Simultaneous Acquisition of Pressure, Temperature, and Velocity

SIMULTANEOUS ACQUISITION OF PRESSURE, TEMPERATURE, AND VELOCITY
USING COHERENT ANTI-STOKES RAMAN SCATTERING
BY
JOEL PAUL KUEHNER
B.S., The Pennsylvania State University, 1997
THESIS
Submitted in partial fulfillment of the requirements
for the degree of Master of Science in Mechanical Engineering
in the Graduate College of the
University of Illinois at Urbana-Champaign, 2000
Urbana, Illinois
© Copyright by Joel Paul Kuehner, 2000
iii
ABSTRACT
Attempts were made to obtain simultaneous pressure, temperature, and velocity
measurements in an underexpanded jet flowfield by employing the N2 coherent anti-Stokes
Raman scattering (CARS) technique. Construction of a new phase-matching scheme, including
counter-propagating pump beams, was performed. Counter-propagating pump beams provide a
Doppler shift in the resolved CARS spectrum that is proportional to the average molecular
velocity in the plane of laser propagation. Temperature and pressure are acquired by interpreting
the temperature- and pressure-sensitive features of the CARS spectrum.
The technique was verified with the detection of a weak vibrational CARS signal. The
low signal levels obtained prompted modifications to the CARS method.
centered on probing pure rotational transitions of diatomic nitrogen.
These changes
Both broadband and
narrowband pure rotational CARS techniques were attempted. Unfortunately, a CARS signal
was not detected for either case after the modifications were made. An in-depth investigation of
the changes revealed unforeseen complications that were added to the system during
modification. Solutions to these new problems could not be practically obtained at the present
time.
A numerical experiment was performed to investigate the theoretical sensitivity of the
technique to a change in velocity. The study investigated the theory governing the process of
pure rotational CARS, providing insight on the effects of the Doppler shift on the CARS
spectrum. Results of the study showed that the CARS technique is most applicable in supersonic
and hypersonic flow fields.
iv
To those who have seen beyond hardship
to the peace that exists in transcendence.
v
ACKNOWLEDGEMENTS
A network of support existed long before this work even began and continued to grow
until its completion. The following is an attempt to recognize all those who have contributed to
my success. I say attempt, because an expression of gratitude equal to the support provided
would be infinite in length.
I would like to thank my advisors, Dr. J. Craig Dutton and Dr. Robert P. Lucht. Their
support and advice throughout the past few years has been priceless. I have also appreciated the
ability to pursue this work by my own methods. In the same light, I extend my gratitude to all
the teachers in my life. In addition, I thank the U.S. Army Research Office, especially the
contract monitor, Dr. Thomas L. Doligalski, for funding this research under Grant No. DAAG5597-1-0194
During the completion of this thesis, I had the pleasure of working with some talented
individuals.
The M&IE Department machine shop has provided many works of art from
particularly crude designs on my part. Without their help, countless hours would have been
wasted while I “improvised.” My thanks go out to Bob Nichols and John Frizzell for the help
they provided on numerous projects. In addition, I must acknowledge the perseverance of all the
storeroom personnel I have interacted with who have always been able to supply the “thing that
kind of looks like this” right when I needed it. I also thank Doug for always having the coffee
ready, I never would make it through the day without it.
This list would certainly be incomplete if I did not mention the members of the Laser
Diagnostics Group and the Gas Dynamics Group. I would like to acknowledge Tom Reichardt,
Josh Styron, Fred Schauer, Terry Meyer, Mike Olsen, Bob Foglesong, and Tim Frazier for
answering the myriad questions I provided. I extend my thanks to Mark “Woody” Woodmansee
for not only his help with the technical questions, but especially for his advice and friendship
vi
throughout the years we worked together. Respect and gratitude go out to Ken Smith for his
advice and concern during some of the more complicated situations I encountered.
For
introducing me to Murphy’s Pub and the random visits to the lab to make sure I had not gone
crazy, I thank Sean Kearney, even though he really likes basketball. Also, I thank Glen Martin
for his help with numerous improvisations. Finally, I must thank Will “The Thrill” Mathews,
Chris Bourdon, and Brad Boswell for not only the “mad-cap hijinx,” but also because the only
reason they probably even opened my thesis was to see if they were in here. Seriously though,
their day-in and day-out assistance with just about everything is greatly appreciated.
My love and gratitude goes out to my family, the first and greatest teachers in my life.
The love, support, and guidance of my parents, Paul and Eileen Kuehner, have been without
bound throughout my life and are without compare. I can only hope that they understand my
appreciation for everything they have done for me, as I am unable to truly express it in words. In
the same breath, I must thank the greatest sister in the whole world, Bethie. I owe my strength
and determination to her, as she is the most perfect role model any brother could ever have.
Perhaps most importantly, I must extend my gratitude to my grandfather. It took me years to
realize all that I had learned during the times we spent together in his basement shoveling coal
and learning how to replace the handle on a hammer.
To save the best for last, I wish to acknowledge my fiancée, Elizabeth Denton. Her love
and support have been beyond what I could have ever hoped for. I thank her for the help she has
provided when none was asked for, the times she took care of me when I had forgotten to,
listening to me complain when she did not have to, and showing me the way when I was utterly
lost. Most importantly, I thank her for all she has taught me and for the ways she has opened my
mind.
vii
TABLE OF CONTENTS
Page
NOMENCLATURE......................................................................................................................ix
1
2
3
4
INTRODUCTION..............................................................................................................1
1.1
Objectives................................................................................................................4
1.2
Outline .....................................................................................................................5
LITERATURE SURVEY..................................................................................................6
2.1
Coherent Anti-Stokes Raman Scattering.............................................................6
2.2
Temperature and Pressure Measurement ...........................................................7
2.3
Velocity Measurement and Velocimetry Techniques .........................................8
2.4
Fabry-Perot Etalon ..............................................................................................12
2.5
Underexpanded Jet..............................................................................................12
2.6
Sensitivity Study ...................................................................................................14
2.7
Summary of the Literature Survey ....................................................................15
EQUIPMENT AND FACILITIES .................................................................................16
3.1
Vibrational CARS Setup .....................................................................................16
3.2
Broadband Pure Rotational CARS Setup .........................................................17
3.3
Narrowband Pure Rotational CARS Setup.......................................................18
3.4
Underexpanded Jet Facility ................................................................................19
3.5
Summary of Equipment Setups ..........................................................................19
EXPERIMENTAL RESULTS........................................................................................21
4.1
Vibrational CARS ................................................................................................21
4.2
Broadband Pure Rotational CARS ....................................................................22
4.3
Narrowband Pure Rotational CARS..................................................................24
viii
4.4
5
6
Summary of Experimental Results.....................................................................25
SENSITIVITY STUDY ...................................................................................................26
5.1
Theory ...................................................................................................................26
5.2
Results ...................................................................................................................29
5.3
Summary of the Sensitivity Study ......................................................................30
CONCLUSIONS AND RECOMMENDATIONS.........................................................32
6.1
Experimental Findings ........................................................................................32
6.2
Numerical Findings..............................................................................................32
6.3
Recommendations ................................................................................................33
6.3.1
Recommendations for the Current System ...........................................33
6.3.2
Recommendations for the Sensitivity Study ..........................................33
6.3.3
Recommendations for a New CARS System.........................................34
TABLES........................................................................................................................................35
FIGURES......................................................................................................................................37
REFERENCES.............................................................................................................................53
ix
NOMENCALTURE
English Symbols
F
finesse
ƒ
focal length (mm)
h
enthalpy (J/kg)
I
intensity (W/cm2)
J
rotational quantum number
K
line strength
r
k
wave vector (cm-1)
l
probe volume length (m)
V
velocity (m/s)
v
vibrational quantum number
Greek Symbols
α
crossing angle
Γ
linewidth of transition (cm-1)
∆
change in quantity
λ
wavelength (nm)
ν
frequency (cm-1)
χ
susceptibility; chi-squared value
ω
circular frequency (rad/s)
Symbols
a'
scattered value of variable a
a′
real part of variable a
a ′′
imaginary part of variable a
x
Subscripts
b
backward-propagating spectrum
CARS
CARS signal beam (also denoted by subscript 3)
center
center of distribution
f
forward-propagating spectrum
j
transition j
M
molecule-specific value
nr
nonresonant
o
initial or stagnation value
t
transition
1
pump beam
1b
backward-propagating pump beam
1f
forward-propagating pump beam
2
probe or Stokes beam
3
CARS signal beam (also denoted by subscript CARS)
Physical Constants
c
speed of light in a vacuum = 2.998 x 108 m/s
εo
permittivity of free space = 8.85 x 10-12 Farad/m
Common Abbreviations
BDL
broadband dye laser
CARS
coherent anti-Stokes Raman scattering
CCD
charge-coupled device
CSRS
coherent Stokes Raman scattering
DFWM
degenerate four-wave mixing
xi
FRS
filtered Rayleigh scattering
FSR
free spectral range
FWHM
full width at half maximum
IRS
inverse Raman scattering
LDV
laser Doppler velocimetry
LIF
laser-induced fluorescence
MTV
molecular tagging velocimetry
NDL
narrowband dye laser
Nd:YAG
neodymium-yttrium-aluminum-garnet laser
PHANTOMM
photo-activated non-intrusive tracking of molecular motion
PIV
particle image velocimetry
PMT
photomultiplier tube
PTDS
photothermal deflection spectroscopy
RELIEF
Raman excitation plus laser-induced electronic fluorescence
SRGS
stimulated Raman gain spectroscopy
1
1
INTRODUCTION
It is well known that the measurement of a physical property often results in a
perturbation of the property itself. This effect is readily apparent when making measurements in
high-speed flows, as intrusive probes cause disturbances in the flow field. Therefore, it is
desirable to develop non-intrusive measurement techniques that will provide accurate data. One
such technique is coherent anti-Stokes Raman scattering (CARS).
This optical diagnostic
method utilizes a nonlinear four-wave mixing process to provide pressure, temperature, density,
concentration, and velocity data in areas where physical probes will not only interfere with the
measurement but also have a chance of breaking. CARS has been developed for many species
including diatomic hydrogen, diatomic oxygen, diatomic nitrogen, carbon dioxide, nitric oxide,
and water vapor, as well as certain hydrocarbons such as methane, ethane, and propane. CARS
can even be employed to measure several properties simultaneously.
Since the mid-1970s, CARS has been used to investigate numerous combustion
phenomena. The determination of pressure, temperature, density, and concentration has been
demonstrated. Pressure effects can readily be seen in the CARS spectrum. As the pressure
increases, the vibrational and rotational transitions are collisionally broadened, and if close
enough in frequency, will experience collisional narrowing. Since the number of photons from a
transition is directly proportional to the population in the ground state, temperature can be
obtained from the knowledge of Boltzmann statistics. With pressure and temperature known,
density can be acquired either through an equation of state or by use of the ground-level
population data. Concentration can be determined from the absolute signal level of a transition
or from the shape of the spectrum itself.
In the 1980s, CARS was extended to non-reacting flows to provide a new means of
thermodynamic property measurement.
While techniques such as laser Doppler velocimetry
2
(LDV) and particle image velocimetry (PIV) are well established for measuring velocity, they
lack the ability to simultaneously measure velocity with any other property. Also, these methods
require particle seeding which makes them partially intrusive techniques. Thus, the velocity of
the seed particle, rather than that of the fluid, is measured. These seed particles have limited
flow-tracking ability, and are unable to accurately represent all flow fields, especially those with
high fluid accelerations. Some examples of this limitation are in the center of vortices, boundary
layers, compressible shear layers, high-speed base flows, and shock and expansion waves. These
are important regions of the flow field, and new measurement techniques that do not require
particle seeding should be pursued.
During the 1980s, other optical-based techniques, including laser-induced fluorescence
(LIF), spontaneous Raman scattering, inverse Raman scattering (IRS), stimulated Raman gain
spectroscopy (SRGS), and degenerate four-wave mixing (DFWM), have been used to measure
velocity. For all of these methods, velocity is determined from the Doppler shift of the signal
frequency as compared to a reference. These methods suffer from various restrictions such as
the need for molecular tracers, a form of seeding, or low signal-to-noise levels. Because CARS
measures the physical state of molecules already existing in the flow, seeding is not needed. In
addition, the coherent nature of the CARS signal leads to good signal-to-noise levels. While
most of the above methods rely on the Doppler shift of the signal compared to a reference,
CARS can also be implemented using counter-propagating pump beams to measure velocity
without a reference signal. Benefiting from relatively high signal-to-noise levels, CARS can also
be extended to measure other physical properties simultaneously.
The wave-mixing process that forms the CARS signal is a vector-based phenomenon, and
the development of CARS has brought about many different phase-matching geometries.
Typically, collinear or “BOXCARS” schemes are utilized, but other arrangements have been
3
discussed or used. In the past, CARS has been utilized to measure velocity by referencing the
signal generated when the flow direction is in the plane of the probe volume to a separate signal
generated when the probe volume is orthogonal to the direction of flow. In the present study, a
planar phase-matching geometry has been developed with counter-propagating pump beams. If
the flow direction in which velocity is desired is in the plane of the laser propagation, one CARS
spectrum generated from the forward-propagating pump beam undergoes a relatively small
Doppler shift, while the backward-propagating pump beam generates a spectrum that undergoes
a relatively large Doppler shift. Therefore, the CARS signal contains two overlapped spectra
that are shifted apart in frequency, allowing the velocity to be obtained. Because measurement
methods for pressure and temperature have been well developed as stated above, simultaneous
measurements of pressure, temperature, and velocity can be acquired, a potential
accomplishment of great import.
The use of CARS allows two forms of Raman resonances to be probed.
These
resonances are a result of diatomic molecules undergoing either a vibrational or pure rotational
transition. The current study was first applied to vibrational transitions of the nitrogen molecule.
Further experiments were then performed utilizing pure rotational transitions of the nitrogen
molecule.
Normally, a broadband CARS signal is resolved using a spectrometer. Because the
linewidths are large enough, the spectrometer allows the signal to be examined so that pressure
and temperature can be determined. While this could be accomplished in the current study, the
Doppler shift expected is not large enough to be resolved by any practical spectrometer available
commercially. Therefore, the current study employed an etalon so that temperature, pressure,
and velocity can all be resolved simultaneously.
4
When developing a new technique, it is often desired to have an understanding of the
parameter ranges in which the technique will be most useful. These ranges can be obtained for
the current study by observing the conditions for which the method is most sensitive to a change
in velocity. It would take years of experimental work and numerous facilities to determine the
potential areas of application for this method.
Therefore, a computer-simulation model of
possible experimental parameters was used to generate a sensitivity study of the velocity
measurement capability of the CARS technique.
These computational results can then be
compared to those obtained by the experiments.
1.1
Objectives
While many methods have been developed to measure velocity, the search for a fully
non-intrusive, instantaneous velocimetry technique that has the ability to simultaneously measure
other properties has continued. The current study is directed at extending CARS, a proven
method for measuring pressure, temperature, and other pertinent properties, to velocity
measurements in the hope of being able to make simultaneous measurements of velocity and
thermodynamic properties.
While the method itself is quite involved, the benefits certainly
outweigh the effort required to perform the measurements.
The current study is not intended to be an immediate replacement for proven velocimetry
techniques. For a signal to be detected at all is an accomplishment. The experiments described
herein are intended to provide another technique for velocity measurements when conventional
methods can not be implemented or are not desired. The technique has its areas of usefulness,
but also suffers from complexity and cost.
5
1.2
Outline
This document is compiled in a standard thesis format. A literature survey of CARS,
velocimetry techniques, and underexpanded jets is provided in Chapter 2. Chapter 3 discusses
the facilities and equipment used. Experimental results are presented in Chapter 4, and Chapter
5 reviews the sensitivity study performed. Chapter 6 concludes with the significant results of the
experiments, a discussion of the predictions of the sensitivity study, and recommendations for
future work.
6
2
LITERATURE SURVEY
2.1
Coherent Anti-Stokes Raman Scattering
CARS, and Raman spectroscopy in general, is a well-documented technique 1-3 that has
been used in various combustion and gas dynamic facilities. Raman and Krishnan4 originally
discovered Raman scattering in 1928 by observing the process in liquids. Raman scattering
occurs when light of frequency νo is scattered from a molecule at a new frequency ν' = νο ± νM.
This scattering occurs because the molecule undergoes a transition to a new rotational,
vibrational, or electronic energy level, the energy required for the transition being νM. The
process can be viewed as an incident photon of frequency νo being destroyed at the same
moment a photon of frequency ν' is created. As the change in energy of the incident light is
completely transferred to the molecule, conservation of energy is upheld. The frequencies at
which the scattering occurs are molecule- and state-dependent. Therefore, by monitoring the
scattered light, the species and its physical state can be determined.
Nonlinear effects were first discovered in 1963 by Terhune et al.,5 but they were not
explored in depth until the advent of more powerful continuous-wave and pulsed lasers. CARS,
a nonlinear mixing process, occurs when two coherent beams of frequency ν1 and ν2, referred to
as the pump and Stokes beams, respectively, are overlapped in a medium. If the frequency
difference:
νM = ν1 − ν2
(2.1)
is in resonance with a molecule being probed, a signal is formed. The resulting scattered light is
coherent and well collimated, and its frequency is determined by:
νCARS = ν1 + νM
(2.2)
7
The pump and probe beams must be aligned in the medium in order to conserve momentum.
This requirement of alignment gives rise to various phase-matching arrangements.1, 6-9 The
conservation of momentum can be realized as:
r
r
r
r
k CARS = k1f + k1b − k 2
(2.3)
r
where k is the corresponding wave vector for each laser beam and the subscripts 1f, 1b, and 2
refer to the forward-propagating pump beam, the backward-propagating pump beam, and the
probe beam, respectively. Thus Eqs. (2.1) and (2.3) dictate the physical restrictions of the laser
diagnostic system. Further modifications can be made1 to extend the application of CARS, such
as using a broadband probe beam, as in this study.
2.2
Temperature and Pressure Measurement
Because CARS has shown great promise for accurate flow-property measurements, much
work has been performed to develop computational models of the spectra generated
experimentally.
Specifically, the CARSFT code10 has been developed at Sandia National
Laboratories to fit the spectra of commonly probed molecules and to predict pressure,
temperature, and concentration. Primarily, CARS has been implemented as a method to obtain
temperature and concentration in combustion applications.1,
11
Temperature measurements are
based on the population distribution among rotational and vibrational levels.11 This distribution
is determined by Boltzmann statistics. The relative intensities of each transition correspond to
the spectroscopic temperature of the molecule at the instant it is probed. In most cases, with the
exception of certain plasmas, the spectroscopic and translational temperatures are the same.
Figure 2.1 shows the change in pure rotational transitions (Äv = ±0, ÄJ = ±2) of the nitrogen
molecule. The effects on the total intensity and the intensity distribution are evident as the
temperature increases from 100 K (Fig. 2.1a) to 300 K (Fig. 2.1b) at a pressure of one
8
atmosphere.
In addition, pressure measurements are dependent on the linewidths of the
transitions.1 The lines broaden as pressure increases until they overlap; at this point, collisional
narrowing occurs. This process has been empirically investigated, documented, and modeled.1, 12
The effects of pressure between 1 atm and 10 atm can be seen in Fig. 2.2, at a temperature of
300 K, using the same transitions of the nitrogen molecule. Because these transitions are well
separated in frequency, collisional narrowing does not occur and pressure sensitivity is low. The
Q-branch (Äv = ±1, ÄJ = ±0) of the nitrogen molecule is more pressure sensitive due to the
effects of collisional narrowing. Figure 2.3 shows the effects of pressure on this set of transitions
for the same conditions as those in Fig. 2.2. The strong effects of pressure on the Q-branch
spectrum are obvious.
Due to the success of CARS in combustion applications, the technique was extended to
measurements in high-speed flows.13-20
Using the methods described above, temperature,
pressure, and other properties were obtained.
The CARS technique is under continued
development in the hope of providing new measurement techniques to investigate flows that are
currently difficult to measure and to provide turbulence, i.e., fluctuating, quantities that are
needed to validate theoretical and computational studies.
2.3
Velocity Measurement and Velocimetry Techniques
Measures21 initially proposed the idea of extending spectroscopic techniques to velocity
measurement in 1968. The idea involves the use of the Doppler effect seen when probing a
medium that is moving in the plane of the beam propagation. Since then, many spectroscopic
techniques have been modified to obtain velocity. These techniques include: absorption, 22-26
LIF,27-33 DFWM,34-35 filtered Rayleigh scattering (FRS),36-40 IRS,41-43 SRGS,44-45 coherent Stokes
Raman scattering (CSRS),46 and CARS.17-20,
47
Another technique involving a time-of-flight
9
velocity measurement has been pursued, termed molecular tagging velocimetry (MTV). This
method uses various tagging methods including: Raman excitation plus laser-induced electronic
fluorescence (RELIEF),48-51 photo-activated non-intrusive tracking of molecular motion
(PHANTOMM),52, 53 and LIF.54-56 Also, photothermal deflection spectroscopy (PTDS) has been
developed using the change of refractive index in the flow due to heating. 57-59
With the exception of IRS and CARS, the majority of these techniques will not be
discussed in detail, but are compared to the current study in Table 2.1. The remaining methods
are considered to be most related to the present study. In order to make a comparison, criteria
must first be established. Thus, the following list has been constructed:
1. Method of obtaining velocity
2. Requirement for seed or tracer particles
3. Method of referencing the measurement
4. Ability to measure other properties simultaneously
5. Accuracy of the measurement.
The techniques listed in Table 2.1 comprise a lengthy list of the velocimetry options
available. While all of the techniques, aside from the current study, may contain advantages
such as no requirement for particle seeding, they inevitably are hampered by other
disadvantages, e.g., requiring a reference. Overall, if certain restrictions can be tolerated, the list
contains numerous alternatives from existing, well-developed techniques. It is seen, though, that
only the current study excels in all categories listed.
Returning to the IRS and CARS studies mentioned earlier, a more in-depth look at some
of the techniques from Table 2.1 can be performed. Originally, She et al.44 proposed using
coherent Raman spectroscopy as a measurement technique in gaseous flows. Initially, SRGS
was used, but then IRS42 was employed for the measurements. IRS involves the use of two laser
10
beams of frequency ν1 and ν2 under the restriction of Eq. 2.1. The loss of power in the higherfrequency beam is monitored as energy is transferred to the molecule being probed. If the
higher-frequency beam is scanned across a transition of the molecule, a map of the signal can be
traced out. The peak loss in power of the higher-frequency beam corresponds to the known
frequency at which the transition occurs. If the molecule is moving in the plane of the beam
propagation, the frequencies ν1 and ν2 that the molecule encounters are Doppler-shifted.
Therefore, the peak loss in power will also be Doppler-shifted, which can be referenced to the
stationary case for a velocity measurement. The Doppler shift recorded is determined by:
(
)
r r
r
Äν = k1 − k 2 • V
(2.4)
Because IRS is based on Raman scattering, the physical state of the molecule being probed can
also be determined. In the three known studies of this method,41-43 velocity was obtained along
with temperature, pressure, or density in various combinations. In all three cases, no seed or
tracer particles were needed because diatomic nitrogen was the molecule being probed in the
flow.
With the exception of the study done by Exton and Hillard,41 the Doppler-shifted spectra
were referenced to stationary spectra through the use of a gas cell. Exton and Hillard employed a
form of counter-propagating pump beams to acquire two spectra from the same measurement
point separated in time by 10 ns.
The pump beams are then Doppler shifted in opposite
directions in the molecule’s reference frame, as are the signals acquired from each. Therefore,
rather than being referenced to a stationary medium, the two signals can be referenced against
each other. Although this obviates the need for a gas-cell reference, two spectra must still be
acquired for each measurement location.
While the other two IRS studies42,
43
reported
accuracies of approximately 5%, the Exton and Hillard study reported an accuracy of
approximately 10%.
11
Around the same time as these IRS studies, CARS was implemented to measure
velocity. 19 The experiment involved a different method of referencing. Measurements were first
made with the velocity vector oriented orthogonal to the beam propagation. Then, the flowfield
was rotated so that the velocity vector was partially in the plane of beam propagation. Similar to
the previously described methods, the differences between the two peaks in the spectra were
used to deduce the velocity. A similar experiment was performed in rarefied flows.20 More
recently, CARS was used to measure velocity by referencing to a gas cell.47 Two other studies
of note, involving more complicated methods of velocity measurement, were performed by
Lefebvre et al.17, 18 These studies reversed the propagation of the laser beams and acquired two
spectra at each location to reference the measurements. All of the previous CARS work could
have been extended to measurement of other properties such as temperature, pressure, and
density, but only two studies included measurements of temperature.20,
47
Because the
experiments probed molecules already present in the flow, no seed or tracer particles were
required. In all cases, the velocity measurement accuracies reported were on the order of 4 to
20%.
The present study differs from the previous IRS and CARS work in one main way:
counter-propagating pump beams are used in a single phase-matching geometry. Figure 2.4
compares a phase-matching scheme of this type with the more commonly used BOXCARS
geometry.
Because the forward-propagating pump beam, ν1F, and the probe beam, ν2, are
primarily in the direction of flow, the signal formed from these two beams will be upshifted on
the order of 1x10-6 cm-1. At the same instant, a signal is generated by the backward-propagating
pump beam, ν1B, and the probe beam, which will be downshifted on the order of 1x10-2 cm-1.
Therefore, one spectrum will contain one upshifted and one downshifted signal that are
12
overlapped. In this way there is no need for a secondary reference, as all the information needed
to determine the velocity is included in one spectrum.
2.4
Fabry-Perot Etalon
As mentioned in Chapter 1, broadband CARS signals are normally resolved using a
spectrometer.13-14 Typical resolutions for spectrometers are on the order of 0.1 to 1.0 cm-1. This
will not resolve the Doppler shift expected in the current experiments. Therefore, a Fabry-Perot
etalon was implemented to resolve the CARS signal. The physics of etalons are well known. 60
A few studies have employed the use of an etalon to resolve optical diagnostic signals.39-40, 61-62
Using an etalon in conjunction with a spectrometer has also been investigated.63 While an
etalon’s higher resolution can be advantageous, its transmissivity is reduced. Thus, the higher
the required resolution, the more intense the signal must be in order for it to be detected.
2.5
Underexpanded Jet
The underexpanded jet is a well-investigated flowfield, as documented in a vast amount
of literature. Figure 2.5 is a schematic of the flow features seen up to and just beyond the first
Mach disk. The flow exits the choked nozzle and encounters a Prandtl-Meyer expansion fan.
This expansion accelerates and turns the flow away from the centerline. The expansion waves
reflect off the constant-pressure atmospheric boundary (the outer shear layer) as compression
waves. These compression waves coalesce and form the intercepting shock. This shock wave
then separates the inner jet region from the outer jet region. The inner jet region continues to
accelerate until reaching the Mach disk.
The outer jet region continues downstream until
reaching the oblique reflecting shock that forms where the intercepting shock and Mach disk
meet, i.e., the triple point. The flow field increases in complexity at this point as the inner jet
13
region is subsonic after the Mach disk, whereas the outer jet region remains supersonic beyond
the reflecting shock. The slip line that exists between the inner and outer jet regions forms an
inner shear layer. Thus, a wide range of flow regimes and thermodynamic conditions exists
within the initial, well-documented flow field of the underexpanded jet.
Due to the ease of facility construction for this flow, its large range of flow properties,
and its excellent optical access, the underexpanded jet has become a benchmark for many flow
diagnostic experiments and calculations. For these reasons, an underexpanded jet was used to
test the accuracy of two CARS methods previously developed in the Laser Diagnostics
Laboratory for measurement of pressure and temperature.13,
14
Two other CARS techniques16, 19
were developed using an underexpanded jet as the test case, one in particular to verify velocity
measurements.19
LIF,29-31 DFWM,35 IRS,43 and MTV49 were all investigated in the same
manner. One experiment pursued the same objectives as the current study using absorption in
the underexpanded jet flowfield.23 LDV has also been performed in the underexpanded jet,
providing centerline velocity measurments.64-68 Due to the complicated flow features, the flowtracking ability of the seed particles was studied in depth. 66 Computational centerline velocity
data have also been provided.69-71
The centerline distribution of pressure has been studied experimentally and
computationally. 72
Pressure-sensitive and temperature-sensitive paint have also been
implemented to study temperature and pressure behavior in an impinging jet. 73 The dynamics of
the Mach disk have been analytically and experimentally investigated.74-76 Imaging of the jet
cross section has been performed,77 complementing studies of the shear layer growth. 78
Streamwise vortices in the jet have also been investigated in depth. The origin of the vortices,
suggested to form from Taylor-Göertler instabilities, has been the subject of various studies.79-81
The effects of nozzle surface roughness on these vortices have also been investigated,79,
81-83
14
along with vortex pairing and merging downstream. 80,
84
Although not as recent, a detailed
overview of the underexpanded jet’s flowfield characteristics has been provided by Ramskill.85
The present study was aimed at making measurements along the centerline of an
underexpanded jet flow in the Laser Diagnostics Laboratory. 13, 14 Due to the need for the fluid
velocity to be in the plane of the laser beam propagation, the region between the jet exit and half
way to the first Mach disk is obstructed by the nozzle itself. Measurements, therefore, continue
from that point past the first Mach disk. Fortunately, velocity has been acquired experimentally
and computationally in previous investigations throughout this region for comparison.
A
summary of these studies is given in Table 2.2, which shows the measurement method used and
the region over which the experiments were conducted.
2.6
Sensitivity Study
While the velocity measurement sensitivity study performed herein provides much-
needed insight into the areas of usefulness of this new CARS technique, little information has
been found concerning previous studies of its kind. The only similar study that was found 26
arbitrarily defined its velocity sensitivity based on the linewidths of the transitions. Also, this
study was conducted only at the measurement points that were obtained experimentally and
referred more to an accuracy of measurement rather than a sensitivity to a change in velocity.
The current sensitivity study involves a wide range of possible operating conditions. The change
in spectral structure determines how sensitive the spectra and, therefore, the method are to a
change in velocity.
15
2.7
Summary of the Literature Survey
Previous optical diagnostic techniques have shown promise of providing a new
velocimetry technique in certain parameter ranges, although no investigation proved to be a
panacea for all flowfields.
Most methods possess limitations with respect to seeding and
referencing. The current study is not intended to resolve all the current issues in the search for
the best non-intrusive velocimetry technique, but rather attempts to perform measurements with
a quality at least equal to those discussed above, while reducing the number of limitations.
Using the results of the sensitivity study, the technique can then be recommended for gas
dynamic flows over specific parameter ranges. The combination of a new technique and the
sensitivity results provides the researcher with one more alternative to the already abundant list
of velocimetry techniques that are available.
16
3
EQUIPMENT AND FACILITES
3.1
Vibrational CARS Setup
The equipment setup for the initial vibrational CARS experiments is shown in Fig. 3.1,
and is very similar to a previous setup used in the Laser Diagnostics Laboratory. 14 The process
begins with a frequency-doubled, injection-seeded, Q-switched Nd:YAG laser (Continuum
Powerlite Precision 8010). The output energy of the Nd:YAG laser, approximately 900 mJ when
injection seeded, is controlled using a zero-order half wave plate in conjunction with a Glan
polarizer. This combination forms what is more generally considered a power attenuator. The
beam then encounters a 20/80 beam splitter.
The reflected portion of this beam becomes the source of the 532 nm pump beams in the
nonlinear wave-mixing process.
The power in this leg is controlled by a second power
attenuator. A 50/50 beam splitter divides this beam into the forward- and backward-propagating
pump beams, corresponding to the frequencies õ1F and õ1B. In order to achieve the angles
specified by the phase matching, reflections involving incident angles other than 45o must occur.
The two critical reflections, shown in Fig. 3.1, were accomplished with special “off-angle”
mirrors. Designed as full reflectors for a center wavelength of 600 nm at 0o incidence (CVI
TLM2-600-0-2025), the reflective properties can be modified.
As the angle of incidence
increases, the center wavelength decreases. At 30o incidence, the center wavelength shifts about
5%, corresponding to 570 nm, with only small effects on the reflected polarization. With a
bandwidth of 120 nm FWHM, these mirrors provide greater than 95% reflectance at the
necessary angles. The pump beams are finally steered using high precision mounts (Newport
610) in conjunction with a 90o turning prism, and are focused using individual plano-convex
spherical lenses (ƒ = 250 mm, CVI PLCX-50.0-128.8-C).
17
The remaining 80% of the 532 nm beam from the Nd:YAG is used to pump the
conventional broadband dye laser (BDL).86 Using 25 mg of Rhodamine 640 dissolved in 500 ml
of methanol in both the oscillator and single amplifier stages, the BDL will lase in and around
the desired wavelength of 607.55 nm. Thus, the BDL supplies the probe beam at frequency õ2.
The slight deviation from the otherwise straight propagation in this leg is accomplished by
misaligning a 90o turning prism. The probe beam is steered and focused similarly to the pump
beams. The phase-matching geometry that forms the probe volume is shown in Fig. 3.2.
At this point the CARS signal is formed at a wavelength of approximately 473.15 nm. It
is collimated using another ƒ = 250 mm lens. Using a narrow bandpass filter centered at 474 nm
(FWHM = 6 nm) to diminish scatter, the signal can be found using a PMT (Hamamatsu R1516).
To spectrally resolve the signal, a Fabry-Perot etalon setup was used, as seen in Fig. 3.3. The
signal was formed into a sheet using two cylindrical lenses (ƒ = -50 mm and ƒ = 240 mm). The
PMT was then replaced by a Photometrics CCH250 unintensifed CCD camera in order to record
the CARS spectrum. The etalon was designed at a center wavelength of 473 nm with a finesse
of F = 50.76 and a free spectral range of FSR = 2.2 cm-1. This provides for a spectral resolution
of approximately 0.04 cm-1.
3.2
Broadband Pure Rotational CARS Setup
Figure 3.4 depicts the system used for the broadband pure rotational CARS experiments.
Modifications to the Nd:YAG laser and the BDL from the vibrational CARS setup were required
in order to accommodate the change in transitions being probed. The first modification to the
system was obtaining frequency-doubled (532 nm) and frequency-tripled (355 nm) light from the
Nd:YAG simultaneously. This was accomplished by removing the full reflector between the
second- and third-harmonic generating crystals and replacing it with a 25/75 beam splitter (CVI
18
BS1-532-25-1012-45S-AR532/1064). The 532 nm output was used as the source for the pump
beams.
A power attenuator provided control of the approximate 140 mJ beam that was
generated. Once again utilizing a 50/50 beam splitter downstream, the forward- and backwardpropagating pump beams were constructed. Due to the phase-matching scheme, no reflections
away from 45o incidence were required.
The 355 nm output of the Nd:YAG, at an energy of approximately 250 mJ, was used to
pump the BDL. All optics in the BDL that consisted of BK-7 glass had to be replaced with
identical fused silica optics.
To achieve the desired probe beam wavelength (534.85 nm),
Coumarin 540A dye was used instead of Rhodamine 640. The optimal concentrations were
determined to be 253 mg dissolved in 400 ml of methanol for the oscillator and 93 mg dissolved
in 400 ml of methanol for the single amplifier. The probe beam, the BDL output, along with the
pump beams were focused at the probe volume using a single plano-convex spherical lens (ƒ =
250 mm). The phase-matching geometry used for this setup is shown in Fig. 3.5.
The CARS signal, formed at 529.18 nm, was collimated and directed into a one-meter
spectrometer (SPEX 1000M). In conjunction with the CCD camera, this system formed the
signal detection portion of the CARS setup. A new etalon was designed to detect the signal
(λ center = 529 nm, F = 39.73, FSR = 1.142 cm-1), providing a resolution of 0.03 cm-1.
3.3
Narrowband Pure Rotational CARS Setup
The final modification to the CARS system was the replacement of the BDL. In order to
achieve smaller probe beam linewidths, a Continuum ND-6000 narrowband dye laser (NDL) was
used.
The wavelength of the NDL was monitored using a WA-4500-0 Burleigh Pulsed
Wavemeter.
Figure 3.6 shows the minor adjustments to the system as compared to the
19
broadband pure rotational CARS system (Fig. 3.4). The phase matching used for this setup was
the same as for the broadband pure rotational CARS setup (Fig. 3.5).
3.4
Underexpanded Jet Facility
The underexpanded jet facility in the Laser Diagnostics Laboratory has been used
extensively in previous investigations.13,
facility.
14
King87 has provided an in-depth description of the
Figure 2.5 presents a schematic of the flowfield encountered with the jet, and a
schlieren image is shown in Fig. 3.7. Along the centerline of the jet, the following dynamic
ranges of pressures, temperatures, and velocities occur: 0.1 to 3.2 atm, 90 to 250 K, and 270 to
640 m/s, respectively. As stated in Chapter 2, this flowfield has been studied in depth and thus
provides a standard against which to test the current CARS techniques.
The intended region of measurement is along the jet centerline from midway between the
jet exit and the first Mach disk to beyond the first Mach disk, a distance of approximately
20 mm. This allows a comparison with previous LDV measurements upstream of the Mach disk
and the opportunity to measure the velocity in a region (downstream of the first Mach disk) that
has not been well investigated experimentally. To perform these measurements, the jet facility
was modified from its usual configuration.
The jet was tilted in the plane of the laser
propagation to allow the axial component of velocity to be measured. This was done by having a
custom mount for the jet made so that the centerline forms a 45º degree angle with respect to the
laser beam propagation direction. This configuration can be seen in Fig. 3.8.
3.5
Summary of Equipment Setups
The experimental setups used throughout the course of this study have been described.
The following chapter on experimental results will explain the reasons for the many changes to
20
the CARS system as time progressed. The technique will then be computationally investigated
in Chapter 5. Finally the conclusions drawn from these findings along with a discussion of the
future of this investigation is covered in Chapter 6.
21
4
EXPERIMENTAL RESULTS
4.1
Vibrational CARS
The first attempt to obtain velocity measurements was based upon vibrational resonances
of the nitrogen molecule. Initial phase-matching calculations were performed based on Eq. (2.3)
and are shown in Fig. 3.2. The results of the calculations provided the minimum crossing angle
of approximately 23.5o. The crossing angle is defined as half of the maximum angle between the
pump and probe beams. After the system was aligned at the calculated angles, attempts at
locating the signal began with the use of a PMT. Once the position of the signal was detected,
attempts were made to spectrally resolve it.
As seen in Fig. 4.1, the signal was indeed resolved using a Fabry-Perot etalon. Evidence
of structure can be seen in the figure, proving that spectroscopic data could be obtained.
Unfortunately, the image was the result of a four-minute CCD exposure, due to the low signal
levels obtained. This low signal level was not unexpected. As given above, the crossing angle
used in this setup can be considered to be extremely large. For comparison, similar vibrational
CARS experiments performed in the Laser Diagnostics Laboratory used crossing angles of less
than 3o. To understand how the crossing angle affects the signal strength, the following relation
used to calculate the theoretical intensity must be studied:
I CARS =
ω23
2 2
I 2I χ
l
4 2 1 2 CARS
c εo
The important parameter under consideration here is
(4.1)
, the length of the probe volume. This
length can be approximated as:
l∝
1
sin α
(4.2)
22
where á is the crossing angle. Thus, for the crossing angles given above, the theoretical signal
strength in this experiment is expected to decrease by a factor of approximately 50 compared to
previously mentioned studies.
The detection of the signal not only validated the phase-matching calculations, but it also
proved that spectral results can be obtained with this technique.
Without any previous
accomplishments of this nature in the literature, this success provided motivation to modify the
experiment to increase the signal strength. It was to this end that the change from vibrational to
pure rotational CARS derived.
4.2
Broadband Pure Rotational CARS
The reason for switching to probing pure-rotational transitions of the nitrogen molecule is
due to the decreased energy required to stimulate these transitions as compared to the vibrational
transitions. This small energy is realized in the minute difference in wavelength of the pump and
probe beam, which in turn results in a small crossing angle, the limiting factor of the previous
vibrational setup. The new crossing angle was calculated to be approximately 3o. As discussed
above, this crossing angle should provide reasonable signal strengths that are comparable to
previous successful CARS experiments.
In order to achieve the wavelength required of the probe beam (534.85 nm),
modifications were made to the BDL, as discussed in Chapter 3. After alignment, the BDL
generated on the order of 4 mJ, in comparison to the 20 to 40 mJ obtained previously. This drop
in energy was mostly due to the change in the lasing medium. Coumarin 540A has a peak
absorption at 423 nm. 88
Therefore, very little of the pump power provided at 355 nm is
absorbed. It is also documented that the conversion efficiency of Coumarin 540A is less than
23
that of Rhodamine 640.88
These two factors combined to decrease the overall conversion
efficiency of the BDL.
In order to detect the signal using this setup, a one-meter spectrometer, in conjunction
with a CCD camera, was employed. This differed from the vibrational CARS setup because of
the close proximity of the wavelength of the CARS signal (529.18 nm) to the input beams. A
narrow bandpass filter in conjunction with a PMT could not be used in this case because the
scattered light from the pump and probe beams would penetrate the narrow bandpass filter and
saturate the PMT above the expected signal levels. Thus, the spectral separation capability of a
spectrometer was utilized. After searching in vain for the CARS signal, it became apparent that
one or more of the changes to the system prohibited the formation or detection of a CARS signal.
The primary change to the system had been the modification of the BDL. In order to
determine if this was causing the problem, the output of the BDL was resolved using the onemeter spectrometer. A portion of the resolved spectrum, including the region of interest, is
shown in Fig. 4.2. While absolute intensities cannot be inferred from this figure, the general
spectral features of the BDL can be observed. The first feature of note is the periodic nature of
the spectrum, which is a result of an etaloning effect of the optics train used to transmit the beam
to the spectrometer.
The second and more important feature of note is the large range of
wavelength that the spectrum encompasses. The figure only displays about two nanometers of
the entire spectrum, but it was observed that the BDL lased over the ranges of 520-550 nm and
570-590 nm. This bandwidth of approximately 2000 cm-1 is an order of magnitude larger than
when Rhodamine 640 is used as the lasing medium.
Thus, the 4 mJ of output energy is
distributed over a large spectral range. Correspondingly, the energy density in the spectral range
desired (533.42-537.72 nm) is far below the threshold required to generate a CARS signal. This
24
discovery prompted the next change to the system: increasing the energy of the probe beam in
the spectral range stated above.
4.3
Narrowband Pure Rotational CARS
Switching to a narrowband source for the probe beam implies several changes to the
CARS system as a whole. First and foremost, the energy density of the NDL is contained in a
very small bandwidth. Therefore, all the output energy of the NDL is put to use in the CARS
signal formation. Second, the bandwidth of the NDL is less than the linewidth of the transition.
This requires the NDL to be scanned in frequency across the transition, eliminating the ability to
acquire single-laser-shot or instantaneous measurements.
The third and final change to the
system derives from the phase-matching scheme, which will be discussed in more detail below.
After alignment using Coumarin 540A, the NDL generated approximately 20 mJ of
energy at 534.85 nm. This energy was distributed over 0.8 cm-1, which is small in comparison to
the bandwidth of the BDL.
Therefore, even though the ability to obtain instantaneous
measurements was lost, the promise of a strong signal was motivation enough to continue. The
remaining portions of the system were aligned with the NDL in place using the same phasematching scheme as that for the broadband pure rotational CARS setup. The detection system
also remained unchanged. At this point, it was quite surprising that a CARS signal could not be
located.
Upon further investigation of the system, it became apparent that the phase-matching
scheme used for the broadband pure rotational CARS setup was not completely applicable here.
The confusion on this subject arose from the fact that the phase matching had been calculated
using the identical code that produced the phase matching for the vibrational CARS setup.
Unfortunately, the tolerances allowed in the calculations were accounted for by the broad
25
bandwidth of the BDL output. In the current case, however, the phase-matching angles would
need to be calculated under tight tolerances due to the narrow bandwidth of the NDL, perhaps
greater than that achievable in practice. This increase in accuracy appears even more impractical
when one realizes that scanning of the NDL output frequency will require the physical placement
of the probe beam to be adjusted. Therefore, as the probe beam is scanned in frequency across a
transition, so too must it be scanned simultaneously across the table at great levels of accuracy.
With these realizations in mind, the search for the CARS signal with this setup ended.
4.4
Summary of Experimental Results
After a review of the attempts performed, it was apparent that this CARS velocimetry
technique, while theoretically sound, was not currently practical. In the hope that equipment
advances in the future will render the technique possible, however, the sensitivity study that was
performed is presented in the next chapter. This computational simulation provides insight not
only into the possible usefulness of the technique, but also into the theory that governs the
physical process.
26
5
SENSITIVITY STUDY
5.1
Theory
In order to determine the sensitivity of the CARS spectrum to a change in velocity, the
effects of velocity on a single spectrum must first be determined. For an isolated transition, the
theoretical intensity of the signal is given by Eq. (4.1). All quantities in the equation would
remain constant during a given experiment, except for the susceptibility. The calculations are
thus simplified to consider changes only in this quantity. Note that pure rotational transitions of
the nitrogen molecule are separated well enough in frequency that they can be considered
isolated. The susceptibility can then be represented as:
2
χ CARS = χ′j( ∆ω j ) + iχ′′j( ∆ω j ) + χ nr
2
(5.1)
Fortunately, for large mole fractions of diatomic nitrogen, the nonresonant susceptibility (last
term) is negligible. Equations for the real and imaginary part of the susceptibility are given by:
χ′j =
χ′j =
2K j∆ ω jΓj
4∆ ω2j + Γ2j
K jΓj2
4∆ ω2j + Γ2j
(5.2)
(5.3)
where Kj, ∆ω j, and Γj are the line strength, departure from resonance, and the homogenous
Raman linewidth, respectively. Figure 5.1 depicts the susceptibility for the S(4) pure rotational
transition of diatomic nitrogen.
As discussed previously, when a fluid velocity is present in the plane of the laser
propagation, the resulting CARS signal is the overlap of two Doppler-shifted spectra. The
change in the peak susceptibility location of each Doppler-shifted CARS signal can be accounted
for by adding the Doppler shift, Eq. (2.4), onto the departure from resonance:
27
(
)
(5.4)
(
)
(5.5)
r
r
r
∆ωf = ωt − (ω1 − ω2 ) + 2π k1f − k 2 • V
r
r
r
∆ωb = ωt − (ω1 − ω2 ) + 2 π k1b − k 2 • V
where ω t is the frequency at which the transition occurs. These two spectra are no longer wellseparated in frequency and will interfere with each other. This interference of susceptibilities is
governed by:
χ CARS 2 = (χf′ + χ′b )2 + (χ′f + χ′b′ )2
(5.6)
where the subscripts f and b represent the upshifted and downshifted parts of the two Dopplershifted spectra. The effects of this interference fall into three regimes, as illustrated in Fig. 5.2.
When a velocity of 300 m/s is introduced, the linewidth of the transition is broadened, Fig. 5.2b,
as compared to the zero velocity case, Fig. 5.2a. Then as the velocity increases further to
650 m/s, an effect termed line splitting occurs, Fig 5.2c, as the peaks of the two transitions
separate. Finally, if the velocity is large enough (5000 m/s), the transitions will become fully
separated and begin acting as isolated transitions again, Fig. 5.2d.
With the effects of velocity on the CARS spectrum now understood, the sensitivity of the
CARS spectrum to a change in velocity can be studied. The following thermodynamic ranges
were chosen for investigation to encompass all practical flow fields:
Pressure: 0.1 to 10 atm
Temperature: 10 to 760 K
Velocity: 100 to 2000 m/s
A chi-squared value based on a change in velocity is defined as:
{
2
χ2forward = ∑ χCARS (V + ∆V) − χCARS (V)
{
2
}
2 2
χ2backward = ∑ χ CARS (V − ∆V) − χ CARS (V)
}
2 2
(5.7)
(5.8)
28
where the summation is over all wavelengths in each spectrum. Note that the velocity being
studied is the component in the plane of laser propagation. The sensitivity can then be defined in
the sense of a central difference as:
S=
∂ χ CARS
∂V
2
χ 2forward − χ 2backward
=
2 ∆V
(5.9)
There were two crucial decisions to be made before the definition of sensitivity could be
complete. First, should the spectrum be normalized prior to calculation of the sensitivity, and
second, what value of ÄV is appropriate?
To address the first question, Figs. 5.3 and 5.4 contain the results with and without
normalization for two values of velocity studied (V = 100 m/s and 500 m/s). In Fig. 5.3 there
seem to be no major differences in the two surfaces presented for the normalized and unnormalized cases. Moving on to Fig. 5.4, though, there are large differences in the two surfaces.
Because there was more structure in the surface at higher velocities, the normalization process
was used.
This decision was supported by the least-squares fitting routine used to fit the
experimental spectra in previous studies.
The second question was answered by performing two additional studies: one for which
ÄV was held constant for the entire range of velocity, and one for which ÄV was set to ten
percent of the specific velocity being studied. As seen in Figs. 5.5 and 5.6, there is little
difference in the structure of the surface between the two cases. In the end, a constant value of
ÄV = 50 m/s was decided upon, as this was the expected accuracy (precision) of the velocity
measurement method. With a final definition of sensitivity in place, the results of the study can
be discussed.
29
5.2
Results
Because diatomic nitrogen liquefies over certain ranges of temperature studied, the
results are only shown for temperatures above 100 K. Also, due to the large variations in
sensitivity, the surfaces are represented as the base 10 log of the sensitivity defined in Eq. 5.9.
Returning to Fig. 5.5a where the velocity considered is 100 m/s, some important features can be
noted. First is the large values of sensitivity at low pressures. This bodes well for measurements
in a high-speed flow field, for which the static pressures are typically low. The second features
of note are the sharp depressions or “stalactites” of the surface seen near 400 K and 500 K at
sub-atmospheric pressures.
While the physics behind the stalactites are not completely
understood, their existence is not merely a numerical construct, as will be discussed below.
Regardless of the physics, the stalactites infer large gradients of sensitivity in the areas
surrounding their location.
To observe the behavior of the surface further at higher velocities, Fig. 5.7 displays the
case of V = 500 m/s. The high levels of sensitivity remain at low pressures. The evidence of
more stalactites in and around this region implies that the large sensitivity gradients at low
pressure have increased. In this case, the stalactites form long ripples in the surface. The peak
values of sensitivity for this case bound what is considered the leading ripple on the surface. As
will become clear below, the ripples move across the surface, starting at low pressure and
moving toward higher pressure as velocity increases. Therefore, the ripple encompassing the
highest pressure range will be the initial ripple to move across the surface.
Finally, returning to Fig. 5.6a, the maximum velocity considered here of V = 2000 m/s
can be discussed. The most drastic change at this extreme velocity is the total drop in sensitivity
over the entire surface. The stalactites still exist at low pressures, and the peak values of
sensitivity again bound the leading ripple.
Notice the position of the ripples in Fig. 5.6a
30
compared to those in Fig. 5.7 at V = 500 m/s. This rightward displacement of the ripples to
higher pressures is indicative of the results for all velocities considered.
5.3
Summary of the Sensitivity Study
The results of this sensitivity study provide some findings of interest. The first is due to
the large gradients in sensitivity that always occur at low pressure for all velocities considered.
This implies that the technique will have a high level of sensitivity in this range of conditions.
This region encompasses flow fields at supersonic and hypersonic speeds. The second is the
existence of the ripples and stalactites.
numerous.
The possible reasons behind their formation are
The most plausible explanation is that they are related to the line splitting
phenomenon. The explanation for this speculation goes as follows. As each spectrum of the
three generated to calculate sensitivity undergoes the onset of line splitting, a ripple is created.
Under certain conditions, the exact onset of line splitting is happened upon and a stalactite forms.
Thus, the first three ripples correspond to the onset of line splitting in each spectrum. The fourth
and final ripple that always exists at low pressure corresponds to the conditions at which the
Doppler shift is so large that the overlapped transitions have become well isolated. The change
in a spectrum for a change in velocity only affects the distance between the two transitions at this
point. Therefore, any change in velocity under these conditions results in a very similar spectral
shape which, in turn, decreases the sensitivity, thereby forming the fourth ripple. Once again,
this explanation is rather speculative, and can only be confirmed after observing all the spectra
generated in the calculation of each surface, which total 975,000. This number is clearly beyond
that which can be examined manually.
31
In summary, the sensitivity study has served the purpose of determining the flow fields
and thermodynamic conditions that the technique would be most applicable to and has also
presented new areas of interest that require further investigation.
32
6
CONCLUSIONS AND RECOMMENDATIONS
6.1
Experimental Findings
The initial success with the vibrational CARS system proved that the technique was
viable.
The calculated phase-matching scheme for counter-propagating pump beams, while
difficult to implement, worked in practice. Even though limited by an extreme crossing angle,
the CARS signal was still generated at the location predicted. Unfortunately, the low signal
levels would not permit enough spectral resolution to study the effects of introducing a velocity
at the probe volume. Therefore, no attempt to validate the existence of line splitting could be
performed.
In hopes of increasing the signal strength, modifications were made to the system. While
the benefits of the alterations would have had large effects on the signal strength, they also added
higher levels of complexity to the system, prohibiting the formation and detection of the CARS
signal. Possible changes to the system still exist, but are either impractical or unavailable at this
time. Therefore, the technique is valid, but it is hampered enough by its own intricacies that it is
not particularly practical at this time.
6.2
Numerical Findings
If the technique becomes possible in the future, the sensitivity study has shown that
supersonic and hypersonic flow fields are the most applicable regions for investigation. Large
levels of sensitivity always exist at low pressure, providing promise for reasonably accurate
velocity measurements.
Continuation of this study is possible, as all aspects of the results
presented in Chapter 5 have not been thoroughly investigated.
33
6.3
Recommendations
While little success was found in the experiments, there is still reason to consider the
CARS velocity measurement technique’s future.
The ability to accurately obtain pressure,
temperature, and velocity simultaneously on a single-laser-shot basis is very desirable. This
prompts the comments made in the next two sections. As seen throughout this study, though, an
alternate form of signal acquisition is also a subject of great intrigue, prompting the discussion in
the final section.
6.3.1
Recommendations for the Current System
The pure rotational CARS method proved to be the more desirable of the two techniques
used here. This is based on the small crossing angle calculated. Specifically, it would be
beneficial to utilize the broadband pure rotational CARS system, as it provides the ability to
measure pressure, temperature, and velocity in one laser shot.
The limiting factor in that
experiment was insufficient probe beam energy density. The underlying cause of the low probe
beam power arises from the use of Coumarin 540A dye. This dye was not developed to be used
with frequency-tripled Nd:YAG light. Unfortunately, it was the only dye known that would lase
in the spectral range desired. Further investigation into recently designed synthetic dyes and
other organic dyes not previously considered is needed. This investigation might solve the only
limiting factor found with the broadband pure rotational CARS system.
6.3.2
Recommendations for the Sensitivity Study
The theory presented in Chapter 5 holds only for isolated transitions. Therefore, a study
of this kind for vibrational transitions of the nitrogen molecule was not performed. A serious
investigation of CARS theory as applied to a spectrum such as the nitrogen Q-branch could be
34
performed. In the event that the signal levels seen in the vibrational CARS system could be
increased, a simulation of this kind would be necessary. Not only would this provide similar
information as that found in the current sensitivity study, it would also provide the theory
necessary to least-squares fit the experimental spectra to acquire pressure, temperature, and
velocity.
6.3.3
Recommendations for a New CARS System
This section derives from a discovery recently made in regards to a previous
experiment. 71 Under the assumptions of a homenergetic flow, velocity could be obtained from:
ho = h +
V2
= constant
2
(6.1)
if the temperature were known. As demonstrated by Woodmansee,71 pressure and temperature
can be acquired with great accuracy, and if applied in an internal flow such as a supersonic wind
tunnel, the homenergetic flow assumption would hold.
Thus, velocity magnitude could be
obtained through temperature measurements. Note that this differs from the current study, as this
is only the calculated velocity magnitude, not the measured component along the direction of the
probe volume. Nevertheless, measurements of this kind made in a high-speed shear layer would
provide a vital contribution to the literature.
35
TABLES
Table 2.1 Comparison of spectroscopic velocimetry techniques
Technique
Absorption
Doppler shift
Seed or
tracer
particle
Yes
LIF
Doppler shift
Yes
DFWM
Doppler shift
Yes
FRS
Doppler shift
No
IRS
Doppler shift
No
SRGS
Doppler shift
No
CSRS
Doppler shift
No
CARS
Doppler shift
or signal decay
rate
Time of flight
No
Gas cell or
two flow positions
Yes
4 to 20%
Yes and no
Multiple pictures
No
3 to 100%
Change in
refractive
index
Yes
No
No
5 to 20%
Doppler shift
No
No
Yes
Not
Available
MTV
PTDS
CARS
(Current
Study)
Method
Reference
Extension
to other
properties
Two flow positions
Yes
Accuracy
reported
Gas cell or
two flow positions
Gas cell or
two probe volumes
Molecular filter or
intensity reference
Gas cell or
two probe volumes
Two flow positions
or two probe
volumes
Not Specified
Yes
2 to 20%
Yes
5 to 100%
Yes
7 to 20%
Yes
5 to 10%
Yes
40%
Yes
Not reported
2 to 20%
36
Table 2.2 Summary of underexpanded jet centerline velocity studies
Reference
19
23
29
30
31
35
43
49
64
66
69
70
71
Method
Region of Measurement
CARS
One point
Absorption
Before and after Mach disk
PLIF
Before Mach disk
PLIF
Before Mach disk
LIF
Before first Mach disk through second Mach disk
DFWM
One point
IRS
Before Mach disk
MTV
Before and after Mach disk
LDV
Through first eight Mach disks
LDV
Through first four Mach disks
Numerical
Before first Mach disk
Numerical
Before first Mach disk
Numerical
Through first two Mach disks
37
FIGURES
(a)
6000
Intensity1/2
5000
4000
3000
2000
1000
0
40
80
120
160
200
160
200
Wavenumber (cm -1)
(b)
1400
1200
Intensity1/2
1000
800
600
400
200
0
40
80
120
-1
Wavenumber (cm )
Figure 2.1 Temperature effects on pure rotational lines of diatomic nitrogen:
(a) T = 100 K, P = 1 atm; (b) T = 300 K, P = 1 atm
38
(a)
1400
1200
Intensity1/2
1000
800
600
400
200
0
40
80
120
160
200
160
200
Wavenumber (cm -1)
(b)
1400
1200
Intensity1/2
1000
800
600
400
200
0
40
80
120
-1
Wavenumber (cm )
Figure 2.2 Pressure effects on pure rotational lines of diatomic nitrogen:
(a) T = 300 K, P = 1 atm; (b) T = 300 K, P = 10 atm
39
(a)
800
700
Intensity1/2
600
500
400
300
200
100
0
2325
2326
2327
2328
2329
2330
2331
2330
2331
Wavenumber (cm -1)
(b)
3000
Intensity1/2
2500
2000
1500
1000
500
0
2325
2326
2327
2328
2329
-1
Wavenumber (cm )
Figure 2.3 Pressure effects on the Q-branch of diatomic nitrogen:
(a) T = 300 K, P = 1 atm; (b) T = 300 K, P = 10 atm
40
(a)
ν1
ν1
νCARS
ν2
(b)
ν1f
νCARS
ν1b
ν2
Figure 2.4 Comparison of (a) BOXCARS and (b) counter-propagating phase-matching schemes
Figure 2.5 Schematic of the underexpanded jet (from Woodmansee71)
41
CCD
Camera
Broadband
Dye
Laser
FrequencyDoubled
Nd:YAG
Jet
Cylindrical Lens
Etalon
Spherical Lens
Off-Angle Mirror
532 nm Mirror
Power Attenuator
νCARS
ν2
ν1f and ν1b
Beam Splitter
Prism
Beam Dump
Figure 3.1 Vibrational CARS setup
ν2
ν1f
è1F = 28.37o
è1B = 229.72o
è2 = 75.31o
èCARS = 270.00o
ν1b
νCARS
Figure 3.2 Vibrational CARS phase-matching scheme
42
CCD
Camera
50 mm camera lens
ƒ = 240 mm cylindrical lens
Fabry-Perot etalon
ƒ = -50 mm cylindrical lens
Figure 3.3 Fabry-Perot etalon setup
Modified
Broadband
Dye
Laser
FrequencyDoubled
and
Tripled
Nd:YAG
One Meter
Spectrometer
355 nm BDL Pump Beam
ν2
ν1f and ν1b
νCARS
CCD
Camera
Power Attenuator
Beam Splitter
Prism
Figure 3.4 Broadband pure rotational CARS setup
Jet
Beam Dump
Spherical Lens
532 nm Mirror
43
ν1f
νCARS
ν1b
ν2
o
è1F = 174.04
è1B = 0.00o
è2 = 180.00o
èCARS = 5.85o
Figure 3.5 Broadband pure rotational phase-matching scheme
Narrowband
Dye
Laser
FrequencyDoubled
and
Tripled
Nd:YAG
One Meter
Spectrometer
355 nm BDL Pump Beam
ν2
ν1f and ν1b
νCARS
Pulsed
Wavemeter
Jet
CCD
Camera
Power Attenuator
Beam Splitter
Prism
Figure 3.6 Narrowband pure rotational CARS setup
Beam Dump
Spherical Lens
532 nm Mirror
44
0
mm
25
5
20
4
15
3
10
2
5
1
mm
z/dj
5
Figure 3.7 Schlieren image of the underexpanded jet (from Woodmansee71)
jet nozzle
θ = 45o
pressure
transducer
thermistor
Figure 3.8 Schematic of the underexpanded jet facility
flow in
45
Figure 4.1 Image of the vibrational CARS signal resolved by the Fabry-Perot etalon
4
3.7 10
4
3.6 10
Intensity1/2
3.5 104
3.4 104
3.3 104
4
3.2 10
4
3.1 10
4
3 10
532
532.5
533
533.5
Wavelength (nm)
534
Figure 4.2 Spectrum of the BDL
534.5
46
800
700
Intensity1/2
600
500
400
300
200
100
0
42
42.5
43
43.5
44
44.5
45
Wavenumber (cm -1)
Figure 5.1 Susceptibility for the S(4) pure rotational transition of diatomic nitrogen
47
(a)
1.2
1
Susceptibility2
Susceptibility2
1
0.8
0.6
0.4
0.2
0
42.5
(b)
1.2
0.8
0.6
0.4
0.2
43
43.5
44
44.5
0
42.5
45
43
Wavenumber (cm -1)
45
1
Susceptibility2
Susceptibility2
44.5
(d)
1.2
1
0.8
0.6
0.4
0.2
0
42.5
44
Wavenumber (cm -1)
(c)
1.2
43.5
0.8
0.6
0.4
0.2
43
43.5
44
44.5
-1
Wavenumber (cm )
45
0
42.5
43
43.5
44
44.5
-1
Wavenumber (cm )
Figure 5.2 The regimes of interference for the S(4) pure rotational transition of diatomic
nitrogen at 300 K and 1 atm: (a) V = 0 m/s, (b) V = 300 m/s, (c) V = 650 m/s,
(d) V = 5000 m/s
45
48
(a)
80.0
78.0
log(Sensitivity)
76.0
74.0
750
8.25
625
6.50
500
4.75
375
Temperature (K)
3.00
250
Pressure (atm)
1.25
125
74.00
76.00
78.00
80.00
(b)
24
20
log(Sensitivity)
16
12
750
8.25
625
6.50
500
Temperature (K)
4.75
375
Pressure (atm)
3.00
250
1.25
125
12
16
20
24
Figure 5.3 Sensitivity results for V = 100 m/s: (a) with normalization,
(b) without normalization
49
(a)
80.0
78.0
log(Sensitivity)
76.0
74.0
750
8.25
625
6.50
500
Temperature (K)
4.75
375
Pressure (atm)
3.00
250
1.25
125
74.00
76.00
78.00
80.00
(b)
24.00
20.00
log(Sensitivity)
16.00
12.00
750
8.25
625
6.50
500
Temperature (K)
4.75
375
Pressure (atm)
3.00
250
col
1.25
125
12
16
20
24
Figure 5.4 Sensitivity results for V = 500 m/s: (a) with normalization,
(b) without normalization
50
(a)
80.0
78.0
log(Sensitivity)
76.0
74.0
750
8.25
625
6.50
500
4.75
375
Temperature (K)
3.00
250
Pressure (atm)
1.25
125
74.00
76.00
78.00
80.00
(b)
80.0
78.0
76.0
log(Sensitivity)
74.0
72.0
750
8.25
625
6.50
500
Temperature (K)
4.75
375
Pressure (atm)
3.00
250
1.25
125
72.00
74.00
76.00
78.00
80.00
Figure 5.5 Sensitivity results for V = 100 m/s: (a) ∆V = 50 m/s,
(b) ∆V = 10 m/s
51
(a)
80
78
76
log(Sensitivity)
74
72
750
8.25
625
6.50
500
Temperature (K)
4.75
375
Pressure (atm)
3.00
250
1.25
125
72.00
74.00
76.00
78.00
80.00
(b)
80
78
76
log(Sensitivity)
74
72
750
8.25
625
6.50
500
Temperature (K)
4.75
375
Pressure (atm)
3.00
250
1.25
125
72.00
74.00
76.00
78.00
80.00
Figure 5.6 Sensitivity results for V = 2000 m/s: (a) ∆V = 50 m/s,
(b) ∆V = 200 m/s
52
80.0
78.0
log(Sensitivity)
76.0
74.0
750
8.25
625
6.50
500
Temperature (K)
4.75
375
Pressure (atm)
3.00
250
1.25
125
74.00
76.00
78.00
80.00
Figure 5.7 Sensitivity results for V = 500 m/s, ∆V = 50 m/s
53
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