boundaries in each study differed as well with
the present study utilizing a thresholding technique to convert the image to a binary
image of black or white and then detecting the contour of the jet profile. The spreading
angle was found by drawing a linear fit through the left and right jet contour in the near
nozzle momentum dominated region. The image processing techniques differed
between all three studies and thus another uncertainty is introduced into the data.
The plot shows that beyond the density ratios where either the jet or the ambient
environment is at supercritical conditions with respect to the injectant critical properties,
the images of the jets exhibit liquid and gas-like properties. In the supercritical regime,
78
the images of the jets exhibit gas jet-like appearance and show similar behavior with
respect to spreading angle.
3.4 Droplet Size and Distribution Analysis
The droplet size and distribution were further measured from shadowgraph
visualization data with the results of the droplet distribution and mean size is reported in
Figures 3-6 and 3-7, respectively. When injection temperatures are supercritical and
chamber conditions are subcritical, condensation of the supercritical fluid occurs and
droplet formation is apparent. This has been attributed to the reassertion of surface
tension that was also observed in previous studies [75]. As chamber temperatures
approach the critical point and the injection temperature is supercritical, the rate of
droplet production decreases significantly due to the loss of surface tension even under
subcritical chamber pressures. Analysis of the normalized droplet diameters and droplet
population shows no dependence on chamber pressure. A decreasing trend relative to
increasing chamber temperature is seen in the droplet population data. The trend
observed in the plot of normalized mean diameter and normalized Sauter mean
diameter versus the geometric mean of the injection and chamber temperature show a
linear increase in droplet size with increasing injection and chamber temperature. This
is attributed to evaporation of smaller droplets occurring much quicker than larger
droplets relative to their residence time in the field of view. The appearance of larger
droplets is the result of the inability to undergo breakup due to higher surface tension
relative to the aerodynamic forces experienced in the chamber. The increase in the
mean droplet sizes can be attributed to the decrease in the overall number of droplets
present. The uncertainty in the droplet data is a result of the spatial resolution of the
79
images. Droplets that are much smaller than the spatial resolution of the images difficult
to quantify using image analysis software.
3.5 Conclusions
A flow visualization study of a subcritical and supercritical jets injected into
environments in the sub-to-supercritical range was undertaken to compare quantitative
spreading angle data obtained by two different imaging techniques in the same facility.
The images were obtained using high speed parallel light shadowgraphy and compared
to previously obtained PLIF data.
The selected images from the shadowgraph and PLIF studies show a decrease
in surface tension with increased injection temperature and pressure and complete
breakdown of the jet surface at supercritical conditions where surface tension no longer
plays a role in the disintegration process. In cases where the chamber temperatures are
subcritical, local subcritical conditions exist and thus condensation and droplet formation
occurs in those regions. The appearance of gas/gas mixing behavior is observed when
all chamber and injectant conditions are supercritical with droplet formation no longer
occurring and a much smoother appearance of the jet boundary. A widening of the jet
lateral profile is also observed which is indicative of increased mixing.
The visualization data obtained in the present study was used to measure the jet
spreading angle over the density ratio range of 0.0035-0.1280. The trend reported
shows a square root dependence of the jet spreading angle with respect to the
chamber-to-injectant ratio. Thus, the jet lateral spreading rate shows an increase with
increased density ratio. The trend found in the present study shows agreement with
previous studies performed in the same facility under similar conditions with the same
working fluid. The difference in the magnitude is attributed to the different imaging
80
technique utilized in each study. While the magnitude of the data closely agrees with
that of Reitz & Bracco, the shadowgraph technique is integrative through the entire jet
while the PLIF diagnostic technique images a single jet plane. Thus, the PLIF data
should more closely represent the magnitude of the spreading angle of the jet.
The results of the droplet distribution study show a decreasing number of
particles with an increase in the chamber temperature approaching the critical point.
The size of these particles increase in size as the critical point is approached. This is
attributed to the smaller diameter droplets evaporating much quicker than the larger
droplets as well as the inability of the larger droplets to breakup due to their higher
surface tension. The appearance of droplets under supercritical injection temperatures
is a direct result of condensation of the supercritical fluid under subcritical chamber
temperatures. Uncertainty in measuring small droplet diameters are present when
droplet diameters are much smaller than the spatial resolution of the experimental
images.
81
Figure 3-1. Experimental conditions for selected binary single orifice jet disintegration experiments. MFR represents mass flow rate in kilograms per second. The reduced temperatures and pressure are reported with respect to the critical point for fluoroketone (FK). Critical properties of fluoroketone (FK) are 441 K and 18.4 atm. Figure subscripts are for fluoroketone (FK), nitrogen (N2), and chamber (ch).
Figure 3-2. Shadowgraph images of case 1 from Figure 3-1. Surface instabilities are amplified downstream of the nozzle and the breakup mode is within the Rayleigh regime. The high density region of the jet persists beyond 10 jet diameters as determined from the PLIF density map.
82
Figure 3-3. Shadowgraph image and PLIF density map of case 2 from Figure 3-1. In case 2, the supercritical jet is in injected into a chamber of subcritical temperature and thus condensation of the jet should be expected where local subcritical conditions exist.
Figure 3-4. Shadowgraph images for case 3 reported in Figure 3-1. Chamber temperatures are supercritical. Fully supercritical behavior is observed. Single phase turbulent gas/gas jet mixing is observed in the shadowgraph and PLIF images.
83
Figure 3-5. Plot of jet spreading angle versus chamber to injectant density ratio for fluoroketone/nitrogen single orifice jets. An increase in jet spreading angle is apparent with an increase in the chamber-to-injectant density ratio. The results follow similar trends reported by Reitz & Bracco [76] as well as Roy [27].
Figure 3-6. Plot of number of particles versus geometric mean of reduced injection and chamber temperature. The reduction in overall number of particles can be attributed to evaporation of smaller droplets occurring much quicker than larger droplets.
84
Figure 3-7. Plot of normalized drop diameter versus the geometric mean of injection and chamber temperature. The increase in normalized drop diameter can be attributed to the evaporation of smaller droplets with increasing chamber temperature. This results in the remaining larger droplets increasing the mean droplet size due to their inability to evaporate within the frame of view.
85
CHAPTER 4 COAXIAL INJECTION
4.1 Experimental Conditions
The current study of coaxial jets injected into a chamber of supercritical pressure
was focused on the effect of the momentum flux ratio on the jet disintegration process.
The selected experimental conditions are listed in Figure 4-1. Each case was selected
to increase in momentum ratio with subcritical injection temperatures and supercritical
chamber pressures with the exception of the first case which was taken as a reference
for the condition with no annular flow, hence M = 0.
The momentum ratio ranged from 0.13 – 4.3 to overlap results of previous
studies. Density of the jet center plane were obtained for all cases listed below.
Measurement of the core length was performed based on the technique previously
developed. The threshold for determining the core length was taken as the point of
maximum gradient as in Roy [40]. Fluoroketone injection velocities were kept constant
at 2 m/s. Figure 4-1 subscripts are for fluoroketone (FK), nitrogen (N2), and chamber
(ch). Spreading angle measurements were determined by finding the boundary of the jet
and fitting a line through the contour for the length of the jet core.
4.2 Jet Morphology and Density Map Analysis
Density and density gradient maps as shown in Figure 4-2 represent the first and
second case in Figure 4-1. In the first case, the central jet momentum is unaffected by
the annulus flow and the behavior observed is typical of a single nozzle configuration.
Surface instabilities are amplified downstream of the nozzle. The formation of ligaments
and droplets is apparent on the jet surface and droplets are ejected from the core
structure. Case 2 in Figure 4-2 represents an increase in the momentum flux ratio to M
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= 0.13. The results from the dimensionless number analysis shows that the flow
conditions exist at the beginning of the fiber type atomization regime with We > 500.
Droplet and ligament production have decreased in size under these conditions as the
fluid inertia dominates the surface tension forces.
Continuing to increase in the annular flow rate shows further signs of its influence
in the breakup process. Figure 4-3 shows these results indicating earlier separation of
core structures, i.e. a decrease in the core length. Case 3 shows droplet production on
a much smaller scale and Case 4 continues these trends with the appearance
approaching the wavy behavior characteristic of fiber type atomization. Its core length
has further decreased and core separation has accelerated due to the imparting of
momentum of the annular flow on the central jet.
With the momentum ratio exceeding unity, the dominance of the annular jet is
fully realized in cases 6-8. The jet core length is reduced to nearly a single nozzle
diameter and the fiber type breakup mechanism is apparent with detection of ligaments
and droplets. A smoothing of the density gradient profile is also observed in Figure 4-4
with the transition to increased momentum flux ratios.
The Reynolds and aerodynamic Weber numbers have been calculated for the
data points reported in Figure 4-1. The behavior of the jet approaching a momentum
flux ratio of zero is in the wind stress induced regime when compared with Figure 1-22
and confirms the wind assisted and Rayleigh type breakup for Weg < 15 [52]. The
remainder of the data points are in the fiber type atomization regime as expected by
Reynolds and Weber number analysis. This behavior is reported for Weg> 70 with the
super pulsating fiber type behavior reported when ReL/We1/2 < 100 [52]. Case 6-8 nearly
87
meet this condition and exhibit early visual characteristics such as a short core length, a
wavy appearance, and large detached masses, droplets, and ligaments. The core
length and inner jet spreading angle are measured using the results of the visual data
and are reported in the following section.
4.3 Core Length Analysis
The results of the core length analysis are shown in Figure 4-6. The data show a
reduction in core length with an increase in momentum flux ratio as also noted in
previous studies [77], [53], [63]. The image-to-image variation in core length can be
attributed to the stability of the jet with stable operation reported at velocity ratios above
10 [59].
The varying definitions of core length among researchers make comparison of
the experimental data, at times, imprecise. Therefore, the trends reported at similar
operating conditions are of more interest. The results presented in Figure 4-7 show an
agreement with the trends of various previous studies as reported by Chehroudi in
Figure 1-25. The magnitude of the core length measurements in the present study are
considerably lower owing to the systematic definition of the core length adopted here,
but the role played in explaining the mixing and disintegration process remains the
same. The large error bars are likely due to unstable behavior and flapping of the jet.
Further difficulties arise when comparing single phase and two phase coaxial jets.
Single phase coaxial jets (liquid/liquid or gas/gas) exhibit a much quicker decay in core
length than two-phase jets as indicated in Figure 1-25.
There are several correlations available for the liquid core length of coaxial jets
proposed by different studies. The trends in these correlations indicate an inverse
dependence on M in for form:
88
𝐿
𝐷=
𝐴
𝑀𝑛
(4-1)
Correlations of this form generally report n to be in the range 0.2 < n < 0.67 with
the experimental constant, A. Correlations by Mayer [77], Eroglu [71], and Raynal [51]
even attempt to include the effects of surface tension with limited success in predicting
the core length as surface tension vanishes. The core lengths reported in the study
show good agreement with the trends reports by Mayer [77] and Engelbert et al. [53]
particularly in the range of M > 1. These findings are shown in Figure 4-7. Agreement
with other correlations found limited success in predicting the magnitude of the core
length, likely due to the applied definition of core length in each study. Mayer [77]
developed a semi empirical expression using capillary wave theory to include the
surface tension and density ratio effects. Engelbert et al. [53] measured core lengths
from high speed images, thus, applying a different definition of the core length to the
study. In fact, when considering the accuracy of these measurements the previous
correlations seem to indicate the same results.
4.4 Inner Jet Spreading Angle Analysis
The inner jet spreading angle was based here on a criterion similar to Rodriguez
et al. [66] measuring on the fluorescence of the liquid core. The boundaries of the inner
jet were detected and the jet spreading angle was calculated for the jet core length.
The results are compared to the results of Rodriguez et al. [66] from Figure 1-27. The
outer-to-inner jet density ratios reported in this study were relatively unchanged so that
the thermodynamic conditions remain constant between test cases. Thus, when
comparing the effects of the density ratio on the inner jet spreading angle, the trends
differ from the results reported by Chehroudi in the previous studies [78]. This could be
89
due to the applied definition of spreading angle (combined outer and inner jet). The
momentum flux ratio dependence proved to have a much stronger effect with a trend
similar to Rodriguez et al. [66] observed.
A plot of inner jet spreading angle versus momentum flux ratio is reported in
Figure 4-8. An increase in jet spreading angle to a maximum value is noted with a quick
decay with increasing momentum flux ratio. Rodriguez et al. [66] found that the thick
inner post results in a delayed interaction between the inner and outer jet. A
recirculation zone is formed near the injector exit. Two-dimensional planar jets assume
immediate contact between the two jets and this discrepancy is apparent by the
behavior observed in the experimental results [66]. In the present study, the post
thickness is large compared to the central and annular flow areas results in a similar
behavior observed by Rodriguez et al. [66]. Shear is dominant at low momentum ratios
leading to large spreading angles; with increased momentum inertia dominates shear
effects resulting in a decay of the spreading angle.
90
4.5 Conclusions
This study evaluated the effects of the outer-to-inner momentum flux ratio on the
mixing characteristics of coaxial jets. PLIF was applied to measure density in coaxial
jets and provide density gradients of the central jet. The behavior observed in the
images were characteristic of the effects of varying the momentum flux ratio, namely,
the shedding of masses and formation of droplets, acceleration of the mixing process
and a reduction in core length. The behavior of jets with momentum flux ratios less than
one approaches the point where the regimes of coaxial and single round jets converge.
The jet in case 1 exhibits classic Rayleigh breakup behavior with the formation of
droplets and the growth of surface instabilities downstream of the injector as M
approaches zero and with Weg < 15. As the velocity of the annulus flow is increased, it’s
effect on the jet disintegration process becomes more pronounced. The amplitude and
frequency of the surface disturbances increases considerably with increased
momentum flux ratio. The Weber number of the remaining cases in this study exist in
the fiber type breakup mode. Furthermore, a smoothening of the density gradient profile
becomes more apparent as the rate of mixing increases due to the annular flow. The
accelerated mixing behavior is ideal in hot fire tests where adequate mixing is
necessary before combustion.
The core length and inner jet spreading angle were measured from the imaging
data and compared to experimentally derived correlations and theoretical models. The
core length data showed an inversely proportional relationship between the core length
and momentum flux ratio which agrees with trends reported by various studies. In
addition, the trends observed in the spreading angle analysis showed an increase in the
inner jet spreading angle to a maximum and subsequent decay at elevated momentum
91
flux ratios. Accelerated destruction of the liquid core and a wide jet spreading angle are
characteristic of enhanced mixing. Stable operation of the coaxial has been reported in
the range of velocity ratios greater than 10. Cases 6-8 with operating conditions in the
range, 1.28 < M < 4.32 and 9.97 < VR < 17.14, most closely resemble the ideal
simulated operating conditions for this injector geometry. Enhanced mixing features, i.e.
short core length, wide spreading angle, and a smoothening of the density gradient
profile, are observed under these conditions. The maximum and decay behavior
observed in the spreading angle data shows a transition in the dominance between
shear and inertia forces.
Figure 4-1. Experimental conditions for binary coaxial jet disintegration experiments. MR and VR represent the momentum and velocity ratios. The reduced temperatures and pressure are reported with respect to the critical point for fluoroketone (FK). Critical properties of fluoroketone (FK) are 441 K and 18.4 atm. Fluoroketone injection velocities are constant at 2 m/s. Figure subscripts are for fluoroketone (FK), nitrogen (N2), and chamber (ch).
92
Figure 4-2. Density and density gradient maps of cases 1 and 2 from Figure 4-1. In Case 1, the central jet momentum is unaffected by the annulus flow and the behavior observed is typical of a single nozzle configuration. Surface instabilities are amplified downstream of the nozzle. The formation of ligaments and droplets is apparent on the jet surface and droplets are ejected from the core structure. Case 2 represents an increase in the momentum flux ratio to M = 0.13. The results from the dimensionless number analysis shows that the flow conditions exist at the beginning of the fiber type atomization regime with We > 500. Droplet and ligament production have decreased in scale.
93
Figure 4-3. Density and density gradient map of cases 3 and 4 from Figure 4-1. Increasing in the annular flow rate shows further signs of its influence in the breakup process. The results indicate earlier separation of core structures, i.e. a decrease in the core length. Case 3 shows droplet production on a much smaller scale and Case 4 continues these trends with the appearance approaching the wavy behavior characteristic of fiber type atomization.
94
Figure 4-4. Density and density gradient map of cases 5 and 6 from Figure 4-1. The momentum flux ratio in case 5 is below 1 while case 6 is above 1. A nominal decrease in core length is observed. The core length is case 6 is almost a single nozzle diameter. A transition to fiber type atomization is apparent.
95
Figure 4-5. Density and density gradient map of cases 7 and 8 from Figure 4-1. Full fiber type atomization is observed in case 7 and 8. The density gradient profile begins to smooth. Droplet formation has increased with droplet sizes decreasing significantly.
96
Figure 4-6. Plot of normalized core length as a function of momentum flux ratio of the outer-to-inner jet. Fluoroketone (inner jet) and gaseous nitrogen (outer jet) are injected into a chamber filled with gaseous nitrogen. The data point in red on the far left represents the case where there is no annulus flow and hence the behavior is characteristic of a jet emanating from a single round orifice. The remainder of the data show an inversely proportional dependence on the core length with respect to the momentum flux ratio. The large error bar for M = 0.57 is due to jet flapping in the set of images employed.
97
Figure 4-7. Theoretical core length correlations proposed by Mayer [77] and Engelbert et al. [53] compared with the measured core length values reported in Figure 45. Agreement between the measured data and correlations is seen above M = 1. The correlations and experimental data exhibit the same M inversely proportional dependence on the core length.
98
Figure 4-8. Plot of inner jet spreading angle versus momentum flux ratio for fluoroketone/nitrogen coaxial jets. An increase in jet spreading angle to a maximum value is noted with a quick decay with increasing momentum flux ratio. This behavior has been attributed to the transition from shear to inertia dominance of the annular jet on the central jet.
99
CHAPTER 5 RECOMMENDED STUDIES
The work presented in this study focused on the disintegration of single orifice
and coaxial jets injected into environments ranging from subcritical to supercritical
thermodynamic conditions. The study aimed to expand the database of reliable
experimental data and further characterize the operational facility under similar working
conditions as previous researchers while applying new diagnostic techniques and
expanding upon the injection configurations of previous studies.
For the single orifice injection shadowgraph studies, further work is needed to
increase the field of view of the images to measure the jet penetration length for
comparison with shadowgraph data from similar binary species injection studies. The
trend of decreased penetration length with increased density ratio is apparent in with the
current data set but quantification and of this trend is still necessary.
There are still many injection conditions worth exploring in the coaxial injection
configuration. A study over a wide range of momentum flux ratios with the chamber
temperature and pressure supercritical would be of great interest. Furthermore,
increasing the injection temperature beyond the critical point while varying the chamber
conditions from sub-to supercritical conditions over a range of momentum ratios would
consist of another study worth exploring.
100
APPENDIX A FLUORESCENCE THEORY AND CALIBRATION
Fluorescence is a radiative decay process by which an atom or molecule
is excited from its ground state to a higher singlet state by absorption of photons
and subsequently decays to a lower energy level. The decay process includes
both radiative and non-radiative transitions. The emitted visible radiation is at a
longer wavelength and lower energy level (i.e. Stokes shift) which includes
fluorescence and phosphorescence. The non-radiative processes result in heat
production by release of phonons.
The working fluid in this experiment, fluoroketone, has a broadband
excitation in the range of 260-355 nm with fluorescence emission in the range of
350-550 nm. The number of molecule excited can be calculated by considering a
differential volume of fluid, dV, and a differential length, dL, traversed by the laser
onto an area, A, perpendicular to the direction of laser propagation. Thus, the
number of molecules excited from the ground state can be calculated as:
𝛥𝑁𝑒 =𝑁𝑝ℎ
𝐴𝑁𝑔𝜎𝑔
(A-1)
The number of molecules excited from the ground state is shown to be
proportional to the number of incident photons, Nph, number of ground state
molecules, Ng, and the absorption cross sections of the ground and excited state,
σg and σe, respectively. An expression can also be formed for the number of
molecules removed from the excited state due to stimulated emission:
−∆𝑁𝑒 =𝑁𝑝ℎ
𝐴𝑁𝑒𝜎𝑒
(A-2)
101
This expression is independent of laser loss processes during excitation
such as intersystem crossing, internal conversion, and collisional quenching due
to the time scales necessary for such processes to occur relative to the short
laser pulse duration. The instantaneous rate of change of the population in the
excited state can be calculated as:
𝑑𝑁𝑒
𝑑𝑡=
𝑁𝑝ℎ
𝐴(𝑁𝜎𝑔 − 𝑁𝑒(𝜎𝑒 + 𝜎𝑔))
(A-3)
This formulation considers the total number of molecules, N=Ng+Ne, as a
constant with no photo dissociation effects taken into account. To determine the
number of excited molecules during saturation, the previous equation must be
equated to zero and yields:
𝑁𝜎𝑔 = 𝑁𝑒,𝑠𝑎𝑡(𝜎𝑔 + 𝜎𝑒) → 𝑁𝑒,𝑠𝑎𝑡 = 𝑁(𝜎𝑔
𝜎𝑔 + 𝜎𝑒)
(A-4)
Solving equation 3-4 with the initial condition Ne(0)=0 and expressing the
solution in terms of the number of photons delivered in one pulse yields:
𝑁𝑒 = 𝑁 (𝜎𝑔
𝜎𝑒 + 𝜎𝑔) [1 − 𝑒
−𝑁𝑝ℎ(𝜎𝑔+𝜎𝑒)
𝐴 ] (A-5)
This function is plotted in Figure A-1 is used to approximate the linear
regime of the curve which begins at the origin and ends at the saturation line.
The linear regime exists when Nph << Nτph. Since all experiments performed are
in the non-linear regime we can express the number of fluorescing molecules as:
𝑁𝑓𝑙 = 𝑁𝜑 (𝜎𝑔
𝜎𝑒 + 𝜎𝑔) [1 − 𝑒
−𝑁𝑝ℎ(𝜎𝑔+𝜎𝑒)
𝐴 ] (A-6)
Where φ, the fluorescence quantum yield, is the ratio of excited photons
emitted to the number of photons absorbed. The fluorescence yield is considered
102
here to be a function of pressure, temperature, laser intensity (I), and
wavelength. The number of incident photons, Nph, can be expressed as:
𝑁𝑝ℎ =𝐼
ℎ𝑐/𝜆𝐴
(A-7)
This substitution can be made into (3-10) and it is assumed that (σg +
σe)≈σg or just σ. The optics efficiency and solid of angle of collection can now be
taken into account and an expression can be formed for the number of
fluorescing molecules collected.
𝑁𝑓𝑙,𝑐𝑜𝑙𝑙 = 𝜂𝑜𝑝𝑡𝑖𝑐 (𝛺
4𝜋) 𝑁𝜑 [1 − 𝑒
−𝐼(𝜆
ℎ𝑐)𝜎
] (A-8)
Two further substitutions must be made into this equation to obtain an
expression for the signal recorded on a single pixel. The number of absorbing
molecules, N, is proportional to the fluoroketone density, ρ(x,y) and the Beer-
Lambert law is used to account for the drop in laser intensity due to absorption
when scattering is neglected. All constants are grouped into two constants, F,
and k in the exponent to obtain the final expression for the signal recorded on a
single pixel:
𝑆(𝑝𝑥, 𝑝𝑦) = 𝐹𝜌(𝑥, 𝑦)𝜑[1 − 𝑒−𝑘𝑒−𝜎𝑛𝑥] (A-9)
The determination of φ is necessary to obtain concentration
measurements from the fluorescence signal and has been performed by Roy
through the gas and liquid phase [27]. This is done by obtaining fluorescence
signals for various fluoroketone densities and laser intensities. The image
processing for density calculations are reliable only if both φ and σ are constants.
This results a fluorescence signal that is linearly dependent on the density. A
summary of the calibration procedure follows.
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A.1 Gas Phase Calibration
To perform the calibration through the gas phase, the chamber is partially
filled with fluoroketone and the chamber walls are heated to increase the
temperature. A pressure increase occurs since the temperature change occurs at
constant volume. This effectively increases the vapor density inside the chamber.
Once a uniform vapor has formed, the laser sheet is passed through the
chamber and the fluorescence intensity signal is recorded. The results are
plotted in Figure A-2. The laser enters a column 1 and leaves at column 512. It is
apparent that the intensity variation is significant as the vapor density is
increased. A plot of intensity signal versus vapor density was obtained by
observing a region close the point where the laser entered the chamber. Figure
A-3 shows a weak second order dependence of laser intensity with vapor
density. It can be approximated as a straight line at low vapor densities with non-
linear behavior becoming more prominent as the critical point is approached. The
fluorescence signal is proportional to the density with fixed values of quantum
yield, laser intensity, optics efficiency, and absorption cross section at the point
x=0. Under this assumption, the quantum yield varies only slightly from a
constant as the critical point is approached.
The fluorescence intensity dependence on laser power is reported in
Figure A-4. This plot is obtained by fixing the vapor density, optics efficiency, and
absorption cross section while varying the laser power. Under these
assumptions, the expression for the fluorescence intensity signal yields:
𝑆(𝑝𝑥, 𝑝𝑦) = 𝑎[1 − 𝑒−𝑏𝐼(0,𝑦)] (A-10)
104
All constants have been grouped into the constants a and b. The curve fit
in Figure A-4 shows agreement with this expression for the laser intensity and
thus it can be assumed that φ is a constant in experiments under similar
conditions.
The final calibration is that of the absorption coefficient and its variation
with laser intensity through the length and width of the chamber. A sample
image is chosen and plots of the laser sheet fluorescence intensity is plotted
versus horizontal and vertical position is shown in Figure A-5. The plots are also
normalized by the maximum intensity for a given row and column and are also
shown. The top plots show the laser sheet profile from top to bottom in the
chamber while the plots on the bottom report the variation from left to right. It is
observed the plots of the horizontal profile that the variation in laser intensity from
left to right cannot be ignored as there is a decrease from 100% to 5% within 300
pixels of the origin. Since the sample image is that of a dense fluoroketone
vapor, the intensity drop can only be attributed to the absorption through the
gaseous phase. Hence, this effect must be taken into account for single species
mixing unlike binary mixing where laser absorption does not occur through the
nitrogen surroundings. Since it has been shown that φ is essentially a constant
over the range of thermodynamic conditions of interest, equation 3-17 has been
validated and can be expressed as such:
𝑆(𝑝𝑥, 𝑝𝑦) = 𝐴𝜌(𝑥, 𝑦)𝜑[1 − 𝑒−𝑘𝑒−𝜎𝑛𝑥] (A-11)
A new constant is introduced in this equation, A=Fφ. An analysis of the
normalized fluorescence signal versus horizontal displacement shows an
105
exponential decrease in signal intensity as shown in Figure A-6. A curve is fitted
to the experimental data points according to the equation obtained, 3-20. The
exponential coefficient in the curve fit equation is the absorption coefficient as
given by the Beer-Lambert law. The value of the absorption coefficient is only
valid at the given thermodynamic conditions. An increase in chamber
thermodynamic conditions results in an increase in chamber vapor density and
thus, a resulting increase in the value of the absorption coefficient. A calibration
curve of absorption coefficient versus vapor density is report in Figure A-7. The
result is a linear dependence of the absorption coefficient versus vapor density
and the slope is constant throughout the vapor phase. The absorption coefficient
can now be related to the absorption cross section in the form:
𝛼 = 𝜎×𝑛 = [𝜎×𝑁𝐴
𝑀] ×𝜌
(A-12)
The slope of the calibration curve is proportional to the absorption cross
section and can be approximated as a constant for the range of densities
reported in the Figure A-7. This analysis validates the assumption of a constant
absorption cross section through the vapor phase that was made earlier in the
analysis. The absorption cross section through the vapor phase is calculated to
be 3.81 x 10-19 cm2/molecule from this data and the known molecular weight of
fluoroketone (316 g/mol). The fluorescence yield is found to be a constant up to
vapor densities of 0.25 g/cm3.
A.2 Liquid Phase Calibration
A similar procedure is performed for the calibration through the liquid
phase. The chamber is filled with fluoroketone and heated to the desired
temperature but kept below the vapor pressure. After steady conditions were
106
met, the laser sheet was passed through the chamber and images of the laser
sheet profile were obtained. Figure A-8 shows the result of the curve fit obtained
for the normalized laser intensity versus horizontal distance in the chamber along
with the curve fit obtained through the gaseous phase. The curve fit obtained for
the liquid data utilizes the sum of exponents fit. It can be seen that the gas
calibration curve fit does not agree well with the sum of exponents curve fit. This
is attributed to several competing phenomena. Since the absorption is higher for
liquids than gases, there is a greater chance of fluorescence trapping. In
addition, the absorption cross section values may differ significantly and the
possibility of quenching can also occur. Quenching has been shown to occur in
the presence of oxygen for ketone fluorescence. It is shown to affect the
phosphorescence more significantly than fluorescence and it is assumed that a
similar phenomenon occurs for fluoroketone. To observe the difference between
the liquid and vapor absorption behavior, fluorescence data was obtained for a
range of thermodynamic conditions approaching the critical point. A single case
for a chamber pressure of 12.7 atm and chamber temperature of 145oC is
reported in Figure A-9. It can be seen that there is agreement between the
experimental data and the obtained curve fit. To understand these observations,
the coefficients must be analyzed. For the sum of exponents case, the coefficient
c was two orders of magnitude less than a. This observation shows that the
second exponent term becomes less significant and lower liquid densities.
Observations at higher liquid densities showed that the coefficients were of the
same order of magnitude which signifies that they are equally important at higher
liquid densities. Figure A-10 shows the fluorescence data obtained over a range
107
of thermodynamic conditions as well as the corresponding curve fits. An analysis
of this plot shows that the calibration curve for the vapor phase works well for
liquid densities below 1401.7 kg/m3 which occurs at 3 atm and 80oC. It is
concluded that the non-linear effects that observed between the liquid and vapor
fluorescence signal are less important as chamber thermodynamic conditions are
increased towards the critical point.
Since the sum of exponents curve fit agrees well with the liquid
fluorescence data, an observation is made between the primary calibration
variable, b, and the calibration for the gas curve fit, c. The result is plotted in
Figure A-11. The differences are observed at higher liquid densities as expected.
The values for the coefficients show agreement below liquid densities of 1350
kg/m3 and vary about 0.0045 in magnitude. There is a steep decline in the value
of the coefficients between the range of liquid densities of 1600 kg/m3 and 1350
kg/m3 after which the value of the coefficient is relatively independent of density.
It is concluded that other competing phenomena cannot be quantified with the
current data but the curve fits obtained can be used with the liquid exists in
experiments with similar thermodynamic conditions.
A.3 Conclusions
A study of the optical properties of fluoroketone was performed by Roy
and a summary of those results is reported in this Appendix. A theoretical
analysis of fluorescence behavior in the non-linear regime of excitation was
developed. He criteria developed to use fluoroketone for quantitative
measurements in PLIF applications were verified which included the linear
variation of fluorescence intensity with concentration for fixed laser intensity as
108
well as the exponential variation of fluorescence intensity with laser power at
fixed concentrations. These criteria were found to be true in the range of
fluoroketone vapor densities of 20 kg/m3 to 200 kg/m3 and laser intensities of 20
mJ/pulse to 140 mJ/pulse. This was done to justify the assumption that the
quantum fluorescence yield is a constant within the range of laser intensities and
concentrations that were used in the experiments performed. A vapor phase
calibration curve was obtained for the density range of 0.03-0.24 g/cm3. The
curve obtained was a straight line which verified that the slope of the line, i.e.
absorption cross section, is a constant as assumed in the beginning of the
analysis. A calibration curve could not be obtained for the liquid phase using a
similar technique employed in that gas phase calibration. The absorption cross
section was calculated to be 3.81 x 10-19 cm2/molecule and can be used for any
experiment utilizing fluoroketone under similar experimental conditions.
Figure A-1. Plot of excited molecules versus the number of exciting photons.
109
Figure A-2. Plots of fluorescence intensity variation of the laser sheet profile as it
passes through the chamber. The laser sheet enters at column 1 and exits at column 500. It can be seen from these plots that the intensity variation is significant as thermodynamic conditions are increased. A) 2.7 atm, 85oC. B) 5.9 atm, 110oC. C) 10.4 atm, 150oC. D) 14.7 atm, 165oC.
110
Figure A-3. Plot of fluorescence signal intensity versus vapor density. The curve
fit is nearly linear for low vapor densities and non-linearity become more important as the critical point of the fluid is approached.
Figure A-4. Fluorescence intensity as a function of laser power. A non-linear
dependence of fluorescence signal intensity is observed over the operating range of the current experiments.
111
Figure A-5. Plots of vertical and horizontal laser sheet intensity variation. The
plots on the left represent the actual intensity variation while the plots on the right have been normalized by the maximum intensity for each row or column. A significant variation of laser sheet intensity is seen in all plots.
112
Figure A-6. Plot of normalized fluorescence intensity versus the length traversed
by the laser in pixels. An exponential curve is fitted to the experimental data which is used to obtain the absorption coefficient given by the Beer-Lambert law.
Figure A-7. Calibration line for the absorption coefficient as a function of the
fluoroketone vapor density. A linear dependence is noted from the plot.
113
Figure A-8. Plot of normalized fluorescence intensity versus length traversed by
the laser in pixels at 1.25 atm and 17oC.
Figure A-9. Plot of normalized fluorescence intensity versus length traversed by
the laser in pixels at 12.7 atm and 145oC.
114
Figure A-10. Plot of normalized fluorescence intensity versus length traversed by
the laser in pixels at various liquid densities. The pressure and temperature for each experimental condition is noted in the legend.
115
Figure A-11. Plots comparing the coefficients obtained from the gas curve fit and
liquid sum of exponents fits. The difference is noted at higher densities while little variation is seen at lower densities.
116
APPENDIX B SHADOWGRAPH EXPERIMENTAL CONDITIONS
Table B-1. Table of experimental conditions for all cases represented in spreading angle data in Figure 3-5.
Case Tch Tinj Pch FK velocity
FK density [kg/m3]
N2 density [kg/m3]
Density Ratio
Mass flow rate [g/s]
1 0.68 0.98 0.80 24.33 300.90 30.74 0.10217 23.74
2 0.68 0.99 0.82 31.39 326.00 30.30 0.09293 33.19
3 0.72 0.99 0.85 34.73 308.00 30.41 0.09873 34.69
4 0.71 0.97 0.61 24.55 362.70 30.33 0.08362 28.88
5 0.71 1.00 0.60 29.84 296.60 29.65 0.09998 28.70
6 0.71 0.97 0.59 32.37 283.90 29.57 0.10416 29.80
7 0.71 0.96 0.60 37.08 257.10 29.69 0.11548 30.92
8 0.71 0.99 0.60 36.43 276.23 29.68 0.10745 32.63
9 0.69 0.80 0.53 29.96 271.10 29.26 0.10794 26.34
10 0.69 0.84 0.34 32.27 319.21 28.76 0.09008 33.41
11 0.69 0.83 0.23 23.20 413.80 39.16 0.09464 31.13
12 0.70 0.80 0.24 19.83 404.24 39.74 0.09831 26.00
13 0.69 1.15 1.49 20.92 407.40 39.91 0.09795 27.64
14 0.69 1.13 1.47 59.44 209.44 25.19 0.12028 40.37
15 0.69 1.14 1.48 49.97 213.18 24.95 0.11702 34.55
16 0.71 1.11 1.50 53.38 222.78 24.97 0.11209 38.56
17 0.70 1.15 1.46 29.47 353.59 41.15 0.11638 33.79
18 0.71 1.17 1.47 32.48 328.83 40.01 0.12168 34.64
19 0.71 1.20 1.48 37.82 320.42 41.04 0.12808 39.30
20 0.71 1.19 1.47 23.88 524.02 40.68 0.07762 40.57
21 0.71 1.19 1.46 39.58 246.42 16.76 0.06803 31.63
22 0.70 1.17 1.41 38.06 225.40 16.99 0.07538 27.82
23 0.70 1.18 1.92 27.81 415.15 16.70 0.04022 37.45
24 0.71 1.18 1.97 34.68 469.99 12.18 0.02592 52.86
25 0.70 1.18 1.97 56.19 140.99 12.15 0.08621 25.69
26 0.71 1.20 1.25 6.33 162.72 11.79 0.07244 3.34
27 0.71 1.18 1.23 10.78 839.47 12.15 0.01448 29.34
28 0.71 1.17 1.24 61.58 133.23 12.62 0.09472 26.61
29 0.70 1.24 2.02 35.57 128.74 12.01 0.09326 14.85
30 0.71 1.27 2.00 5.68 1414.04 10.95 0.00774 26.06
31 0.70 1.28 2.02 6.71 1320.16 7.03 0.00533 28.74
32 0.69 1.12 1.96 0.64 1339.11 4.69 0.00350 2.78
33 0.71 1.00 0.63 3.93 1397.17 5.01 0.00358 17.79
34 0.89 1.14 1.59 0.74 1162.38 4.21 0.00363 2.78
35 0.88 1.14 1.59 23.34 625.22 24.70 0.03951 47.31
36 0.87 1.12 1.59 26.42 514.69 24.64 0.04787 44.10
117
Table B-1: Continued.
Case Tch Tinj Pch FK velocity
FK density [kg/m3]
N2 density [kg/m3]
Density Ratio
Mass flow rate [g/s]
37 0.90 1.15 1.54 25.53 512.56 24.79 0.04836 42.44
38 0.90 1.16 1.55 23.64 488.17 25.52 0.05228 37.42
39 0.89 1.15 1.54 31.48 364.72 25.21 0.06913 37.23
40 1.03 1.12 1.54 34.94 350.88 25.62 0.07301 39.76
41 1.02 1.16 1.54 22.20 650.48 25.91 0.03983 46.83
42 1.02 1.14 1.55 39.68 314.56 24.07 0.07651 40.48
43 1.02 1.12 1.54 39.62 311.26 24.36 0.07827 40.00
44 1.02 1.15 1.56 40.46 312.76 24.44 0.07816 41.04
45 1.02 1.13 1.54 27.09 359.63 21.17 0.05887 31.59
46 1.03 1.07 1.52 31.30 310.40 21.29 0.06858 31.51
47 1.02 1.08 1.52 27.65 333.76 21.44 0.06423 29.93
48 1.02 1.07 1.53 27.89 369.14 21.22 0.05748 33.39
118
APPENDIX C MATLAB SCRIPTS FOR DATA PROCESSING
A description of the MATLAB codes used for data processing are
presented along with the annotated codes.
Beam_Correction.m: This program is used to calculate the variation of the
intensity of the laser sheet profile. The laser sheet profile is then corrected along
the direction of propagation of the laser as well as from top to bottom. The
calculated absorption coefficient for the gas phase and the user-defined liquid
absorption coefficients are used to correction for the absorption effects through
their respective mediums.
Core_Length.m: This function calculates the core length of the jet defined as the
length along the axial coordinate for which the largest change in density occurs
signifying the end of the unbroken length of the jet. This is accomplished by
dividing the jet into sub-matrices using the diameter of the nozzle to create
matrices along the jet axis. The average density and eigenvalues of these
matrices are calculated and the location of the largest change in density is
determined.
Data_Analysis.m: This program calls Core_Length.m and Spreading_Angle.m to
perform their respective measurements. The program calculates the average,
standard deviation and also corrects for outliers in the data set. The calculations
are then written to a user-defined location in an Excel workbook.
Divergence_Angle.m: This function calculates the spreading angle of the jet by
first detecting the boundaries of the jet. A linear fit is drawn through the boundary
along one third of the jets length and slope of this curve is used to determine the
divergence angle from the jet axis.
119
Goodeqn_liq.m: This function calculates the density of the working fluid using the
PRSV equation of state and utilizing the manufacturer provided constants. It
provides an accurate calculation of the density from the subcritical to supercritical
regime.
Idealgas.m: This function is used to calculated the density of the nitrogen gas in
the chamber and annular flow of the coaxial nozzle using the ideal gas equation
of state.
Image_Processor.m: The program calls Beam_Correction.m and the
background.mat file to correct the experimental image of the jet. Density images
are created by applying a colormap to the corrected intensity profile of the image.
Density gradients are then calculated from the density maps. Each individual
density and density gradient map is saved in the source folder.
Jet_Boundary.m: This function is used to detect the boundaries of the jet by first
taking into account the variation of the laser from top to bottom and detecting the
location of the boundary by finding a gradient in the positive and negative radial
direction along the center axis of the jet.
Lmu_jet_angle_UF_REV2.m: This program was written by Lukas Muser of the
German Aerospace Institute under the guidance of Steffen Baab. This program
calculates the jet spreading angle at various downstream locations of the jet.
LMU_ROTATEIMAGE_REV2.m: This function was written by Lukas Muser of the
German Aerospace Institute under the guidance of Steffen Baab. This function
rotates the image to correct for any skewness of the camera during image
acquisition.
120
Run_background.m: This program reads the background image and creates a
‘.mat’ file of the intensity profile. The background intensity profile will be used to
eliminate the noise associated with background emission from the experimental
image. This program must be run before any other image analysis can be done.
Run_Preview.m: This program reads the sensor data file written by LabVIEW
during an experiment and plots the relevant data to ensure the run was
successful. The program outputs the data to a text file.
Spreading_Angle.m: This function is called by the Data_Analysis.m program to
perform the jet spreading angle calculations.
Shadowgraphy_Processing.m: This program performs the image processing on
the shadowgraphy data. The test image and background image are provided and
the corrected image as well as the averaged image are produced.
Shadowgraphy_Sensor_Data_Processing: This program processes the sensor
data file produced by the LabVIEW experimental control program.
Test_Conditions.m: This program is used to perform the flow calculations from
the acquired sensor data and write the experimental conditions to an excel file.
The velocities, velocity ratio, and momentum flux ratio are determined.
121
Beam_Correction.m
%% Modified Laser Sheet Program
% Takes into account the loss of intensity through the jet
% This matrix has to be used for point-by-point division
with the Image
% Prepared by Arnab Roy on 20th October, 2011
% Modified by Shaun DeSouza on 30th March, 2016
function
[mod_laser,Origin_new,degree]=Beam_Correction(pathname,orig
in,Noz)
%% Defining the location of the Laser Sheet Profile and
Background Image
location=strcat(pathname(1:49),
'\Laser_Sheet_Profile\Laser_Sheet_Profile.TIF');
bckgrdlocate=[pathname(1:49) 'Background\background.mat'];
bckgrd=load(bckgrdlocate);
background=bckgrd.background;
size(background);
%% Creating an Average Laser Sheet Profile
know=imfinfo(location);
n=length(know);
sum1=0;
for i=1:n
X=double(imread(location,i));
X1=X;
X1=X1-background;
sum1=sum1+X1;
end
profile=sum1/n;
[row,col]=size(profile);
avgprof=mean(profile(:,1:25)')';
profile=avgprof/max(avgprof);
profile=profile(Noz:end);
%% Finding the start and the end points of the jet for each
row
location2=strcat(pathname, 'Test.TIF');
[start,finish,imgtemp]=Jet_boundary_latest(location,locatio
n2,origin,Noz);
clrimg=imgtemp*64/max(max(imgtemp)); % Creating a color
image
mymap=(load(strcat(location(1:end-23),'mymap.txt'))); %
Loading the color map
ans1='n';
while (ans1=='n')
degree= 0; %input('Angle of rotation (clockwise):');
clrimg1=imrotate(clrimg,-degree,'crop');
figure(3)
122
colormap(mymap);
image(clrimg1);
grid on;
grid minor;
ans1= input('Satisfied with image
rotation?(y/n):','s');
end
Origin_new= 150; %input('Enter new origin:');
%% Creating the Modified Laser Image with exponential
decays after the Jet
%% starts and ends
location3=strcat(pathname,'ProcessedData.txt');
Pdata=load(location3);
samples=length(Pdata);
TimeIndex=1;
gradflow=gradient(Pdata(:,8));
for l=1:samples
if (gradflow(l)==max(gradflow))
TimeIndex=l;
break;
end
end
LiqTemp=mean(Pdata(TimeIndex:end,2));
% LiqPres=mean(Pdata(TimeIndex:end,6));
% ChmTemp=mean(Pdata(TimeIndex:end,3));
ChmPres=mean(Pdata(TimeIndex:end,5));
Tl=mean(LiqTemp);
Pg=mean(ChmPres);
% alpha_gas=(goodeqn_vap(Tg,Pg)*4e-5)+0.00092;
%alpha_liq=(goodeqn_liq(Tl,Pg)*1.2e-6)+0.0029; % For heated
jet injection
alpha_liq=0.003; % For cold jet injection
alpha_gas=0; % For binary injection
ans2='n';
while (ans2=='n')
%% Using the newly derived non-linear formula for laser
absorption inside the jet and beyond it
for k=1:row-Noz
for i=1:start(k)
mod_laser(k,i)=profile(k)*4.55*(1-exp(-
.25*exp(-alpha_gas*i)));
end
end
for k=1:row-Noz
for i=start(k):finish(k)-1
123
mod_laser(k,i+1)=mod_laser(k,start(k))*(1-exp(-
.25*exp(-(alpha_liq*(i-start(k)))-alpha_gas*start(k))))/(1-
exp(-.25*exp(-alpha_gas*start(k))));
end
for i=finish(k)+1:col
mod_laser(k,i)=mod_laser(k,finish(k))*(1-exp(-
.25*exp(-(alpha_gas*(i-finish(k)))-(alpha_liq*(finish(k)-
start(k)))-(alpha_gas*start(k)))))/(1-exp(-.25*exp(-
(alpha_liq*(finish(k)-start(k)))-(alpha_gas*start(k)))));
end
end
mod_laser=mod_laser/max(max(mod_laser));
clrimg_new=clrimg(1:end-1,:)./mod_laser;
clrimg_new=imrotate(clrimg_new,-degree,'crop');
clrimg_new=clrimg_new/max(max(clrimg_new));
figure(3)
image(clrimg_new*64);
colormap(mymap);
count=1;
for l=1:25:row-Noz-24
avg_profile(count,:)=mean(clrimg_new(l:l+24,:));
grad_profile(count,:)=gradient(avg_profile(count,:));
count=count+1;
end
count=count-1;
xlimit1=round(0.15*col);
xlimit2=round(2*Origin_new-0.15*col);
figure(4)
plot((xlimit1:xlimit2),avg_profile(:,xlimit1:xlimit2)');
grid on;
hold on;
plot(ones(count,1)*Origin_new,(0:1/(count-1):1),'r');
hold off;
figure(5)
plot((xlimit1:xlimit2),grad_profile(:,xlimit1:xlimit2)');
grid on;
hold on;
plot(ones(count,1)*Origin_new,(0-
max(max(grad_profile)):2*max(max(grad_profile))/(count-
1):max(max(grad_profile))),'r');
hold off;
ans2= input('Satisfied with image quality?(y/n):','s');
alpha_liq=alpha_liq+0.0005;
end
124
disp(strcat('The alpha used for this injection case
was:',num2str(alpha_liq-0.0005)));
figure(6)
plot(mod_laser');
title('Corrected laser profile image');
xlabel('Length (Pixels)');
ylabel('Actual Intensity');
sum=0;
for i=1:length(mod_laser)
sum=sum+(mod_laser(i,:)/max(mod_laser(i,:)));
end
sum=sum/length(mod_laser);
figure(7);
plot(sum);
title('Mean normalized laser intensity from left to
right');
xlabel('Length (Pixels)');
ylabel('Normalized Intensity');
125
Core_Length.m
%% This program calculates the core length and standard
deviation of
%% measurements.
function core_std=Core_Length(location,count,origin)
%% Initializing variables
JetDia=0.223; %[cm]
per1=0.1;
diffeig1=0.9;
core(1:count)=0;
%% Calculating core lengths of individual images
for i=1:count
clear outline coremaybe length Density AVG H V D M gH
gHroots gHrootsr x y1 y2 y3 p1 p2 p3 limit r counter c j k
g r r1 start finish center l count1 count2;
img=load(location(i,:));
Density=img.DensMatrix;
mymap=load([location(1,1:end-22)
'Laser_Sheet_Profile\mymap.txt']);
[row col]=size(Density);
count1=0;
start=origin-25;
finish=origin+25;
width=50+1;
width2=50+1;
height2=10+1;
center=origin;
for r=1:length(Density)-width-1
M(1:width,1:width)=Density(r:r+width-1,center-
((width-1)/2):center+((width-1)/2));
M2(1:height2,1:width2)=Density(r:r+height2-
1,center-((width2-1)/2):center+((width2-1)/2));
AVG(r)=sum(M2(:))/numel(M2);
[V,D]=eig(M);
H(r)=abs(det(eye(size(D))+D));
if AVG(r)<0.5*max(AVG);
break
end
end
x=1:r;
p1=polyfit(x,log(H(1:r)),20);
y1=p1(1)*x.^20+p1(2)*x.^19+p1(3)*x.^18+p1(4)*x.^17+p1(5)*x.
^16+p1(6)*x.^15+
p1(7)*x.^14+p1(8)*x.^13+p1(9)*x.^12+p1(10)*x.^11+p1(11)*x.^
10+p1(12)*x.^9 +
126
p1(13)*x.^8+p1(14)*x.^7+p1(15)*x.^6+p1(16)*x.^5+p1(17)*x.^4
+p1(18)*x.^3 + p1(19)*x.^2+p1(20)*x.^1 + p1(21)*x.^0;
gH=gradient(y1);gHroots=roots([20*p1(1) 19*p1(2)
18*p1(3) 17*p1(4) 16*p1(5) 15*p1(6) 14*p1(7) 13*p1(8)
12*p1(9) 11*p1(10) 10*p1(11) 9*p1(12) 8*p1(13) 7*p1(14)
6*p1(15) 5*p1(16) 4*p1(17) 3*p1(18) 2*p1(19) 1*p1(20)]);
gHrootsr=floor(abs(gHroots));
counter=1;
g=length(gHrootsr);
while g>=1
if (g>1 && gHrootsr(g)==gHrootsr(g-1)&&(gHrootsr(g)<r))
coremaybe(counter)=gHrootsr(g);
counter=counter+1;
g=g-1;
else
if ((gHrootsr(g)>1)&&(gHrootsr(g)<r))
coremaybe(counter)=gHrootsr(g);
counter=counter+1;
end
end
g=g-1;
end
counter=counter-1;
H20=((y1(coremaybe(1:counter))-
min(y1(coremaybe(1:counter))))/max(y1(coremaybe(1:counter))
-min(y1(coremaybe(1:counter)))))';
%% Normalized eigen vector at the inflexion points.
core1=0;
diffeig=diffeig1;
while (core1<=0)&&(diffeig>=.025);
per=per1;
while (core1<=0)&&(per<=0.99)
for j=2:counter-2
if (abs(H20(j)-H20(j-1))>diffeig &&
AVG(coremaybe(j))/AVG(coremaybe(j-1))<per &&
coremaybe(j)>0.1*row)
core1=coremaybe(j);
break
end
end
per=per+.025;
end
diffeig=diffeig-.025;
end
core2=0;
per=per1;
while (core2<=0)&&(per<=0.99)
127
diffeig=diffeig1;
while (core2<=0)&&(diffeig>=.025);
for j=2:counter-2
if (abs(H20(j)-H20(j-1))>diffeig &&
AVG(coremaybe(j))/AVG(coremaybe(j-1))<per &&
coremaybe(j)>0.1*row)
core2=coremaybe(j);
break
end
end
diffeig=diffeig-.025;
end
per=per+.025;
end
%% Normalize with the injector diameter
core(i)=min(core1,core2)/(JetDia/0.0044);
figure(1);
colormap(mymap);
scale=64/max(max(Density));
image(Density*scale);
hold on;
plot(1:col,core(i)*(JetDia/0.0044));
end
%% Eliminating outliers and plotting %
cnt=1;
for i=1:count
if (abs(core(i)-mean(core))<std(core))
core_final(cnt)=core(i);
cnt=cnt+1;
end
end
%% Plotting core length measurements for each image and
writing to xls
plot(core,'o-');
hold on;
avg_core(1:count)=mean(core);
plot((1:count),avg_core,'g',(1:count),avg_core-
std(core),'r-.',(1:count),avg_core+std(core),'r-x');
avg_final=mean(core_final);
plot(avg_final*ones(1,cnt),'k');
xlabel('No. of images considered','Fontsize',14);
ylabel('Normalized Core Length (L/D_i_n_j)','Fontsize',14);
legend('All core lengths','Mean core length','Lower
standard deviation','Upper standard deviation','Modified
mean');
disp(strcat('Average core length is: ',num2str(avg_final),'
jet diameters'));
128
disp(strcat('Standard deviation is:
',num2str(std(core_final)),' jet diameters'));
core_std=[avg_final std(core_final)];
%xlswrite('D:\Shaun\Tests\Corelength.xlsx',core_std,'J37:K3
7');
129
Data_Analysis.m
%% This program calculates the core lengths and spreading
angle of each
%% image and writes the data to a spreadsheet
% Created by Arnab Roy on 14th June, 2010
% Modified by Shaun DeSouza on 30th March, 2016
clc
clear all;
close all;
hold off;
%% Finding images to be processed by picking the first and
last files
JetDia=0.223;
pathname='C:\Shaun\Tests\';
[filename1, pathname1] = uigetfile('*.mat','Pick first
image file to Process',pathname);
[filename2, pathname2] = uigetfile('*.mat','Pick last image
file to Process',pathname1);
start=str2double(filename1(1:2));
finish=str2double(filename2(1:2));
count=1;
for i=start:finish
if (i<10)
location(count,:)=[pathname1
strcat('0',num2str(i)),'d.mat'];
else
location(count,:)=[pathname1
strcat(num2str(i)),'d.mat'];
end
fid=fopen(location(count,:));
if (fid~=-1)
count=count+1;
end
end
count=count-1;
fprintf('There are the %d file locations you have
chosen:\n',count);
disp(location);
%% Calling functinons to calculate the Core Length and
Spreading Angle
Origin=input('Enter the origin:');
warning off;
core_std=Core_Length(location,count,Origin);
angle_std=Spreading_Angle(location,count,Origin);
core_angle=[core_std angle_std];
130
xlswrite('C:\Users\Shaun\Desktop\AIAA
Paper\Coaxial_PLIF_Logbook.xlsx',core_angle,'AIAA Data
Set','R11:U11');
131
Divergence_Angle.m %% Spreading angle calculation function
% Prepared by Arnab Roy on 1st April, 2012
% Modified by Shaun Desouza on 30th March, 2016
function [alpha1,alpha2] =
Divergence_Angle(clrimg,origin,row)
%% Storing the boundaries of the jet for each row
initial(1:row)=0;
for i=1:row
for j=1:origin
if ((clrimg(i,j)>0) && (clrimg(i,j+1)>0))
initial(i)=j;
break;
end
end
end
final(1:row)=0;
for i=1:row
for j=size(clrimg,2):-1:origin
if ((clrimg(i,j)>0) && (clrimg(i,j-1)>0))
final(i)=j;
break;
end
end
end
plot(final,1:row,'k');
plot(initial,1:row,'r');
%% Fitting a line through the left and right boundaries of
the jet
p2=polyfit((1:round(row)),initial(1:round(row)),1);
y2=p2(1)*(1:round(row))+p2(2);
p3=polyfit((1:round(row)),final(1:round(row)),1);
y3=p3(1)*(1:round(row))+p3(2);
plot(y2,(1:round(row)));plot(y3,(1:round(row)));
%% Calculating the divergence angle of the jet
alpha1=atan(p2(1));
alpha2=atan(p3(1));
132
Goodeqn_liq.m
function density=goodeqn_liq(To,Po)
%PRSV.m
%Peng-Robinson-Stryjek-Vera equation of state applied to
fluoro-
%ketone FK-5-1-12mmy2. Parameter values from Owens, J,
"PHYSICAL
%AND ENVIRONMENTAL PROPERTIES OF A NEXT GENERATION
EXTINGUISHING
%AGENT", Proceedings of HOTWC-2002 12th Halon Options
Technical
%Working Conference, Albuquerque, NM, April 30 – May 2,
2002
%Modified through introduction of kappa variable replacing
old
%variable alpha - now in accordance with original PRSV
model in
%Stryjek&Vera (1986)
T=(0:1:600)'+273.15;
R=8.3144;
Tc1=441.81; Pc1=18.646E5; rhoc1=639; omega1=0.471;
kappa11=0.052; Mw1=.316046; %FK properties molar weight
kg/m^3
Tc2=748; Pc2=40.5E5; rhoc2=315.29; omega2=0.30295;
kappa12=0.03297; Mw2=.12817;
x1=1; x2=0.0; % molar fractions
Mw=x1*Mw1+x2*Mw2;
rho=0.1:1:1800;
V=Mw./rho; %m3/mole
b1=0.077796*R*Tc1/Pc1;
b2=0.077796*R*Tc2/Pc2;
Tr1=T/Tc1;
Tr2=T/Tc2;
kappa01=0.378893+1.4897153*omega1-
0.17131848*omega1^2+0.0196554*omega1^3;
kappa02=0.378893+1.4897153*omega2-
0.17131848*omega2^2+0.0196554*omega2^3;
kappa1=kappa01+kappa11*(1+Tr1.^0.5).*(0.7-Tr1);
kappa2=kappa02+kappa12*(1+Tr2.^0.5).*(0.7-Tr2);
alpha1=(1+kappa1.*(1-Tr1.^0.5)).^2;
alpha2=(1+kappa2.*(1-Tr2.^0.5)).^2;
a1=alpha1*0.457235*(R*Tc1)^2/Pc1;
a2=alpha2*0.457235*(R*Tc2)^2/Pc2;
133
a=x1^2*a1+2*x1*x2*sqrt(a1.*a2)+x2^2*a2;
b=x1*b1+x2*b2;
p=R*T*(1./(V-b))-a*(1./(V.*(V+b)+b*(V-b)));
pb=p/10^5;
To=To+273.15;
[ vl ,Ind ]=min(abs(T-To));
for i=length(pb(Ind,:)):-1:1
if (pb(Ind,i)-Po)<0
break
end
end
density=rho(i)*.97;
%pb(i,Ind)
% % figure(1)
% [c,h]=contour(rho-.03*rho,T-273.15,pb,[0:1:60]);
% clabel(c,h);
% shading flat;
% xlabel('\rho, kg/m^3');
% ylabel('T, C');
% grid minor
% % figure(2)
% % C = contourc(rho,T,pb,[25]);
134
Idealgas.m function densityN2=idealgas(T,P)
Ru=8.314;
Mw=28;
Tch=T+273.15;
Tch=T+273.15;
Pch=P*101.325;
densityN2=(Pch*Mw)/(Ru*Tch);
135
Image_Processor.m % Modified `run_processor.m' Program for single component
injection
% Accounts for point-by-point division with the Laser Image
% Prepared by John Gaebler. Modified by Arnab Roy on 7th
April, 2010
% Modified by Shaun DeSouza on 30th March, 2016
clear all;
close all;
%% Declaration of Variables and Initialization
DataCols=9;
CamHz=10;
x=0.044; % mm per one pixel
y=0.044; % mm per one pixel
JetDia=2.235; % [mm]
JetDia=JetDia/1000; % [m]
TimeCol=1; % Col stands for column, in ProcessedData.txt
LiqTempCol=2;
ChmTempCol=3;
ExtSyncCol=4;
ChmPresCol=5;
LiqPresCol=6;
GasPresCol=7;
LiqFlowCol=8;
GasFlowCol=9;
ExtSyncSpikeLev=4;
%TotalFrames=25;
%% Choosing the Files to process
pathname='C:\Shaun\Tests\';
[filename, pathname] = uigetfile('*.*','Pick
ProcessedData.txt file for data run to Process',pathname);
% Loading the necessary files from their respective
locations
location=[pathname filename];
Pdata=load(location);
TotalFrames=round(length(Pdata)/1000);
samples=length(Pdata); % Total number of samples
step=Pdata(2,TimeCol); % This position is first step from
time(1)=0
%% Finding the jet boundary
Noz= 130; %input('\nEnter start of nozzle:');
Origin_init= 150; %input('Enter origin:');
[weight,Origin,degree]=Beam_Correction(pathname,Origin_init
,Noz);
[row,col]=size(weight);
xlimit=round(0.45*col);
ylimit=round(0.9*row);
136
weight=weight(1:ylimit,:);
hold off;
%% Loading background and laser sheet
location=[pathname(1:49) 'Background\background.mat'];
eval(['load ' location ' background']) % Loading the
background image
background=background(Noz:ylimit+Noz-1,:);
ImageLocate=[pathname 'Test.TIF'];
location=[pathname(1:49) 'Laser_Sheet_Profile\mymap.txt'];
mymap = load(location); % Loading the colormap to be used
for images
clear location fid
%% Finding the index of each image wrt 'ProcessedData.txt'
Frame=0;
LengthCounter=0;
check=0;
for k=1:samples
if Pdata(k,ExtSyncCol)>=ExtSyncSpikeLev
LengthCounter=LengthCounter+1;
IndexOfSpike(LengthCounter)=k;
check=1;
else
if check==1
Frame=Frame+1;
FrameIndex(Frame)=round(mean(IndexOfSpike));
check=0;
LengthCounter=0;
clear IndexOfSpike
end
end
end
% Calculation of the TimeIndex %
TimeIndex=1;
% for l=1:samples
% if (Pdata(l,LiqFlowCol)==max(Pdata(:,LiqFlowCol)))
% TimeIndex=l;
% break;
% end
% end
gradflow=gradient(Pdata(:,LiqFlowCol));
for l=1:samples
if (gradflow(l)==max(gradflow))
TimeIndex=l;
break;
end
end
clear LengthCounter check i
if Frame==0 % check if there are any images present
137
fprintf('There are no images associated with this
data.\n')
fprintf('Check test.TIF and External Sync Channel in
DAQ\n')
return
end
InitialFrame=1;
ScreenSize=double(imread(ImageLocate,1));
X=0:x:(length(ScreenSize(1,:))-1)*x; % converting pixels to
mm.
Y=0:y:(length(ScreenSize(:,1))-1)*y; % converting pixels to
mm.
clear ScreenSize
scrsz = get(0,'ScreenSize');
%% Analysing each image separately starts here
for pic=1:Frame
Current=InitialFrame+pic-1;
if Current>TotalFrames
break
end
ImageMatrix=double(imread(ImageLocate,Current));
ImageMatrix=ImageMatrix(Noz:ylimit+Noz-1,:);
ImageMatrix=ImageMatrix-background; % Image is weighted
point-by-
ImageMatrix=ImageMatrix./weight; % point using
LaserWeight matrix
% Check for need to process the file
ImageMatrix1=imrotate(ImageMatrix,-degree,'crop');
figure(1)
YZ=ImageMatrix1*64/max(max(ImageMatrix1));
Pdata(FrameIndex(pic),TimeCol);
colormap (mymap);
image(YZ);
% xz=input(`Do you want this image to be
processed?(y/n)(1/anything)');
% if xz~=1
% clear YZ
% close(figure(1))
% end
xz=1;
%% Image Processing starts here
% Converts each image from Intensity Matrix to Density
Matrix
if (xz==1)
clear YZ
close(figure(1))
count1=1;
high=0;
138
for m=1:5:length(ImageMatrix)/2
mat_avg(count1,:)=mean(ImageMatrix(m:m+4,:));
if (count1>1)
if (max(mat_avg(count1,:))>high)
pos=count1;
high=max(mat_avg(count1,:));
end
end
count1=count1+1;
end
top_avg=mat_avg(pos,:);
for m=1:length(top_avg)
if (top_avg(m)==max(top_avg))
loc=m;
end
end
if (max(top_avg)==0)
loc=Origin;
end
left=loc-5;
right=loc+5;
%% Defining reference intensity
RefInt=mean(top_avg(left:right));
imcv=sort(reshape(ImageMatrix,numel(ImageMatrix),1));
%sorts intensities from smallest to largest and reshaping
to 1D array
ima=numel(ImageMatrix)*x*y; %calculates the area of
the image in mm^2
%RefInt=imcv(round(length(imcv)*(1-1/ima))); %
Using Jonas' method of weighting the image - reference
intesity is 99.7% highest value but only 55% of highest
value
% Storing the Temperature, Pressure, Velocity and
Mass Flowrate %
%% Flow Calculations
Time=Pdata(FrameIndex(pic)+TimeIndex,TimeCol);
LiqTemp=mean(Pdata(:,LiqTempCol));
ChmTemp=mean(Pdata(:,ChmTempCol));
ChmPres=mean(Pdata(:,ChmPresCol));
LiqPres=mean(Pdata(:,LiqPresCol));
MassFlow=mean(Pdata(:,LiqFlowCol)); % g/s
RefDen=goodeqn_liq(LiqTemp,ChmPres); % Units
(kg/m^3)
Velocity=(MassFlow/1000)/(RefDen*(pi/4)*JetDia^2);
% Units (m/s)
n2mdot=mean(Pdata(:,GasFlowCol)); % N2 mdot
(g/s)
139
Pch=ChmPres*101325; % Chamber Pressure [Pa]
Tch=ChmTemp+273.15; %Chamber Temperature [K]
rhoinj= Pch/(296.8*Tch); % Injection Density
[kg/m^3]
D=5.03; % Outer diameter of annulus [mm]
d=3.76; % Inner diameter of annulus [mm]
A=(pi/4)*(D^2-d^2); % Area of annulus [mm^2]
Am=A*0.000001; % [m^2]
V=(n2mdot/1000)/(Am*rhoinj); % Nitrogen Injection
velocity [m/s]
Tchr=(ChmTemp+273.15)/441;
Tfkr=(LiqTemp+273.15)/441;
Pchr=ChmPres/18.4;
Pout=rhoinj*V^2;
Pin=RefDen*Velocity^2;
M=Pout/Pin;
Vr=V/Velocity;
ChmTempr=(ChmTemp+273)/441;
ChmPresr=ChmPres/18.4;
LiqTempr=(LiqTemp+273)/441;
%% Calibrating Image Intensity Matrix to Density
Matrix
DensitySlope=RefDen/RefInt; % Calibration number
DensMatrix=ImageMatrix*DensitySlope; % Matrix of
Densities
DensMatrix1=DensMatrix;
for k=1:length(DensMatrix(1,:))
DensMatrix1(:,k)=smooth(DensMatrix(:,k),5);
end % Smoothening the Density Matrix
for k=1:length(DensMatrix(:,1))
DensMatrix1(k,:)=smooth(DensMatrix1(k,:),5);
end
CutOff_low=0; % Setting the cutoffs for the density
CutOff_high=RefDen;
% if (ChmTemp>LiqTemp)
% CutOff_high=RefDen;
% else
% CutOff_high=goodeqn_liq(ChmTemp,ChmPres);
% end
for k=1:length(DensMatrix(1,:))
for j=1:length(DensMatrix(:,1))
if DensMatrix(j,k)<CutOff_low
DensMatrix(j,k)=0;
end
if DensMatrix(j,k)>CutOff_high
DensMatrix(j,k)=CutOff_high;
end
end
140
end
sf=64/max(max(DensMatrix));
clear i j ;
X=X-X(Origin);
Y=Y-Y(Noz);
%% Forming Density Gradient from to Density Matrix
[DX,DY] = gradient(DensMatrix1,x,y);
clear DensMatrix1
GradMatrix=sqrt(DX.^2+DY.^2); % Forming the
Gradient Matrix
clear DX DY
gmcv=sort(reshape(GradMatrix,numel(GradMatrix),1));
gma=numel(GradMatrix)*x*y;
RefGrad=gmcv(round(length(gmcv)*(1-1/gma)));
mingrad=0;
for k=1:length(GradMatrix(1,:))
for j=1:length(GradMatrix(:,1))
if GradMatrix(j,k)<mingrad
GradMatrix(j,k)=0;
end
if GradMatrix(j,k)>RefGrad
GradMatrix(j,k)=RefGrad;
end
end
end
sf2=64/max(max(GradMatrix));
DensMatrix=imrotate(DensMatrix,-degree,'crop');
GradMatrix=imrotate(GradMatrix,-degree,'crop');
trim=Noz+round(tan(degree*pi/180)*(col-Origin));
%% Plotting the image and saving the files
h=figure('Name','Density/Gradient Plot
Window','NumberTitle','off','Position',[2 2 scrsz(3)
scrsz(4)-70]);
image(X(Origin-
xlimit:Origin+xlimit),Y(trim:ylimit),DensMatrix(trim-
Noz+1:end,Origin-xlimit:Origin+xlimit)*sf);
grid off;
% grid minor;
% axis ij
% axis square
axis equal
axis tight
colormap (mymap);
colorbar;
xlabel('Distance (mm.)','Fontsize',16)
ylabel('Distance (mm.)','Fontsize',16)
bet=strcat('T_c_h_,_r = ',num2str(ChmTempr,2),',
T_l_i_q_,_r = ',num2str(LiqTempr,2),', P_c_h_,_r =
141
',num2str(ChmPresr,2),', Velocity Ratio, VR =
',num2str(Vr,'%.1f'),' Momentum flux ratio, M =
',num2str(M,'%.2f'));
title(bet,'Fontsize',16)
k=get(gcf,'Children');
set(k(1),'YLim',[1 64]);
set(k(1),'YTick',1:63/8:64);
set(k(1),'YTicklabel',num2str(roundn((0:63/8:64)'./sf,1)),'
Fontsize',16);
set(k(2),'XTick',-6:2:6,'Fontsize',16);
set(get(k(1),'YLabel'),'String','\rho (kg/m^3)');
set(get(k(1),'YLabel'),'Fontsize',16);
if Current<10
saveloc=strcat(pathname,'ProcessedFiles\',int2str(0),int2st
r(Current),'d.fig');
saveas(h,saveloc)
saveloc=strcat(pathname,'ProcessedFiles\',int2str(0),int2st
r(Current),'d.emf');
saveas(h,saveloc)
eval(['save ' pathname 'ProcessedFiles\'
int2str(0) int2str(Current),'d.mat DensMatrix X Y']);
else
saveloc=strcat(pathname,'ProcessedFiles\',int2str(Current),
'd.fig');
saveas(h,saveloc)
saveloc=strcat(pathname,'ProcessedFiles\',int2str(Current),
'd.emf');
saveas(h,saveloc)
eval(['save ' pathname 'ProcessedFiles\'
int2str(Current),'d.mat DensMatrix X Y']);
end
close(h)
clear DensMatrix
h=figure('Name','Density/Gradient Plot
Window','NumberTitle','off','Position',[2 2 scrsz(3)
scrsz(4)-70]);
image(X(Origin-
xlimit:Origin+xlimit),Y(trim:ylimit),GradMatrix(trim-
Noz+1:end,Origin-xlimit:Origin+xlimit)*sf2);
grid off;
% grid minor;
% axis ij
% axis square
142
axis equal
axis tight
colormap (mymap);
colorbar;
title(bet,'Fontsize',16)
xlabel('Distance (mm.)','Fontsize',16);
ylabel('Distance (mm.)','Fontsize',16);
m=get(gcf,'Children');
set(m(1),'YLim',[1 64]);
set(m(1),'YTick',1:63/8:64);
set(m(1),'YTicklabel',num2str(roundn((0:63/8:64)'./sf2,1)),
'Fontsize',16);
set(m(2),'XTick',-6:2:6,'Fontsize',16);
set(get(m(1),'YLabel'),'String','d\rho/dx(kg/m^4)');
set(get(m(1),'YLabel'),'Fontsize',16);
if Current<10
saveloc=strcat(pathname,'ProcessedFiles\',int2str(0),int2st
r(Current),'g.fig');
saveas(h,saveloc)
saveloc=strcat(pathname,'ProcessedFiles\',int2str(0),int2st
r(Current),'g.emf');
saveas(h,saveloc)
eval(['save ' pathname 'ProcessedFiles\'
int2str(0) int2str(Current),'g.mat GradMatrix']);
else
saveloc=strcat(pathname,'ProcessedFiles\',int2str(Current),
'g.fig');
saveas(h,saveloc)
saveloc=strcat(pathname,'ProcessedFiles\',int2str(Current),
'g.emf');
saveas(h,saveloc)
eval(['save ' pathname 'ProcessedFiles\'
int2str(Current),'g.mat GradMatrix']);
end
if Current<10
fid =
fopen(strcat(pathname,'ProcessedFiles\',int2str(0),int2str(
Current),'t.txt'), 'w');
fprintf(fid, bet);
fclose(fid);
else
143
fid =
fopen(strcat(pathname,'ProcessedFiles\',int2str(Current),'t
.txt'), 'w');
fprintf(fid, bet);
fclose(fid);
end
close(h)
clear GradMatrix
end
end
clear Frame FrameIndex scrsz
144
Jet_Boundary.m %% Jet boundary calculation function
% Prepared by Arnab Roy on 14th June, 2010
% Modified by Shaun DeSouza on 30th Marth, 2016
function [initial,final,imgtemp] =
Jet_boundary_latest(location1,location2,origin,Noz)
%% Creating an Average Laser Sheet Profile
bckgrdlocate=[location2(1:48)
'\Background\background.mat'];
bckgrd=load(bckgrdlocate);
know=imfinfo(location1);
n=length(know);
sum1=0;
for i=1:n
X=double(imread(location1,i));
X1=X;
X1=X1-bckgrd.background;
sum1=sum1+X1;
end
profile=sum1/n;
profile=profile(Noz:end,:);
[row,col]=size(profile);
%% Creating a laser weighting profile considering the top
to bottom variation in intensity
sum2=0;
for i=1:length(profile)
sum2(i)=sum(profile(i,:));
end
weight=sum2/max(sum2);
% plot(weight);
%% Choosing the images of the jet to be averaged and
averaging them
Pdatalocate=[location2(1:49) 'ProcessedData.txt'];
Pdata=load(Pdatalocate);
camcol=Pdata(:,4);
tot=length(camcol);
for i=1:tot
if (camcol(i)>4)
start=i;
break;
end
end
for i=tot:-1:1
if (camcol(i)>4)
finish=i;
break;
end
145
end
Frames=round((finish-start)/1000);
% InitialFrame=round(tot/1000)-Frames+1;
InitialFrame=1;
shuru=InitialFrame; % starting frame number
shesh=Frames; % ending frame number
sum3=0;
for i=shuru:shesh
X=double(imread(location2,i));
X=X-bckgrd.background;
sum3=sum3+X;
end
imgtemp=sum3/(shesh-shuru);
imgtemp=imgtemp(Noz:end,:);
%% Weighing the jet vertically and creating a colored image
for i=1:length(imgtemp)
img(i,:)=imgtemp(i,:)./weight(i);
end
clrimg=(img/max(max(img)))*64;
%% Setting the color of the jet surroundings to white
halfnoz=0; % Half width of nozzle
for i=1:row
for j=1:col
if ((j<(origin-halfnoz)) && (clrimg(i,j)<25)) %20
clrimg(i,j)=0;
end
if ((j>(origin+halfnoz)) && (clrimg(i,j)<20)) %15
clrimg(i,j)=0;
end
end
end
% clrimg(:,1:(origin-50))=0; % Anything 50 pixels away
% clrimg(:,(origin+50):end)=0; % from the origin is set to
white
figure(2);
image(clrimg);
colormap(load([location1(1:48)
'\Laser_Sheet_Profile\mymap.txt']));
%% Storing the boundaries of the jet for each row
initial(1:row)=origin;
final(1:row)=origin;
for i=1:row
for j=1:origin
if ((clrimg(i,j)>0) && (clrimg(i,j+1)>0))
initial(i)=j;
break;
end
end
146
end
for i=1:row
for j=col:-1:origin
if ((clrimg(i,j)>0) && (clrimg(i,j-1)>0))
final(i)=j;
break;
end
end
if ((final(i)==origin) && (i>1))
final(i)=final(i-1);
end
end
hold on;
plot(final,1:length(final),'k.');
plot(initial,1:length(initial),'r.');
147
lmu_jet_angle_UF_REV2.m %% SCRIPT HEADER FOR lmu_jet_angle
% SUPERIOR: none
% INFERIOR: LMU_ROTATEIMAGE_REV2
%
%
% LAST MODIFICATION: 09.01.2015
% AUTHOR: Lukas Muser
% DESCRIPTION: This script determines jet angles in the
near nozzle
% region in shadowgraphic images.
%% Input
close all
clear all
clc
%range in pixel (size of interval in which the angle is
determined)
n=50;
%x/D evaluation start (distance between nozzle exit and
point to start with
%evaluation)
xstart = 3; %in x/D
%nozzle diameter in mm
D=2.032;
%image size calibration in mm/pixel, if available
% im_calib=0.000984183;
%set fontsize
fontsize=14;
%% load image
%get directory of experimental data
% path = uigetdir('D:\','Select folder experimental data');
path = 'Averages\';
%get names of experiments
148
experiment = dir(path);
experiment = setdiff({experiment.name},{'.','..'});
% for pic=1:size(experiment,2)
pic=1;
im=imread([path experiment{pic} '\B00001.tif']);
immean=imadjust(im);
%% binarize and rotate image
%create binary image, delete "holes"
thresholdValue = graythresh(immean);
imbinary = im2bw(immean,thresholdValue);
imbinary(:,end+1) = 0;
[hohe,breite] = size(imbinary);
fillup = zeros (size(imbinary));
fillup(round(hohe/2)-10:round(hohe/2)+10,1:150) = ...
fillup(round(hohe/2)-10:round(hohe/2)+10,1:150) <
1;
fillup = logical (fillup);
intersec = fillup & imbinary;
imbinary = fillup | imbinary;
imbinary = imfill(imbinary,'holes');
imbinary = imbinary < 0.5;
imbinary = imfill(imbinary,'holes');
imbinary = imbinary < 0.5;
imbinary = imbinary - fillup;
imbinary = imbinary | intersec;
%rotate image
[imbinary,immean] =
LMU_ROTATEIMAGE_REV2(imbinary,immean);
% figure
% imshow(imbinary);
%% detect jet boundary
[hohe,breite]=size(imbinary);
%x constraint nozzel exit
figure('name','determine coordinates of nozzel exit,
click on upper AND lower branch');
imshow(immean);
149
[x0 ynozzlerand]=ginput(2);
close
x0=round((x0(1)+x0(2))/2);
% % columns=sum(imbinary(1:1200,:),1);
% % x0=find(columns==min(columns),1,'first');
if exist('im_calib','var') == 0
im_calib = D/abs(ynozzlerand(1)-ynozzlerand(2));
end
%y value middle of nozzle
ynozzle=(ynozzlerand(1)+ynozzlerand(2))/2;
% % %y constraint upper branch
% % y0_up=find(imbinary(1:1200,x0),1,'first');
% %
% % %y constraint lower branch
% % y0_low=find(imbinary(1:1200,x0),1,'last');
% detect jet boundary
bound = bwtraceboundary(imbinary,...
[find(imbinary(:,floor(x0+xstart*D/im_calib)),1,'first')
floor(x0+xstart*D/im_calib)]...
,'S',8,inf,'clockwise');
%detect upper and lower boundary seperately (of bound)
% % x_ind=find(bound(:,2)==x0);
% % bound=bound(1:x_ind(2),:);
xbound_up=[];
ybound_up=[];
xbound_low=[];
ybound_low=[];
for i=1:size(bound,1)
if (bound(i,1)>ynozzle) && (bound(i,1)<hohe) &&
(bound(i,2)>x0+xstart*D/im_calib) && (bound(i,2)<breite)
xbound_low(end+1,1)=bound(i,2);
ybound_low(end+1,1)=bound(i,1);
elseif (bound(i,1)<ynozzle) && (bound(i,1)>1) &&
(bound(i,2)>x0+xstart*D/im_calib) && (bound(i,2)<breite)
xbound_up(end+1,1)=bound(i,2);
ybound_up(end+1,1)=bound(i,1);
end
150
end
%% jet angle with least squares method
%upper branch
Aeq_up=[1 x0];
beq_up=min(ynozzlerand);
gradient2_up=[];
for i=xbound_up(1):n:xbound_up(end)
if (xbound_up(end)-i)/n >= 1 || (xbound_up(end)-
i)/n == 0
%fill Vandermonde-matrix V2_up
xint_up=[];
upy2_sel=[];
for m=1:size(xbound_up,1)
if xbound_up(m) >= i && xbound_up(m) < i+n
xint_up(end+1,1)=xbound_up(m);
upy2_sel(end+1,1)=ybound_up(m);
end
end
V2_up=[ones(size(xint_up,1),1) xint_up];
%solve upper jet angle (gradient2_up)
p2_up = lsqlin(V2_up, upy2_sel, [], [], Aeq_up,
beq_up);
gradient2_up(end+1)=p2_up(2);
end
end
%lower branch
xbound_low=flipud(xbound_low);
ybound_low=flipud(ybound_low);
Aeq_low=[1 x0];
beq_low=max(ynozzlerand);
gradient2_low=[];
for i=xbound_low(1):n:xbound_low(end)
if (xbound_low(end)-i)/n >= 1 || (xbound_low(end)-
i)/n == 0
%fill Vandermonde-matrix V2_low
xint_low=[];
upy2_sel=[];
for m=1:size(xbound_low,1)
if xbound_low(m) >= i && xbound_low(m) <
i+n
xint_low(end+1,1)=xbound_low(m);
upy2_sel(end+1,1)=ybound_low(m);
151
end
end
V2_low=[ones(size(xint_low,1),1) xint_low];
%solve lower jet angle (gradient2_low)
p2_low = lsqlin(V2_low, upy2_sel, [], [],
Aeq_low, beq_low);
gradient2_low(end+1)=p2_low(2);
end
end
%transform angle into deg
gradient2_up=-180/pi*atan(gradient2_up);
gradient2_low=180/pi*atan(gradient2_low);
%calculate total jet angle out of upper and lower angle
if size(gradient2_up,2) == size(gradient2_low,2)
gradient_ges=gradient2_up+gradient2_low;
elseif size(gradient2_up,2) < size(gradient2_low,2)
gradient_ges=gradient2_up(1,:)+gradient2_low(1,1:size(gradi
ent2_up,2));
else
gradient_ges=gradient2_low(1,:)+gradient2_up(1,1:size(gradi
ent2_low,2));
end
%% create plots and save files
%save files and plots into selected folder
% path_save = uigetdir('D:\','Select folder to save
in');
%save adjusted and rotated immean
% imwrite(immean,[path experiment{pic}
'\imadjust.png']);
f1=figure;
imshow(immean);
% saveas(f1,[path_save '\Winkelgemittelt.eps'],'epsc');
f2=figure;
hold on
imshow(imbinary);
% line(bound(:,2),bound(:,1),'color','r');
line(xbound_low,ybound_low,'color','r','linewidth',2);
line(xbound_up,ybound_up,'color','r','linewidth',2);
152
set(gca,'position',[0 0 1 1],'units','normalized');
% saveas(f2,[path experiment{pic}
'\binaryimage.tif'],'tif');
% subplot(3,3,1);
% imshow(immean);
% % Maximize the figure window.
% set(gcf, 'Position', get(0, 'ScreenSize'));
% % Force it to display RIGHT NOW (otherwise it might
not display until it's all done, unless you've stopped at a
breakpoint.)
% drawnow;
%
% % Just for fun, let's get its histogram.
% [pixelCount grayLevels] = imhist(immean);
% subplot(3, 3, 2);
% bar(grayLevels,pixelCount); title('Histogram of
original image');
% xlim([0 grayLevels(end)]); % Scale x axis manually.
%
%
% % Display the binary image.
% subplot(3, 3, 3);
% imagesc(imbinary); colormap(gray(256)); title('Binary
Image, obtained by thresholding');
%
% subplot(3,3,4);
% imshow(imbinary);
% line(bound(:,2),bound(:,1),'color','r');
% hold on
xD_up=xstart+n*size(gradient2_up,2)*im_calib/D;
xD_low=xstart+n*size(gradient2_low,2)*im_calib/D;
xD_end=(breite-x0)*im_calib/D;
figure1=figure;
set(figure1,'defaultTextInterpreter','Latex');
xvec2_up=(xstart+n*im_calib/(2*D):n*im_calib/D:xD_up-
n*im_calib/(2*D));
xvec2_low=(xstart+n*im_calib/(2*D):n*im_calib/D:xD_low-
n*im_calib/(2*D));
xvec_ges=(xstart+n*im_calib/(2*D):n*im_calib/D:min(xD_up,xD
_low)-n*im_calib/(2*D));
153
plot(xvec2_up,gradient2_up,'b.',xvec2_low,gradient2_low,'g.
',xvec_ges,gradient_ges,'r.')
set(gca, 'XTick', 0:2:ceil(xD_end), 'YLim', [0
20],'fontsize',fontsize);
% if max(gradient_ges) <= 85
% set(gca, 'XTick', 0:0.5:xD_end, 'YLim', [0 90]);
% else
% set(gca, 'XTick', 0:0.5:xD_end, 'YLim', [0
max(gradient_ges)+5]);
% end
xlabel('$x/D$');
ylabel('Winkel [$\circ$]');
I=legend('$\alpha_{oben}$','$\alpha_{unten}$','$\alpha_{ges
}$');
set(I,'interpreter','Latex','fontsize',fontsize);
%save jet angle data
result=cell(2,size(gradient_ges,2)+1);
result{1,1}='x-coordinate(x/D)';
result{2,1}='spray angle [deg]';
for q=1:size(gradient_ges,2)
result{1,q+1}=xvec_ges(q);
result{2,q+1}=gradient_ges(q);
end
% save([path experiment{pic} '\result'],'result');
versuch=experiment{pic}(13:26);
resultstruct.(sprintf(['Experiment_' versuch]))=result;
% saveas(figure1,[path_save '\winkel_' versuch
'.eps'],'epsc');
% xlswrite(['jet_angle.xls'],{versuch},'Sheet1',['A'
num2str(pic*2)]);
% xlswrite(['jet_angle.xls'],result,'Sheet1',['B'
num2str(pic*2)]);
close all
% end
% save('result_all','resultstruct');
154
LMU_ROTATEIMAGE_REV2.m function [imbinary,immean] =
LMU_ROTATEIMAGE_REV2(imbinary,immean)
%% FUNCTION HEADER FOR LMU_ROTATIONANGLE
% SUPERIOR: various
% INFERIOR: none
%
%
% LAST MODIFICATION: 19.01.2015
% AUTHOR: Lukas Muser
% DESCRIPTION:
% detects the rotation angle for tilted near nozzle spray
images
% INPUT: imbinary - binary image
% immean - average image
%
% OUTPUT: imbinary - rotated binary image
% immean - rotated average image
%
%
%%
[m,n] = size(imbinary);
imbin = imbinary(ceil(0.1*m):floor(0.8*m),ceil(0.2*n):n-1);
columns = sum(imbin,1);
%detect rotation angle
symLine = [];
ind = [];
for i=1:size(imbin,2)
if columns(1,i) ~= 0
ind(1,end+1) = find(imbin(:,i),1,'first');
symLine(1,end+1) = i;
symLine(2,end) = ind(1,end) + 0.5*columns(1,i);
end
end
V = [ones(size(symLine,2),1) symLine(1,:)'];
gradient = lsqlin(V,symLine(2,:)',[],[]);
angle = 180/pi * atan(gradient(2));
%rotate images
155
immean = imrotate(immean,angle);
imbinary = imrotate(imbinary,angle);
%delete "rotation boundary"
im_size = size(immean);
row_del = (im_size(2) * tan(pi/180 * -angle) - im_size(1) *
tan(pi/180 * -angle)^2) / (1 - tan(pi/180 * -angle)^2);
col_del = (im_size(1) - row_del) * tan(pi/180 * -angle);
immean(1:ceil(row_del)+1,:) = [];
immean(end-ceil(row_del):end,:) = [];
immean(:,1:ceil(col_del)+1) = [];
immean(:,end-ceil(col_del):end) = [];
imbinary(1:ceil(row_del)+1,:) = [];
imbinary(end-ceil(row_del):end,:) = [];
imbinary(:,1:ceil(col_del)+1) = [];
imbinary(:,end-ceil(col_del):end) = [];
end
156
Run_Background.m
clear all
[filename, pathname] = uigetfile('*.*','Find background
image','C:\Shaun\Tests\');
location=[pathname filename];
if filename==0
fprintf('No file was selected!\n')
return
end
X=double(imread(location,1));
vert=length(X(:,1))
horz=length(X(1,:))
sum=zeros(vert,horz);
know=imfinfo(location);
nimg=length(know);
total=0;
for k=1:nimg
X = double(imread(location,k));
sum=sum+X;
total=total+1;
end
background=sum/total;
figure(1);
image(background*64/max(max(background)));
doit=input('Would you like to save this image y/n?','s');
if doit=='y'
eval(['save ' pathname(1:end) '\background.mat
background']);
else
fprintf('This was not saved.\n');
end
157
Run_Preview_Coaxial.m % Shaun DeSouza
% 03/11/16
%
% Shows graphs of sensory data to check that experiental
conditions
% have been hit
% Saves data in proceessed and meaningful form to
'ProcessedData.txt'
% This program must be run before full processing can be
done
% Folders must be organized prior to running this program
% 1 time [s]
% 2 liquid temperature [C]
% 3 chamber temperature [C]
% 4 ext sync [V]
% 5 chamber pressure [atm]
% 6 liquid pressure [atm]
% 7 gas pressure [atm]
% 8 flow liquid [V]
% 9 gas flow [V]
%% Importing Data File
clear all
[filename, pathname] = uigetfile('*.*','Find run to
process','D:\Shaun\Tests\Data_03_24_16');
location=[pathname filename];
fid = fopen(location);
data = fscanf(fid,'%f %f %f %f %f %f %f %f %f',[9 inf]); %
It has nine rows now.
data = data'; % transpose to 9 columns
fclose(fid); % close the file, all relavant data has been
stored
%% Data Timing
samples=length(data); % total number of samples
time=data(:,1); % first column of data represents time
in steps
step=time(2); % this position is first step from
time(1)=0
fs=1/step; % sample rate
%% Processing Liquid Flow Data
[num1,den1]=butter(6,0.1);
f_data=filter(num1,den1,data(:,8));
158
NofB=20; % number of blocks that will be fit in total
time
delta=step*floor((samples-1)/NofB); % length in time of
block
chunk=floor((samples-1)/NofB); % indexed size of
block
for i=1:NofB
Block(:,i)=data(chunk*(i-1)+2:chunk*i+1,8);
BlockTime(i)=delta*(i-1/2); % at center of
block
end
for i=1:NofB
[Pxx,f] = pwelch(Block(:,i),[],[],[],fs);
[val,ind]=max(Pxx);
domfreq(i)=floor(f(ind));
end
% liqflow=6.545151*(0.0054*domfreq+0.2483); %[cm^3/s]
% liqflow2=6.545151*(0.0069*domfreq+0.0087); %[cm^3/s]
% liqflow3=6.545151*(0.0842*domfreq+2.1921); %[cm^3/s]
% liqflow4=0.0808*domfreq+1.5095; %[cm^3/s]
% liqflow5=0.081*domfreq+1.2899;
% liqflow=(1.6251609933+0.0353438154*domfreq); %Labview
% liqflow=0.0082*domfreq+1.1009; %[cc/s] calibration data
with zero 4/11/16
liqflow=0.0057*domfreq+1.2794; %[cc/s] calibration data
4/11/16
for q=1:NofB
data(chunk*(q-1)+1:chunk*q,8)=liqflow(q);
end
data(chunk*q:end,8)=liqflow(q); % save processed liquid
flow data to file
%% Processing Temperature Data
Fc = fs/200; % carrier frequency
F = Fc/fs; % change F to vary the filter's cutoff
frequency.
[num,den] = butter(6,F); % design butterworth filter.
scrsz = get(0,'ScreenSize');
h=figure('Name','Sensor output
plots','NumberTitle','off','Position',[2 2 scrsz(3)
scrsz(4)-70]);
%Filter Liquid Temperature
spot1=filter(num,den,data(:,2)); % temporary variable to
filter data
data(:,2)=spot1; % save processed liquid temperature to
data file [C]
159
%Filter Chamber Temperature
spot2=filter(num,den,data(:,3));
data(:,3)=spot2; % save processed chamber temperature to
data file [C]
%Plot Temperature Data
subplot(2,2,1);plot(time,spot1)
hold on % all temperature's appear on same plot
plot(time,spot2,'r')
title('Temperature Readings')
xlabel('Time (s)')
ylabel('Temperature ({\circ} C)')
legend('Liquid','Chamber top',1)
%% Process Pressure Data
%Filter Pressure Data
[num2,den2]=butter(6,F);
f_data_1=filter(num2,den2,data(:,5)); % Chamber Pressure
f_data_2=filter(num2,den2,data(:,6)); % Liquid Pressure
f_data_3=filter(num2,den2,data(:,7)); % Gas Pressure
data(:,5)=f_data_1; % save processed pressures to data file
data(:,6)=f_data_2;
data(:,7)=f_data_3;
%% Plotting Pressure Data
subplot(2,2,2);plot(time,data(:,5),'r')
hold on % All pressures appear on the same plot
plot(time,data(:,6),'b')
plot(time,data(:,7),'g')
title('Pressure Readings')
xlabel('Time (s)')
ylabel('Pressure (atm)')
tempmax=max(data(:,6)); % following finds max pressure
so to scale axis START
if max(data(:,5))>tempmax
tempmax=max(data(:,5));
end
ymax=1.1*tempmax; % max found so axis is pretty END
axis([0 1 0 ymax])
axis 'auto x'
legend('Chamber','Liquid',1)
%% Processing Gas Data
g_data=filter(num2,den2,data(:,9));
% Standard Calibration Flow Rate
160
Qcal=g_data*10; % [V]*[SCFM/V]= [SCFM]
% Experimental Conditions
Texp=290; %[K] Temperature through mass flow meter
Pexp=data(:,7)*101325; %Replace with gas line pressure [Pa]
MWexp=28; %Molecular weight of Nitrogen
% Calibration Conditions
MWcal=28.97; %%[kg/kmole]
Pcal=689476; % [Pa]
Tcal=294; %[K]
% Standard Conditions
Tstd=273; %[K]
Pstd=101325; %[Pa]
% Group Correction Factors
A=Pstd/Tstd;
B=Tcal./Pexp;
C=Texp/Pcal;
D=MWcal/MWexp;
E=sqrt((C*D).*B);
F=A*E;
% Actual Experimental Conditions
Qact=Qcal.*F; % [ACFM]
% Conversion to mass flow rate [g/s]
Qsi=Qact.*0.0283168; % conversion to m^3/min
Qs=Qsi./60; % Conversion to m^3/s
Qcs=Qs*1000000; % [cm^3/s]
rho=Pexp./(296.8*Texp);%[kg/m^3] % density of nitrogen
through flow meter
mn2=Qs.*rho; % [kg/s] mass flow rate of nitrogen
n2=mn2.*1000; % [g/s]
data(:,9)=mean(n2); % save processed gas flow to data file
%% Gas Velocity Calculations
Pch=data(:,5)*101325; % chamber pressure [Pa]
Tch=data(:,3)+273.15; %chamber temperature [K]
rhoinj= Pch./(296.8.*Tch); % injection density [kg/m^3]
D=5.03; % outer diameter of annulus [mm]
d=3.76; % inner diameter of annulus [mm]
A=(pi/4)*(D^2-d^2); % area of annulus [mm^2]
Am=A*0.000001; % [m^2]
V=mn2./(Am.*rhoinj); % nitrogen injection velocity [m/s]
%% Liquid Velocity Calculations
161
di=2.235; % injector diameter [mm]
dm=di/1000; % injector diameter [m]
Ai=(pi/4)*(dm^2); % injector area [m^2]
LiqTemp=mean(data(:,2)); % liquid temp [C]
ChmPres=mean(data(10000:end,5)); % chamber pressure [atm]
MassFlow=1.64.*liqflow; % [g/s]
data(:,8)=mean(MassFlow); % [g/s] save processed liquid
flow rate to data file
LiqDen=goodeqn_liq(LiqTemp,ChmPres); % [kg/m^3]
U=(MassFlow/1000)/(LiqDen*Ai); % [m/s]
%% Momentum Flux and Velcity Ratios
Pout=mean(rhoinj)*(mean(V))^2; % outer jet momentum
Pin=mean(LiqDen)*(mean(U))^2; % inner jet momentum
M=Pout/Pin; % momentum flux ratio
Vr= mean(V)/mean(U); % velocity Ratio
%% Group Experimental Conditions
Vm=mean(V); %nitrogen velocity m/s
Um=mean(U); %fk velocity m/s
n2mdot=mean(mn2); %nitrogen flowrate g/s
fkmdot=mean(MassFlow); %fk flow rate g/s
Pchm=mean(f_data_1); %chamber pressure atm
Tchm=mean(spot2); %chamber temperature C
n2den=mean(rhoinj);
exp_cond=[M Vm Um LiqDen n2den LiqTemp Tchm Pchm fkmdot
n2mdot];
%% Plotting Liquid and Gas Data
subplot(2,2,3);plot(BlockTime,liqflow);hold
on;plot(BlockTime,liqflow,'r.');hold off;%spot)
hold on
plot(time, Qcs);
title('Flow Meter Data')
xlabel('Time (s)')
ylabel('Flow (cc/s)')
plot(time, data(:,9));
legend('Gas','Liquid',1);
ymax=1.1*max(Qcs);
axis([0 1 0 ymax])
axis 'auto x'
%% Plotting Camera Sync Data
subplot(2,2,4);plot(time,data(:,4),'g')
title('Camera Sync output') % Camera Sync Output is
connected to the Not Scan output of the ST-133 (Ch 1
labeled).
162
xlabel('Time (s)')
ylabel('Voltage (V)')
%% Saving Data and Plots
hgsave([pathname 'PDI_' filename(9:end) '.fig']);
newloc=[pathname 'ProcessedData.txt'];
eval(['save ' newloc ' data -ascii -tabs']);
163
Shadowgraphy_Processing.m
%% Shadowography image processing
%% Call test image
test = 'exp_2.tif';
info = imfinfo(test);
frames = numel(info);
test_img=[];
for k = 1:frames
t_img = imread(test, k, 'Info', info);
t_img = im2double(t_img);
test_img(:,:,k)=t_img;
end
%% Call background image
bckgrnd='background_1.tif';
know=imfinfo(bckgrnd);
n=length(know);
X=zeros(size(test_img(:,:,1)));
for i=1:n
X=X+im2double(imread(bckgrnd,i));
end
bckgrnd_avg=X/n; % average background image
%% Image adjustmest
for j = 1:frames
a_img=bckgrnd_avg-test_img(:,:,j); % background
subtraction
a_img(a_img<0)=0; % adjusted image
adj_img(:,:,j)=a_img;
end
imshow(imadjust(adj_img(:,:,10)))
sum =zeros(size(adj_img(:,:,1)));
for i = 1:size(adj_img,3)
sum = sum + adj_img(:,:,i);
end
adj_av = sum / size(adj_img,3); % averaged image
164
Shadowgraph_Sensor_Data_Processing.m
clear all;
close all;
%% Delaration of variables
DataCols=7;
CamHz=1000;
x=0.0474; % mm per one pixel
y=0.0484; % mm per one pixel
%x=0.04;
%y=0.04;
maximumden=1700; %
JetDia=0.2032 ; % in cm
Noz=1; % Row Number of Nozzle
TimeCol=1; % Col stands for column, in
ProcessedData.txt
LiqTempCol=2; %
ChmTempCol=3; %
ExtSyncCol=4; %
ChmPresCol=5; %
LiqPresCol=6; %
LiqFlowCol=7; %
ExtSyncSpikeLev=4; %
%% Loading the files to process
pathname='D:\Shaun\Tests\Data_06_25_14';
count=0;
while true
[filename, pathname] = uigetfile('*.*','Pick
ProcessedData.txt file for data run to Process',pathname);
if filename==0
if count==0
return
end
break
end
count=count+1;
paths(count,:)=cellstr(pathname);
files(count,:)=cellstr(filename);
end
%clear pathname filename
fprintf('These are the %d file locations you have
chosen:\n',count)
Locations=strcat(deblank(char(paths)),deblank(char(files)))
fprintf('If this is in error press ''Ctrl+c'' to cancel');
165
clear Locations
for i=1:count
pathname=deblank(char(paths(i)));
filename=deblank(char(files(i)));
location=[pathname filename];
Pdata=load(location);
TotalFrames=round(length(Pdata)/1100);
%TotalFrames=100
samples=length(Pdata); % Total
number of samples
step=Pdata(2,TimeCol); % This position is first step
from time(1)=0
% Finding the index of each image wrt
'ProcessedData.txt'
Frame=0;
LengthCounter=0;
check=0;
count=0;
for i=1:samples
if Pdata(i,ExtSyncCol)>=ExtSyncSpikeLev
count=count+1;
LiqTemp(count)=Pdata(i,LiqTempCol);
ChmTemp(count)=Pdata(i,ChmTempCol);
ChmPres(count)=Pdata(i,ChmPresCol);
LiqPres(count)=Pdata(i,LiqPresCol);
MassFlow(count)=1.64*Pdata(i,LiqFlowCol); %
Units (g/s)
RefDen(count)=goodeqn_liq(LiqTemp(count),ChmPres(count));
% Units (kg/m^3)
velocity(count)=10*MassFlow(count)/(RefDen(count)*(pi/4)*Je
tDia^2);
LengthCounter=LengthCounter+1;
IndexOfSpike(LengthCounter)=i;
else
if check==1
Frame=Frame+1;
FrameIndex(Frame)=round(mean(IndexOfSpike));
check=0;
LengthCounter=0;
clear IndexOfSpike
end
end
166
end
end
%% Average conditions during experiment
LiqTempavg=mean(LiqTemp)
ChmTempavg=mean(ChmTemp)
ChmPresavg=mean(ChmPres)
LiqPresavg=mean(LiqPres)
MassFlowavg=mean(MassFlow)
RefDenavg=mean(RefDen)
velocityavg=mean(velocity)
167
Spreading_Angle.m
function angle_std=Spreading_Angle(location,count,origin)
sprangle(1:count,1:2)=0;
totspread(1:count)=0;
thres(1:count)=0;
%% Calculating the threshold density for jet boundary using
peak density
%% gradients
for k=1:count
current=char(location(k,:));
colormap(load([current(1:49)
'Laser_Sheet_Profile\mymap.txt']));
img=load(current);
clrimg=round(64*img.DensMatrix/max(max(img.DensMatrix)));
if (k==1)
image(clrimg);
inp=input('Do you want to input threshold value
manually? (y/n)','s'); inp='n';
if (inp=='n')
ans1=input('Supercritical Test? (y/n)','s');
ans1='y';
ans2=input('Single Species? (y/n)','s');
ans2='n';
if (ans2=='n')
lower=10;
upper=30;
end
if (ans1=='y') && (ans2=='y')
lower=35;
upper=45;
end
if (ans1=='n') && (ans2=='y')
lower=20;
upper=35;
end
else
lower=input('Enter lower threshold value for
jet boundary:');
upper=input('Enter upper threshold value for
jet boundary:');
end
disp(strcat('Lower threshold=',num2str(lower)));
disp(strcat('Upper threshold=',num2str(upper)));
close all;
end
grad=abs(gradient(img.DensMatrix(50,:)));
[peak,locs]=findpeaks(grad);
168
nozwidth=40;
for l=1:length(locs)
if (locs(l)>(origin-nozwidth)) &&
(locs(l)<(origin+nozwidth))
if ((clrimg(50,locs(l))>lower) &&
(clrimg(50,locs(l))<upper))
thres(k)=clrimg(50,locs(l));
break;
end
end
end
end
%% Forcing a non-zero threshold condition
cnt=1;
for i=1:count
if (thres(i)~=0)
thresh(cnt)=thres(i);
cnt=cnt+1;
end
end
threshold=min(thresh);
%% Calculating the jet spreading angle
for k=1:count
current=char(location(k,:));
img=load(current);
clrimg=round(64*img.DensMatrix/max(max(img.DensMatrix)));
%% Setting the color of the jet surroundings to white
row=length(clrimg);
col=size(clrimg,2);
for i=1:row
for j=1:col
if clrimg(i,j)<threshold
clrimg(i,j)=0;
end
end
end
clrimg(:,1:(origin-100))=0;
clrimg(:,(origin+100):end)=0; % Anything 70 pixels away
from the origin is set to white
figure(1);
image(clrimg);
hold on;
plot(clrimg(50,:));
plot(grad,'k');
colormap(load([current(1:49)
'Laser_Sheet_Profile\mymap.txt']));
[alph1,alph2]=Divergence_Angle(clrimg,origin,row);
169
sprangle(k,1)=(alph1)*180/pi;
sprangle(k,2)=(alph2)*180/pi;
totspread(k)=abs(sprangle(k,2)-sprangle(k,1));
end
cnt=1;
for i=1:count
if (abs(totspread(i)-mean(totspread))<std(totspread))
angle_final(cnt)=totspread(i);
cnt=cnt+1;
end
end
figure(100)
clf
plot(totspread,'o-');
hold on;
avg_spr(1:count)=mean(totspread);
plot((1:count),avg_spr,'g',(1:count),avg_spr-
std(totspread),'r-.',(1:count),avg_spr+std(totspread),'r-
x');
avg_final=mean(angle_final);
plot(avg_final*ones(1,cnt),'k');
xlabel('No. of images considered','Fontsize',14);
ylabel('Spreading Angle','Fontsize',14);
legend('All angles','Mean spreading angle','Lower standard
deviation','Upper standard deviation','Modified mean');
disp(strcat('Average spreading angle is:
',num2str(avg_final),' degrees'));
disp(strcat('Standard deviation is:
',num2str(std(angle_final)),' degrees'));
angle_std=[avg_final std(angle_final)];
170
Test_Conditions.m
%% This program prints the test conditions to the logbook
close all
clear all
%% Initialize variables
JetDia=2.235; % mm
LiqTempCol=2;
ChmTempCol=3;
ExtSyncCol=4;
ChmPresCol=5;
LiqPresCol=6;
GasPresCol=7;
LiqFlowCol=8;
GasFlowCol=9;
pathname='D:\Shaun\Tests\';
count=0;
while true
[filename, pathname] = uigetfile('*.fig','Pick PDI file
to Process',pathname);
if filename==0
if count==0
return
end
break
end
count=count+1;
paths(count,:)=cellstr(pathname);
files(count,:)=cellstr(filename);
end
fprintf('These are the %d file locations you have
chosen:\n',count)
Locations=strcat(deblank(char(paths)),deblank(char(files)))
fprintf('If this is in error press ''Ctrl+c'' to cancel');
clear Locations
%% Flow meter correction
flowmeter=input('Does flowmeter work for this
case(s)?(y/n)','s');
for i=1:count
pathname=deblank(char(paths(i)));
filename=deblank(char(files(i)));
location=[pathname 'ProcessedData.txt'];
Pdata=load(location);
samples=length(Pdata);
TimeIndex=1;
if (flowmeter=='y')
gradflow=gradient(Pdata(:,LiqFlowCol));
171
for l=1:samples
if (gradflow(l)==max(gradflow))
TimeIndex=l;
break;
end
end
else
gradtemp=gradient(Pdata(5000:end-5000,LiqTempCol));
for k=5000:samples-5000
if (gradtemp(k-5000+1)==max(gradtemp))
TimeIndex=k;
break;
end
end
end
LiqTemp(i)=mean(Pdata(TimeIndex:end,LiqTempCol));
LiqPres(i)=mean(Pdata(TimeIndex:end,LiqPresCol));
ChmTemp(i)=mean(Pdata(TimeIndex:end,ChmTempCol));
ChmPres(i)=mean(Pdata(TimeIndex:end,ChmPresCol));
MassFlow(i)=mean(Pdata(TimeIndex:end,LiqFlowCol));
mn2(i)=mean(Pdata(TimeIndex:end,GasFlowCol));
RefDen=goodeqn_liq(LiqTemp(i),ChmPres(i));
end
%% Flow Calculations
LiqTemp=mean(LiqTemp); % [C]
LiqPres=mean(LiqPres); % [atm]
ChmTemp=mean(ChmTemp); % [C]
MassFlow=mean(MassFlow); % [g/s]
mn2=mean(mn2); % [g/s]
RefDen=mean(RefDen); % [kg/m^3]
dm=JetDia/1000; % [m]
U=(MassFlow/1000)/(RefDen*(pi/4)*dm^2); % [m/s]
Pch=ChmPres*101325; % chamber pressure [Pa]
Tch=ChmTemp+273.15; %chamber temperature [K]
rhoinj= Pch/(296.8*Tch); % injection density [kg/m^3]
D=5.03; % outer diameter of annulus [mm]
d=3.76; % inner diameter of annulus [mm]
A=(pi/4)*(D^2-d^2); % area of annulus [mm^2]
Am=A*0.000001; % [m^2]
V=(mn2/1000)/(Am*mean(rhoinj)); % nitrogen injection
velocity [m/s]
Pout=mean(rhoinj)*(mean(V))^2; % outer jet momentum
Pin=mean(RefDen)*(U)^2; % inner jet momentum
M=Pout/Pin; % momentum flux ratio
TestMatrix=[M V U RefDen rhoinj LiqTemp ChmTemp ChmPres
MassFlow mn2];
xlswrite('D:\Shaun\Tests\Coaxial_PLIF_Logbook.xlsx',TestMat
rix,'F33:O33');
172
APPENDIX D LABVIEW CODE FOR EXPERIMENTAL CONTROL
The LabVIEW code used to facilitate the control of experiments and
recording of sensor data is included in this section. The overall architecture of the
wiring and block diagrams are mostly unchanged from the description and details
reported by Polikov [73]. The only changes made to the code is the range of
channels being recorded to the experimental data file. The gas pressure and
temperature as well as the gas flowmeter data are now set to record to the data
file. This allows calculation of the gas velocity as well as the outer-to-inner
velocity ratio, and momentum flux ratio. Images of the block diagram and wiring
diagram follow.
173
Figure D-1. LabVIEW wiring diagrams for the control of the gas valves and the temperature and pressure monitoring charts.
174
Figure D-2. LabVIEW wiring diagram for the gas flow data, shutdown of valves at the end of experiment, and control of the gas heater.
180
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187
BIOGRAPHICAL SKETCH
Shaun DeSouza was born in Port of Spain, Trinidad and Tobago and grew up
Wesley Chapel, Florida where he completed high school in 2006. He attended the
University of South Florida and earned a Bachelor of Science in Mechanical
Engineering with a minor in Physics in 2011. He began his graduate work in Aerospace
Engineering at the University of Florida in 2012 and joined the Combustion and
Propulsion Laboratory in 2013 under the advisement of Professor Corin Segal. He
received his Ph.D. from the University of Florida in Fall 2016.
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