Chang, Leyen (2011). - The Hanson Group

Transcription

DEVELOPMENT OF A DIODE LASER SENSOR FOR MEASUREMENT OF
MASS FLUX IN SUPERSONIC FLOW
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
TSD-184
Leyen S Chang
August 2011
© 2011 by Leyen S Chang. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons AttributionNoncommercial 3.0 United States License.
http://creativecommons.org/licenses/by-nc/3.0/us/
This dissertation is online at: http://purl.stanford.edu/fq899hc0553
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I certify that I have read this dissertation and that, in my opinion, it is fully adequate
in scope and quality as a dissertation for the degree of Doctor of Philosophy.
Ronald Hanson, Primary Adviser
Brian Cantwell
Mark Mungal
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in
electronic format. An original signed hard copy of the signature page is on file in
University Archives.
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Abstract
Mass flux is one of the most critical parameters in the calculation of engine thrust
and assessment of aeroengine performance.
Knowledge of mass flux also provides
information about the engine specific impulse, thermal efficiency, and drag – parameters
which can be used to evaluate and optimize engine operating conditions. Conventional
mass-flux measurements are facilitated with a combination of static and total temperature
and pressure probes. These instruments have multiple drawbacks: they tend to disturb the
flow, generate shock structures, have limited lifetimes, and require frequent maintenance.
In response, there is a growing opportunity for tunable diode laser (TDL) diagnostics,
which can be deployed noninvasively with fast time response and high accuracy.
Another benefit of diode laser sensing is the ability to exploit mature telecommunications
laser technology overlapping the absorption transitions of many common molecules such
as H2O, CO2, and O2.
The sensor developed in this work builds on a detection technique developed at
Stanford beginning in the 1990’s, where mass flux was measured as the product of gas
density and velocity. Density was measured by comparing the attenuation of the detected
laser signal with the value predicted by theory. Velocity can be measured from the
relative Doppler shift of an absorption transition detected on beams directed upstream
and downstream in the flow. A major improvement is made to this sensing scheme by
taking advantage of the unique noise-rejection and signal-to-noise ratio increase afforded
by the 1f-normalized wavelength-modulation spectroscopy with second harmonic
detection (WMS-2f/1f ) technique. While WMS-2f/1f has been successfully employed as
a tunable diode laser diagnostic for many years, the behavior of the lineshape in response
to varying degrees of absorption and laser modulation has not been thoroughly explored.
Here the WMS-2f/1f lineshape is analyzed under various conditions and optimized for
velocity sensing.
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An important – and often overlooked – concern in absorption spectroscopy is the
influence of flow nonuniformity on line-of-sight (LOS) measurements.
Because
absorption is a path-integrated measurement, the detected lineshape can be distorted due
to a nonuniform distribution of the gas properties (temperature, pressure, velocity, or
composition) along the laser beam path. An analysis of nonuniformity effects on the
absorption signal is performed by simulating path-integrated lineshapes from
computational fluid dynamics (CFD) solutions; the results are quantified in order to
develop a correction to the path-integrated measurements obtained in this work.
The primary goal of this thesis is the development of a TDL mass-flux sensor
based on water vapor absorption that can be deployed in high-enthalpy, high-velocity
flows simulating hypersonic atmospheric flight (specifically a combustion-driven Mach
2.7 wind tunnel at NASA Langley). The WMS-2f/1f technique was incorporated in the
sensor to improve velocity precision while simultaneously measuring temperature;
density was then inferred from an independent pressure measurement and the ideal gas
law. The sensor temperature measurements were first validated against thermocouple
readings in a heated cell at Stanford from 650 – 1000K to within 1%. Measurements of
velocity were made in a low-speed wind tunnel from 2 – 18m/s with accuracy within
0.5m/s; a reduction of 50% in the standard deviation of the velocity measurement was
also observed by using optimized WMS-2f/1f.
The capstone mass-flux measurements were made during a field campaign at the
NASA Langley Direct-Connect Supersonic Combustion Test Facility.
Spatially and
temporally resolved measurements were performed in the facility isolator; these
measurements were used for comparison with a facility predictive code (a 1-D
thermodynamic equilibrium solver) and a CFD solution. The improvement in velocity
precision afforded by the optimized WMS-2f/1f technique was again confirmed, with
standard deviations of less than 1% in a 1630m/s flow. Temporally resolved velocity
data was corrected according to the nonuniformity analysis of path-integrated lineshapes,
bringing the sensor velocity measurement within 0.25% of the value predicted by the
facility code. Temperature measurements were made with high precision (10K standard
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deviation in a 990K flow), and agreement with the predicted value was also within 1%.
Mass-flux measurements had similar precision (standard deviation less than 1% of full
scale) and accuracy (within 1% of predicted value). Finally, spatially resolved velocity
and mass-flux data taken along both the height and width of the isolator were found to be
in close agreement with the CFD solution. These results demonstrate that TDL mass-flux
sensing based on WMS-2f/1f can produce temporally and spatially resolved
measurements with high precision and accuracy in a supersonic flow, thus proving the
sensor’s potential for future deployment in unknown mass-capture environments such as
inlet models and flight tests.
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Acknowledgments
The road to completing graduate study has been both arduous and fulfilling, and I
am thankful for the many challenges and lessons learned that have enriched my
experience in research, academics, and life in general. Needless to say, this has not been
an individual effort, and I wish to thank the many people who have helped me along the
way, first and foremost my advisor Professor Ronald Hanson. I came to work with
Professor Hanson in 2005 with a fairly vague idea of my research interests, and perhaps
an even more nebulous idea of my own strengths and weaknesses. Over the years it has
truly been a pleasure to learn both by guidance and example from a world-class
researcher like Professor Hanson. He has helped me realize a great deal about myself
both inside and outside of the laboratory and fostered the research and technical skills
necessary for a successful career in any discipline. I would also like to thank Professors
Cantwell and Mungal for taking the time to serve on my reading and exam committees,
as well as Professors Alonso and Mitchell for serving on my exam committee.
Drs. Dave Davidson and Jay Jeffries have been integral to my success here at
Stanford. One can always count on Dr. Davidson’s cheerful assistance with the daily
vicissitudes of laboratory work, whether it is a broken pump or a missing piece of
equipment. Dave’s help over the years has been invaluable in making my experiments at
Stanford run smoothly. I also had the pleasure of working closely with Dr. Jeffries in my
research. Jay’s passion for discovery and years of experience with field measurements
proved to be a great asset throughout my career at Stanford. I have truly appreciated
having the weight of such an accomplished researcher behind me during measurement
campaigns, when the word of a graduate student may not have held as much sway.
Working in the Hanson research group was also a rewarding experience; it was a
pleasure to be surrounded by so many brilliant, motivated, and friendly individuals. And
when sitting in front of the 3-zone furnace for hours on end, it didn’t hurt to have good
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company. In particular I’d like to thank Chris Strand for helping me with wind tunnel
measurements at Stanford and NASA Langley and Greg Rieker for our countless
discussions on the vagaries of WMS. To the many others not mentioned by name, I truly
appreciate your assistance and friendship throughout my time here at Stanford.
My research could not have continued without the generous support of my
colleagues at NASA Langley. I wish to acknowledge Glenn Diskin, Diego Capriotti, and
Barry Lawhorne and the DCSCTF team for assisting with the measurement campaigns,
Richard Gaffney for computing the CFD solution for our test section, and Troy Custodio
of ATK for helping with the test-section design. My thanks also go to Professor Eaton
and his students for providing me with access to his wind tunnel for our velocity
measurements at Stanford.
Last but certainly not least, I would like to thank my parents for their support,
guidance, and dedication throughout my entire academic career. Both being teachers, I
suppose the decision to continue my education and pursue a doctoral degree came as no
surprise. I am grateful for the values and work ethic my parents instilled in me, and
know that I stand where I am now because of them. I would also like to thank all the
friends and family that have helped me enjoy the past few years at Stanford – sometimes
the extracurriculars that keep a graduate student functioning happily are as important as a
day in the lab.
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Table of Contents
Abstract .......................................................................................................................... v
Acknowledgments .........................................................................................................ix
Table of Contents ..........................................................................................................xi
List of Tables ............................................................................................................... xv
List of Illustrations ....................................................................................................xvii
Chapter 1: Introduction ................................................................................................ 1
1.1
Motivation and Background.............................................................................. 1
1.2
Overview of Dissertation .................................................................................. 5
Chapter 2: Absorption Spectroscopy Theory and Measurement Techniques ............ 7
2.1
Absorption Spectroscopy Theory ...................................................................... 7
2.2
H2O Overtone and Combination Band at 1.4 μm............................................. 13
2.3
Direct Absorption Spectroscopy ..................................................................... 15
2.4
Wavelength Modulation Absorption Spectroscopy ......................................... 16
2.5
Temperature Measurement Methodology........................................................ 23
2.6
Density Measurement Methodology ............................................................... 24
2.7
Velocity Measurement Methodology .............................................................. 25
Chapter 3: 1f-Normalized Wavelength Modulation Spectroscopy with 2fDetection ...................................................................................................................... 29
3.1
Theory and Background.................................................................................. 29
3.2
Influence of Optical Depth.............................................................................. 34
3.3
Influence of Modulation Depth ....................................................................... 37
Chapter 4: Line-of-Sight Measurements in Nonuniform Flow Fields ....................... 41
4.1
Nonuniformity in Non-Reacting Flow Fields .................................................. 41
4.2
Modeling WMS Lineshapes in Nonuniform Flow ........................................... 43
4.3
Nonuniformity Analysis for NASA Langley DCSCTF ................................... 44
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4.4
Case Studies of LOS Measurements in Nonuniform Flow .............................. 49
4.4.1 Line Selection for Nonuniform Flow....................................................... 50
4.4.2 Nonuniformity Analysis of NASA HDCR Isolator ................................... 52
4.4.3 Nonuniformity Analysis of T2 Free-Piston Facility ................................. 56
4.5
Sensor Design to Minimize Nonuniformity Effects ........................................ 60
Chapter 5: Sensor Design and Experimental Methodology ...................................... 63
5.1
Sensor Architecture ........................................................................................ 63
5.2
Line Selection and Spectroscopy .................................................................... 66
5.3
Experimental Hardware .................................................................................. 72
5.3.1 Lasers, Fiber Optics, and Detectors ....................................................... 72
5.3.2 Optomechanical Components ................................................................. 77
5.3.3 Translation Stages ................................................................................. 78
5.3.4 Sensor Control and Data Acquisition System ......................................... 80
Chapter 6: Temperature and Velocity Validation Experiments at Stanford ........... 83
6.1
Validation of Temperature Measurement........................................................ 83
6.1.1 Experimental Setup ................................................................................ 83
6.1.2 Results of Temperature Velocity Validation ............................................ 84
6.2
Velocity Measurement Validation in Low-Speed Tunnel................................ 86
6.2.1 Facility and Experimental Setup............................................................. 86
6.2.2 Results of Sensor Velocity Validation ..................................................... 89
Chapter 7: Mass-Flux Measurements at the NASA Langley Direct-Connect
Supersonic Combustion Test Facility (DCSCTF) ...................................................... 91
7.1
Facility Overview ........................................................................................... 91
7.2
Test-Section Design and Experimental Setup ................................................. 94
7.2.1 Scramjet Isolator Section ....................................................................... 95
7.2.2 Modified Isolator with Optical Access .................................................... 96
7.2.3 Hardware and Experimental Setup......................................................... 99
7.3
Sensor Operation.......................................................................................... 102
7.4
Measurements of Velocity, Temperature, and Mass Flux.............................. 103
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7.4.1 Temporally Resolved Velocity Measurements ....................................... 105
7.4.2 Temporally Resolved Temperature Measurements ................................ 106
7.4.3 Temporally Resolved Mass-Flux Measurements ................................... 108
7.4.4 Spatially Resolved Velocity Measurements ........................................... 109
7.4.5 Spatially Resolved Mass-Flux Measurements........................................ 110
Chapter 8: Summary and Future Work ................................................................... 113
8.1
Summary of Thesis ....................................................................................... 113
8.2
Future Research ............................................................................................ 115
8.2.1 Improvements to TDLAS Mass-Flux Sensor .......................................... 115
8.2.2 Pressure and Composition Nonuniformity Analysis .............................. 116
8.2.3 Investigation of Higher-Order WMS Harmonics ................................... 117
8.2.4 Single-Beam Mass-Flux Sensing ........................................................... 119
Appendix A: Polarization-Maintaining Hardware .................................................. 121
A.1 Background and Theory................................................................................ 121
A.2 Polarization-Maintaining Fibers .................................................................... 122
Appendix B: Velocity-Measurement Technique ...................................................... 129
References .................................................................................................................. 135
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List of Tables
Number
Page
Table 2.1: Selection criteria for WMS parameters.................................................... 21
Table 4.1: Gas conditions along laser LOS for NASA HDCR isolator. .................... 53
Table 4.2: Gas conditions along laser LOS for T2 shock tunnel. .............................. 57
Table 5.1: Linestrengths and self-broadening coefficients (HWHM) at 296K. ........ 70
Table 5.2: Air-broadening coefficients (HWHM) at 296 K. ...................................... 71
Table 7.1: Nozzle exit plane conditions for Mach 6 and 7 set points at NASA
Langley DCSCTF. .................................................................................... 104
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List of Illustrations
Number
Page
Figure 1.1: Wavelength range of availability for semiconductor diode lasers
[42]. ............................................................................................................... 3
Figure 2.1:
Lineshape function with full width at half-maximum (FWHM)
indicated [47]. ............................................................................................. 10
Figure 2.2: H2O fundamental vibrational modes. ..................................................... 13
Figure 2.3: H2O transition linestrengths from 1 – 2 μm. Primary vibrational
modes present in each band are labeled. ................................................... 14
Figure 2.4: Implementation of scanned-wavelength direct absorption technique. .. 15
Figure 2.5: Implementation of wavelength-scanned WMS technique. Data is
shown for signals collected during the NASA Langley test campaign:
λ=1349nm, T=990K, P=72kPa, XH2O=0.26, L=18.7cm. ............................. 17
Figure 2.6: Intensity (top panel) and frequency (bottom panel) modulation for
NEL diode laser at 50kHz. Modified from Reference [65]. ..................... 19
Figure 2.7: Intensity (top panel) and frequency (bottom panel) modulation of
slow-scan signal at 250Hz for NEL diode laser.
High-frequency
modulation is 255kHz. High-frequency modulation in the frequency
vs. time signal has been omitted for clarity. .............................................. 20
Figure 2.8:
a) Schematic of crossed-beam configuration for Doppler-shift
velocimetry.
b) Simulated frequency shift for direct absorption
lineshapes with λ=1349nm, 2θ = 90o, U = 1600m/s, T = 915K, P =
0.68atm, XH2O = 0.26, L = 18.7cm. ............................................................. 26
Figure 3.1: Simulations of H2O transition at 1341nm for P=72kPa, T=990K,
XH2O=0.25, and L=18.8cm.
a) Absorbance.
b) 1st derivative of
absorbance. c) Absolute value of 2nd derivative of absorbance................ 30
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XH2O=0.25, and L=18.8cm. a) Absorbance. b) WMS-1f lineshape. c)
WMS-2f lineshape. d) WMS-2f/1f lineshape. Modulation index for
WMS simulations is 1.6. Absorption linecenter frequency indicated
by dashed line............................................................................................. 32
Figure 3.3: Simulated WMS signals for varying absorbance (or optical depth).
Same conditions as those for Figure 3.2 are used, and absorbance is
varied by changing path length. Modulation index m=2.2. a) WMS-1f
lineshape. b) WMS-2f lineshape. c) WMS-2f/1f lineshape..................... 36
Figure 3.4:
Simulation of lock-in amplifier outputs for WMS-1f signals in
Figure 3.3: a) X1f . b) Y1f. ....................................................................... 37
Figure 3.5: Normalized amplitudes of: a)
index.
WMS-2f signal versus modulation
b) 1f-normalized WMS-2f signal versus modulation index.
Simulation is for H2O transition at 1341.5nm with absorbance = 15%. .. 38
Figure 3.6:
Simulations of WMS signals with varying modulation index:
a) WMS-1f. b) WMS-2f. c) WMS-2f/1f. Same conditions as Figure
3.2 are used with absorbance = 15%. ........................................................ 39
Figure 4.1: a) NASA DCSCTF isolator section with TDLAS mass-flux sensor
configured for vertical translation. b) CFD geometry for DCSCTF
isolator (symmetry about vertical axis is assumed) with vertical
translation configuration shown.
c)
CFD geometry for DCSCTF
isolator with horizontal translation configuration shown. ....................... 45
Figure 4.2:
a) CFD pressure data along laser LOS in vertical translation
configuration (units are Pa). b) Temperature, pressure, and velocity
data along LOS at the vertical center of duct. .......................................... 46
Figure 4.3: Frequency-shifted path-integrated WMS-2f/1f lineshapes simulated
from CFD data. Frequency shift corresponds to a 1600m/s core flow. .... 47
Figure 4.4: a) Measured velocities from path-integrated lineshapes with varying
boundary-layer thickness. The position along lineshape refers to the
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location on the lineshape used for Doppler-shift measurement, with 0
corresponding to the valley and 1 corresponding to the central peak.
b) Mean difference between measured velocity of Figure 4.4a and core
velocity versus combined boundary-layer thickness as percentage of
an 18.7cm path length. ............................................................................... 48
Figure 4.5: Energy-temperature curve for water vapor. .......................................... 51
Figure 4.6: Velocity and temperature distributions along simulated beam path in
NASA HDCR isolator................................................................................. 53
Figure 4.7: Measured velocities from path-integrated lineshapes for: a)
1365.6nm line. b) 1487nm line. Modulation index is 0.9. The position
along lineshape refers to the location on the lineshape used for
Doppler-shift measurement, with 0 corresponding to the valley and 1
corresponding to the central peak. ............................................................ 54
Figure 4.8: Measured velocities from path-integrated lineshapes for: a)
1365.6nm line. b) 1487nm line. Modulation index is 2.2. The position
along lineshape refers to the location on the lineshape used for
Doppler-shift measurement, with 0 corresponding to the valley and 1
corresponding to the central peak. ............................................................ 55
Figure 4.9: Temperatures measured from path-integrated WMS lineshapes.
High E” refers to 1487nm line, low E” refers to 1365.6nm line. ............... 56
Figure 4.10: Velocity and temperature distributions along simulated beam path
in T2 shock tunnel. ..................................................................................... 57
Figure 4.11: Measured velocities from path-integrated lineshapes for:
a) 1365.6nm line. b) 1487nm line. Modulation index is 0.9. The
position along lineshape refers to the location on the lineshape used
for Doppler-shift measurement, with 0 corresponding to the valley
and 1 corresponding to the central peak. .................................................. 58
Figure 4.12: Measured velocities from path-integrated lineshapes for:
a) 1365.6nm line. b) 1487nm line. Modulation index is 2.2. The
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position along lineshape refers to the location on the lineshape used
for Doppler-shift measurement, with 0 corresponding to the valley
and 1 corresponding to the central peak. .................................................. 59
Figure 4.13: Temperatures measured from path-integrated WMS lineshapes.
High E” refers to 1487nm line, low E” refers to 1365.6nm line. .............. 60
Figure 5.1: Two-laser frequency-multiplexed WMS sensor for mass flux at H2O
wavelengths λ 1 and λ2 (~1349 and 1341.5nm). The two lasers are
combined on a single fiber and then split to be directed upstream and
downstream in the supersonic flow with a crossing angle 2θ. Velocity
is determined from the relative Doppler shifts of the absorption
lineshape, and gas temperature from the ratio of the two absorption
signals. ........................................................................................................ 64
Figure 5.2: Schematic of data flow for WMS-based TDLAS mass-flux sensor.
Temperature is measured from WMS signals for both wavelengths
and velocity is simultaneously measured from the relative Doppler
shift of an absorption feature. Temperature and pressure are used to
determine density, and coupled with the velocity measurement to
determine mass flux. .................................................................................. 65
Figure 5.3: Experimental setup for measurement of linestrength and pressurebroadening coefficients in Stanford heated cell [55]. ................................ 67
Figure 5.4:
a) Measurement of linestrength at 400K for 1349nm line.
b) Measurement of self-broadening coefficient (FWHM) at 400K for
1349nm line. ............................................................................................... 69
Figure 5.5:
a) Measured linestrength versus temperature for 1341nm and
1349nm lines.
b) Measured air-broadening coefficient (HWHM)
versus temperature for 1349nm line.
Best fits from HITRAN
database also shown for comparison. ........................................................ 70
Figure 5.6: Simulated absorbances for 1349nm (left panel) and 1341.5nm (right
panel) lines. Spectroscopic data from Tables 5.1 and 5.2 are used.
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Conditions are P=72kPa, T=990K, XH2O=0.26, L=18.7cm (vertical
translation) or L=10.35cm (horizontal translation). ................................. 71
Figure 5.7: Schematic of a DFB diode laser. .............................................................. 73
Figure 5.8:
Transmission of light in a step-index single-mode fiber optic
waveguide. Core enlarged for illustration. ............................................... 74
Figure 5.9: Schematic of 2x2 evanescent wave 50/50 coupler. Inset shows crosssection of coupler. ....................................................................................... 75
Figure 5.10: TDLAS sensor optomechanical components: a) Pitch assembly.
b) Catch assembly. Red dashed lines indicate window surface. .............. 78
Figure 5.11: Zaber T-LSR 150B translation stage. ................................................... 79
Figure 5.12:
Fully assembled TDLAS mass-flux sensor mounted on NASA
Langley wind tunnel: a) Pitch assembly. b) Catch assembly. ................ 80
Figure 5.13: Signal flow between computer and DAQ system. Computer is used
to generate laser current modulation waveforms; voltage signals are
produced by the DAQ cards and sent to the laser controller which
modulates laser injection current. Detector signals are digitized by
DAQ cards and sent to computer for storage. ........................................... 81
Figure 5.14:
Generation of laser drive signals.
Slow scan shown on left,
complete WMS laser drive signals shown on right. Amplitudes are in
volts. ............................................................................................................ 82
Figure 6.1: Experimental setup for temperature validation in 3-zone heated cell.
Single-pass setup shown; actual experiment performed for 3 passes ....... 84
Figure 6.2: Measured and calculated 1f-normalized 2f peak ratio for the high E”
line (1341nm) divided by the low E” line (1349nm). ................................. 85
Figure 6.3: Comparison of sensor- and thermocouple-measured temperatures in
Stanford heated cell. ................................................................................... 86
Figure 6.4:
Stanford Flow Control Wind Tunnel with mounted sensor
hardware. Beam paths through test section indicated by dark arrows. .. 87
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Figure 6.5: Schematic of velocimetry validation experiment at Stanford Flow
Control Wind Tunnel................................................................................. 88
Figure 6.6: Doppler-shifted lineshapes for 1371nm transition in Stanford Flow
Control Tunnel. Shift corresponds to velocity of 18m/s. ......................... 89
Figure 6.7:
Velocity measurements in Stanford high-uniformity tunnel:
a) Time-resolved velocity measurements for modulation index of 0.9
and 1.7. b) Measured velocity with one second resolution versus
tunnel set point. .......................................................................................... 90
Figure 7.1: Photograph of the DCSCTF at NASA Langley showing flowpath
sections as labeled. ..................................................................................... 92
Figure 7.2: Schematic of NASA Langley DCSCTF [120]. ........................................ 93
Figure 7.3: Illustration of flow through a scramjet engine [129].............................. 95
Figure 7.4: Modified DCSCTF isolator section for TDLAS mass-flux sensor.
Beam paths in horizontal and vertical translation configurations also
indicated (red arrows). .............................................................................. 96
Figure 7.5: Cross-sectional view of sidewall window mount for isolator section.
Ray trace for 45o incident beam also shown. ............................................ 98
Figure 7.6: Schematic of experimental setup for TDL mass-flux measurements
at NASA Langley DCSCTF. .................................................................... 100
Figure 7.7: Experimental setup in DCSCTF control room..................................... 101
Figure 7.8: Mass-flux sensor installed on custom-isolator section: a) Sensor
configured to probe vertical planes of the flowpath; arrows illustrate
the beampaths. b) Sensor configured to probe horizontal planes of the
flowpath.................................................................................................... 101
Figure 7.9:
Measurement locations for spatially resolved data acquisition.
Translation directions are indicated with blue arrows, locations
indicated with yellow markers. Flow is into the page. ........................... 103
Figure 7.10: Signals collected for 1341.5nm laser in the vertical translation
configuration with beams crossing in the center horizontal plane
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during NASA Langley DCSCTF measurement campaign: a) Timeresolved WMS-2f/1f signals for both beams.
b) Measured WMS
lineshapes vs. frequency for both beams. ................................................ 104
Figure 7.11: Time-resolved velocity in the middle of the channel, horizontal
plane: a) no correction b) with correction for nonuniformity along
LOS. .........................................................................................................................
Figure 7.12: Gas temperature for downstream- and upstream-pointing beams:
a) In the center horizontal plane for the Mach 7 flight condition.
b)
In the center vertical plane for the Mach 6 flight condition.
Facility model value also shown. .............................................................. 108
Figure 7.13:
Mass flux using temperatures taken with downstream- and
upstream- pointing beams and BL-corrected velocity: a) In the center
horizontal plane for the Mach 7 flight condition. b) In the center
vertical plane for the Mach 6 flight condition. Facility model value
also shown. ................................................................................................ 109
Figure 7.14: Spatially resolved velocity (no correction applied) plotted from:
a) Left to right of channel (facing downstream) in vertical planes.
b) Top to bottom of channel in horizontal planes. Solid data points
indicate measurements taken during facility startup transient. ............. 110
Figure 7.15 Spatially resolved mass flux (no correction applied) at Mach 7
condition plotted from: a) Left to right of channel (facing
downstream) in vertical planes.
b) Top to bottom of channel in
horizontal planes. ..................................................................................... 111
XH2O=0.25, and L=18.8cm.
a) WMS-3f lineshape.
b) WMS-4f
lineshape. c) WMS-5f lineshape. d) WMS-6f lineshape. Modulation
index is 2.2. ............................................................................................... 118
Figure 8.2: Simulation of WMS-4f/2f signal for same conditions as Figure 8.1. .... 119
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106
Figure 8.3: Experimental setup for single-beam TDLAS mass-flux sensor. Inset
shows basic principle of retroreflector operation. .................................. 120
Figure A.1: Illustration of electromagnetic wave propagation for: a) Linear
polarization. b) Circular polarization. c) Elliptical polarization.
Direction of electric field vector is indicated by arrows. ........................ 122
Figure A.2:
Various types of polarization-maintaining fiber:
a) PANDA.
b) Elliptical cladding. c) Bow-tie. ........................................................... 123
Figure A.3: Illustration of polarization for light transmitted in: a) Standard
single-mode fiber.
b) PM single-mode fiber.
direction of electric field vector.
Arrows indicate
Relative size of internal fiber
components not drawn to scale................................................................ 124
Figure A.4: Illustration of bend loss in a fiber. Bend is exaggerated for display
purposes. .................................................................................................. 125
Figure A.5: Experimental setup for zero-velocity measurements. A single laser
is split into two beams and passed through the isolation pipe. The
beams are focused with mirrors onto detectors to monitor absorption
of atmospheric water vapor, and velocity is measured from the
frequency shift between absorption features measured on either
beam. ........................................................................................................ 127
Figure A.6: Comparison of zero-velocity measurements using 1349nm transition
at atmospheric pressure with ambient water vapor and L=68.6cm.
Left panel shows velocity measurements taken with a non-PM laser;
right panel shows measurements with a PM laser. ................................. 127
Figure B.1:
Comparison of zero-velocity measurements using WMS-2f and
WMS-2f/1f at atmospheric pressure with ambient water vapor and
L=68.6cm: a) 2f lineshapes for 1371nm line. b) Measured velocity
from 2f signals. Panels c) and d) show the corresponding results for
WMS-2f/1f. ............................................................................................... 130
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Figure B.2: Illustration of Doppler-shift measurement regions on WMS-2f/1f
lineshape: a) WMS-2f/1f signals for 1341nm line on upstream- and
downstream-pointing
beams.
T=990K,
P=72kPa,
XH2O=0.26,
L=18.7cm, m=0.9. b) Doppler-shift measurement regions highlighted
in blue and green. c) Normalized Doppler-shift measurement regions. 132
Figure B.3:
Illustration of velocity measurement algorithm for WMS-2f/1f
lineshapes. The 2f and 1f signals are obtained from detected signals
using a lock-in amplifier and converted to the frequency domain using
the etalon transfer function.
The central peak of the WMS-2f/1f
lineshape is then divided in two halves, normalized, and frequency
shifts are measured and converted to velocity......................................... 133
xxv
xxvi
Chapter 1: Introduction
1.1 Motivation and Background
A major initiative for research in the aerospace and propulsion sector is the
development of next-generation propulsion systems and improvement of the performance
and efficiency of conventional engines. In response, there is a growing need for the
development of accurate diagnostics to monitor and assess the performance of both
propulsion systems and the supporting test facilities.
One of the most essential
diagnostics is the measurement of mass flux, defined as the product of gas density and
velocity. Mass flux is directly used in the thrust equations for air-breathing engines such
as turbojets [1] and scramjets [2,3] as well as rocket propulsion systems [4,5]. Other
parameters related to engine operation such as the intake momentum drag (resulting from
momentum ingested by the engine inlet) [6], inlet flow distortion [7], and combustor
stability [8] are also dependent on mass flux. In a scramjet for example, a measurement
of mass capture to within 1% uncertainty is necessary for a 1% uncertainty in the specific
impulse [9]. Hence there is motivation to include an accurate measurement of gas mass
flux during both in-flight and ground-testing of propulsion systems to monitor vehicle or
facility operation and to determine the aerodynamic parameters of the system.
Conventional methods for measuring mass flux in ground-test facilities use total
and static pressure probes together with total temperature probes or thermocouples
[10,11].
These invasive mass-flux probes tend to disturb the flow, generate shock
structures, and may have limited ability to survive long-duration runs [12]. Furthermore,
water-cooling is often necessary to ensure the survival and operability of total
temperature probes above 755K [13]. Accurate temperature measurements using these
instruments also require complex models for heat transfer from the thermocouple bead
within the probe [14]; this adds further complexity to the data processing as well as
1
additional sources of error. In contrast, optically-based measurement techniques offer a
noninvasive, robust, and highly accurate method for determining gas mass flux.
A variety of laser-based techniques can be deployed for mass-flux measurements.
Gas density can be measured from Rayleigh [15,16] or Raman [17] scattering, laserinduced fluorescence (LIF) [18,19], laser interferometry [20], or laser absorption
spectroscopy. A major disadvantage of scattering and LIF techniques is their reliance on
large, high-power lasers and expensive camera systems. High laser powers are necessary
due to the low signal levels from scattering processes. This inhibits the ability for inflight measurements, and severely limits potential ground-testing facilities since few
institutions can make the sizable capital investment and accommodate large laser systems
at their test facilities. Scattering and LIF techniques provide measurements at a point; in
contrast laser interferometry and absorption are line-of-sight techniques. Interferometry
measurements suffer from high sensitivities to mechanical vibrations and fluctuations in
the gas properties along the line of sight. This limits the usefulness of these techniques to
controlled laboratory settings. However, absorption spectroscopy techniques for density
measurement can be designed to be highly robust, easily implemented, and insensitive to
perturbations of gas conditions in the beam path [10,12,21-27].
A number of laser-based velocity measurement techniques also exist, the most
common being laser Doppler velocimetry (LDV) [15,28-30] and particle image
velocimetry (PIV) [30-32]. While LDV can provide highly resolved measurements of
velocity, its drawbacks include low signal-to-noise ratio (LDV is also a scattering-based
technique), high sensitivity to alignment, the need for particle seeding, and high cost of
lasers and signal processing equipment [28]. PIV can provide spatially resolved images
of velocity components in multiple dimensions; its drawbacks are similar to LDV –
namely expensive equipment and the necessity for flow seeding. Flow seeding can be
particularly troublesome, since it requires modification of facility hardware, routine
cleaning of the facility walls, and proper tracer particle selection (some of which are
toxic). Great care also must be taken to ensure the tracer particles are homogeneously
distributed and properly sized such that they faithfully follow the flow. Other velocity
2
measurement techniques include laser-induced thermal acoustics (LITA) [33,34] and
Raman scattering [35,36]. The LITA technique operates on the basis of a density grating
produced by thermalization or electrostriction at the intersection of two coherent beams;
an interrogation beam can then be scattered into the grating, and velocity can be
determined from the Doppler-shifted scattered signal [37,38]. This technique is capable
of producing highly accurate velocity results (0.2% accuracy in a 150m/s flow [39]).
However, large high-power lasers are required, and the necessity for multiple-beam
mixing significantly increases the experimental complexity. Raman scattering techniques
have also been demonstrated for accurate velocimetry; however, the integration times are
prohibitively long (>10 minutes) and it has the typical problems of scattering techniques:
a reliance on high-power lasers and susceptibility to a low SNR [35,36]. In contrast,
absorption techniques (based on Doppler shift) do not require particle seeding, and can be
deployed with compact, inexpensive diode lasers [10,12,21-25,27,40,41].
The
experimental setup is quite straightforward, and the necessary data processing for
absorption techniques is also far less complex and time-consuming than LDV and PIV.
Another advantage of absorption techniques is the ability to access mature tunable
diode laser technology over a large spectrum of wavelengths. Figure 1.1 illustrates the
range over which room temperature semiconductor lasers are available.
Figure 1.1: Wavelength range of availability for semiconductor diode lasers [42].
3
Of particular relevance for this work is the set of lasers centered around 1.3 µm that have
been produced for the telecommunications industry. Due to decades of development,
TDLs in this wavelength range have decreased in cost, improved in reliability and
performance, and have decreased in both weight and size.
Furthermore, these diode
lasers are often fiber-pigtailed to conveniently interface with fiber optic components.
These characteristics are particularly important for deployment in the field, where
limitations on size, power consumption, and cost are commonly encountered.
Because of these advantages, tunable diode laser absorption spectroscopy
(TDLAS) has been deployed as a robust, noninvasive measurement technique for the
harsh environments commonly experienced in high-speed or combusting propulsion
flows [43,44]. Mass-flux sensing via TDLAS was pioneered by Philippe and Hanson
[27] and patented for thrust measurements in 1993 [45]. Subsequent TDL mass-flux
sensors have been deployed for a variety of field tests including a commercial turbofan
(PW6000) inlet at Pratt and Whitney [23], a full-scale Pratt & Whitney F-100 engine in
an open ground-test stand at the NASA Dryden Flight Research Facility [10], and a
model scramjet combustor at Wright-Patterson Air Force Base [12].
In this work, a TDLAS mass-flux sensor was designed and deployed at a
combustion-heated Mach 2.7 wind tunnel at NASA Langley. The target facility operates
as a part of NASA Langley’s Scramjet Test Complex, simulating hypersonic atmospheric
flight conditions for testing of scramjet components. Because the facility is combustionheated, a large mole fraction of water vapor is present in the test gas; hence H2O was
targeted as the absorbing species for the TDL sensor. A major goal of this work was to
assess the accuracy of TDLAS measurements of mass flux by comparison with facility
predictive code and computational fluid dynamics (CFD) solutions. Validation of the
sensor measurements provides confidence in deploying the sensor in less wellcharacterized flow conditions, e.g. scramjet inlet models where mass capture is poorly
known. Additionally, the facility provided an excellent environment to obtain spatially
resolved measurements for comparison with CFD, allowing for the effects of flow
nonuniformity on line-of-sight measurements to be assessed.
4
1.2 Overview of Dissertation
The dissertation is organized as follows:
1) Chapter 1 describes the motivation for mass-flux measurement in the area of
aerodynamics and propulsion. Benefits of optical diagnostic techniques are
discussed, and the background and history of TDL mass-flux sensing is
reviewed.
2) Chapter 2 examines the fundamentals of absorption spectroscopy, which is
central to the sensor designed in this work. The theory and implementation of
both direct absorption (DA) and wavelength modulation spectroscopy (WMS)
techniques are discussed.
The temperature and velocity measurement
methodologies implemented in this work are then introduced.
3) Chapter 3 examines in further detail 1f-normalized wavelength modulation
spectroscopy with 2f detection (WMS-2f/1f ), a modified form of WMS. The
influence of optical depth and laser modulation on the absorption lineshape is
investigated, and this analysis is used to optimize the lineshape for velocity
measurements.
4) Chapter 4 addresses the issue of nonuniformity with regard to line-of-sight
measurements. Lineshapes are simulated using nonuniform gas conditions,
and the influence on the resulting measurement is assessed. For the case of
the NASA Langley sensor, a simple correction for flow nonuniformity is
formulated for velocity. A general analysis of the effects of temperature and
velocity nonuniformity is presented, leading to the development of design
rules to minimize nonuniformity effects on LOS measurements.
5) Chapter 5 outlines the overall sensor architecture.
Line selection and
fundamental spectroscopy measurements are discussed, and the experimental
hardware for the sensor is described in detail.
6) Chapter 6 presents the temperature and velocity validation experiments that
were performed at Stanford. These experiments proved the sensor’s accuracy
5
in determining both temperature and velocity against well-known conditions,
and successfully tested the sensor hardware and data acquisition systems.
7) Chapter 7 describes the field campaign at the NASA Langley Direct-Connect
Supersonic Combustion Test Facility. The mass-flux sensor was deployed for
temporally and spatially resolved measurements in a modified isolator section.
These results were compared with the facility predictive code and CFD
solutions.
8) Chapter 8 proposes areas for further research and summarizes the work
described in the thesis.
9) Appendix A examines the background of polarization-maintaining optical
components and the associated benefits to using these components for TDLAS
sensing. Appendix B describes the algorithm and data processing scheme
developed for sensitive detection of velocity.
6
Chapter 2: Absorption Spectroscopy
Theory and Measurement Techniques
The sensor developed for this work relies on absorption spectroscopy, through
which the physical properties of a gas can be extracted from interaction with light. This
provides the capability to probe the properties of gases in harsh environments without the
need to physically access the test gas. In this section, the fundamentals of absorption
spectroscopy are introduced, and the primary methods through which spectroscopy can
be applied for quantitative measurements are described. The details of the velocity and
density measurement techniques incorporated into the mass-flux sensor are also
presented.
2.1 Absorption Spectroscopy Theory
Absorption spectroscopy is rooted in quantum theory, which requires that the
interaction between mass and radiation occur in discrete amounts (quanta). This theory,
first proposed by Max Planck, governs the change in energy level, ΔE, that may occur
within an atom or molecule when it interacts with a photon [46].
∆E =
hf
(1)
Here h is Planck’s constant and f is the frequency of the photon. The terms wavelength λ
[nm], frequency f [Hz], and wavenumber ν [cm-1] are often used interchangeably in
spectroscopy, as they are related through a constant – the speed of light, c [m/s]:
c
= cν
=
λ
7
f
(2)
Hence the wavelength (or frequency) of light can be described by any of the three
aforementioned terms.
Because of the quantization of energy, only certain transitions are allowed
between the internal energy modes (nuclear, rotational, vibrational, and electronic) of an
atom or molecule. Illumination by light at a resonant wavelength can cause the target
species to absorb a photon and enter an excited energy state (absorption); conversely, the
atom or molecule can be induced to drop to a lower energy state and emit a photon
(emission). The relative population of molecules in various energy states is governed by
Boltzmann statistics; at a given temperature, some energy states may be more populated
than others, resulting in absorption of more photons by highly populated states.
Since resonance is restricted to particular wavelengths, lasers provide the ideal
light source; they produce coherent, monochromatic light that is rapidly wavelengthtunable and spectrally narrow. Hence the laser can be scanned over the frequency range
of an absorption transition to give full spectral resolution of the lineshape (absorption
transitions do not occur exactly at the resonant wavelength – they are spectrally
broadened through a variety of mechanisms as discussed below).
In order to apply absorption spectroscopy for quantitative measurements, the
Beer-Lambert Law is used to describe the transmitted light intensity of a collimated beam
passing through an absorbing medium.
=
I t ,ν I 0,ν exp(−αν )
(3)
Here It and I0 refer to the transmitted and incident intensities, respectively, and αν is the
spectral absorbance. The subscript ν is retained to indicate dependence on the frequency
of the incident radiation.
For a spatially homogeneous absorbing medium, the
transmitted intensity can be expressed in a more explicit form:
n
m


It=
I 0,ν exp(−kν L=
) I 0,ν exp  − PL
Xi
Si , jφi , j (ν ) 
,ν
 =i 1 =j 1



∑ ∑
8
(4)
The spectral absorbance has now been defined as the product of kν, the spectral
absorption coefficient, and L [cm], the total path length through the absorbing medium.
The spectral absorption coefficient is a function of the static pressure, P [atm], the mole
fraction of absorbing species i, Xi, the linestrength of transition j for absorbing species i,
Sij [cm-2/atm], and the lineshape function of transition j for species i at frequency ν, φi, j (ν )
[cm]. In the 1.3 μm range, where the current sensor operates, the primary absorber is
H2O, and Equation 4 can be simplified to describe a single absorbing species:
m




−
=
−
It=
I
k
L
I
PXL
S
φ
ν
exp(
)
exp
(
)
ν
,ν
0,ν
0,ν
j j


j =1


∑
(5)
The above equations now elicit the functional dependence of light transmission on
temperature, pressure, and gas composition. Pressure and mole fraction appear explicitly,
while the linestrength is solely a function of temperature, and the lineshape function is a
complex function of both temperature and pressure. The temperature dependence of the
linestrength is given by the following equation:

 −hcν 0
1 − exp 


Q(T0 ) T0
hcE "  1 1  
 kT
exp 
S (T ) S (T0 ) *
=
 − 
Q(T ) T
 k  T0 T   1 − exp  −hcν 0


 kT0






 
(6)
The linestrength is referenced to temperature T0 (typically 296K). Also appearing in
Equation 6 are the internal partition function Q, lower-state energy E” [cm-1], the
Boltzmann constant k, and the transition linecenter frequency, ν0. The lower-state energy
refers to the energy state of the molecule prior to absorption; by selecting a transition
from an appropriate E”, the desired temperature dependence of the linestrength can be
chosen. The internal partition function governs the distribution of a molecular population
among its various energy states as a function of temperature; the internal partition
function for H2O including vibrational and rotational modes is given by the following
equation:
9
π  kT 
QH 2O Q=
=
4
rot Qvib
ABC  hc 
3

 hcν i  
1 − exp 

 kT  
i =1...3 
∏
−1
(7)
The internal partition function of water is represented as the product of its rotational and
vibrational partition functions, Qrot and Qvib. In turn, the rotational partition function
depends on the moments of inertia about the three axes of the water molecule, A, B, and
C. The vibrational partition function is dependent on the three fundamental vibrational
modes of H2O as illustrated in Figure 2.2. Equations 6 and 7 will be discussed in further
detail in subsequent sections as the temperature dependence of absorption transitions is
examined.
The lineshape function describes the spectral distribution of the absorption
transition, and is dependent on various line-broadening mechanisms. Broadening arises
as a result of phenomena in the test gas which perturb the energy levels of an absorbing
atom or molecule; these perturbations cause slight changes in the frequencies at which
light is absorbed by the molecule. An illustration of the lineshape function for an isolated
transition (line) is reproduced from Reference [47] below.
∞
∫ φ (ν ) dν
= 1
−∞
Figure 2.1: Lineshape function with full width at half-maximum (FWHM)
indicated [47].
10
As shown in Figure 2.1, the integral of the lineshape function with respect to
frequency is defined to be unity. Hence Equation 5 can be integrated to obtain the
integrated absorbance, A for a single feature:
∞
∫
A=
− ln
−∞
I t ,ν
I 0,ν
dν =
SPXL
(8)
From the above equation, it is seen that the integrated absorbance is a direct function of
linestrength, pressure, and mole fraction; thus A can be used to make quantitative
measurements if two of these parameters (and the path length) are known.
The dominant forms of broadening at atmospheric flight conditions are Doppler
and collisional; other broadening mechanisms are negligible, and are discussed in further
detail in References [47,48]. Doppler broadening is a result of the same Doppler shift
upon which TDL velocity measurement is based (see Section 2.7).
At a given
temperature, the molecules of a gas follow a Maxwellian velocity distribution [49].
Molecules in different velocity classes will absorb photons at a frequency slightly
different from the resonant frequency due to the Doppler-shift effect. This leads to a
Doppler lineshape function, φD , with a Gaussian form:
2  ln 2 
=
φD
∆ν D  π 
1
2
2

 ν −ν 0  

exp −4 ln 2 
 
∆ν D  




(9)
The lineshape function depends on the linecenter frequency, ν0, and the Doppler FWHM,
ΔνD:
∆ν D
 8kT ln 2 
=
ν0 

 mc 2 
1
2
(10)
Here m is the molecular weight of the molecule. Equation 10 indicates that the Doppler
FWHM, and subsequently the Doppler lineshape, is strictly a function of temperature.
11
Collisional broadening is a result of the interaction between the electric fields of
molecules during a collision. Collisions change the distribution of internal energy within
molecules, and shorten the lifetime of a molecule in a particular energy state; in turn this
leads to increased uncertainty and causes collisional broadening following a Lorentzian
form:
φC =
1
2π
∆ν C
(ν −ν 0 )
2
 ∆ν 
+ C 
 2 
2
(11)
The collisional lineshape function, φC , is a function of the collisional FWHM, ΔνC:
∑X
∆ν C =
P
A 2γ
B− A
(12)
A
As seen above, the collisional FWHM increases with pressure. XA refers to the mole
fraction of collision partner A, and 2γB-A refers to the collisional broadening coefficient
between molecule A and the absorbing molecule B.
When Doppler and collisional broadening are dominant, the absorption lineshape
is a convolution of the two profiles, called the Voigt lineshape, φV :
φV =
2
∆ν D
ln 2
π
V ( a, w )
(13)
V(a,w) is the Voigt function, and the Voigt a and w parameters are given by the
following:
12
a=
w=
ln 2 ∆ν C
∆ν D
(14)
2 ln 2 (ν −ν 0 )
(15)
∆ν D
Because of the computational expense of calculating the explicit Voigt function
(involving complex integrals), numerical approximations are typically used. The above
equations now fully model the behavior of the absorption signal as a function of
temperature and partial pressure, setting the groundwork for quantitative absorption
spectroscopy measurements.
2.2 H2O Overtone and Combination Band at 1.4 μm
As previously mentioned, the species of interest for the current sensor is water
vapor due to its presence in large quantities in combustion-driven flows. H2O is a
nonlinear triatomic molecule and possesses three fundamental vibrational modes as
illustrated in Figure 2.2. Vibration of the atoms changes the electric dipole moment of
the molecule, allowing for interaction with light at resonant frequencies [50].
H
O
O
O
H
Symmetric stretch
ν1= 3652 cm-1
H
H
Symmetric bend
ν2= 1595cm-1
H
H
Asymmetric stretch
ν3= 3756 cm-1
Figure 2.2: H2O fundamental vibrational modes.
Absorption of a photon at any of the three H2O fundamental vibrational
frequencies can induce the molecule into an excited vibrational state. Similarly, rotation
of the molecule also causes oscillation of its dipole, and an absorbed photon at a resonant
frequency can excite the molecule to a higher rotational energy state. Transitions are also
13
allowed at overtones (2νi, 3νi, etc.) and combinations (νi+νj, 2νi+νj, etc.) of the
fundamental frequencies, although the transition strength is diminished. Simultaneous
changes in rotational and vibrational energy (vibrotational transitions) or rotational,
vibrational, and electronic energy (rovibronic transitions) can also occur.
The water vapor vibrotational transitions in the region of 1.3 – 1.5 μm originate
from five vibrational bands: 2ν1, 2ν3, ν1+ν3, 2ν2+ν3, 2ν2+ν1 [51,52]. A total of 3523 H2O
transitions are documented in the HITRAN [53] database from 6700 – 7700cm-1, making
this wavelength region attractive when selecting lines for a tunable diode laser absorption
spectroscopy (TDLAS) sensor. The linestrengths for water vapor transitions in the 1 – 2
μm range are plotted in Figure 2.3.
HITRAN database, H2O at 300 K
1
10
0
-1
10
-2
S [cm /atm]
10
Telecom diode lasers available
ν2+2ν3
2ν1+ν2
ν1+ν2+ν3
2ν3, ν1+ν3, 2ν1
ν1+ν2
ν2+ν3
-2
10
-3
10
-4
10
1.0
1.2
1.4
1.6
Wavelength [µm]
1.8
2.0
Figure 2.3: H2O transition linestrengths from 1 – 2 μm. Primary vibrational modes
present in each band are labeled.
As previously discussed, a major benefit to working in the 1.4 μm absorption
band is the widespread availability of telecommunications diode lasers and fiber optic
components. Robust, inexpensive light sources are readily available to access a wide
array of wavelengths. This facilitates the development of multiple-wavelength sensors to
simultaneously investigate multiple gas parameters.
14
In particular, the rapid tuning
characteristics, compact size, and low power requirements of tunable diode lasers make
them an ideal choice for deployment in field campaigns.
2.3 Direct Absorption Spectroscopy
Scanned-wavelength direct absorption spectroscopy has been the traditional
technique for absorption-based measurements in gases for many years. Implementation
of a direct absorption sensor is quite straightforward, and measurements of line-of-sight
gas temperature and species concentration can be made with excellent accuracy [54-56].
The implementation of scanned-wavelength direct absorption spectroscopy is illustrated
Gas
sample
Baseline fit
+
Beer’s Law
Intensity
Laser
Detector
Time
Absorbance
in Figure 2.4.
Integrated
absorbance
Time
Figure 2.4: Implementation of scanned-wavelength direct absorption technique.
For diode lasers, wavelength scanning is typically accomplished by temperaturestabilizing the laser and modulating the injection current with a sawtooth waveform. This
causes a simultaneous ramping of the laser intensity and wavelength. A laser can then be
wavelength-tuned over the spectral range of an absorption transition, producing the
detected signal shown in the intensity vs. time plot of Figure 2.4. Using a baseline fit and
applying Beer’s Law (Equation 3), the detected signal can be converted to absorbance,
which in turn can be used to determine properties of the absorbing species such as
temperature and mole fraction. The advantage of the DA technique is its simplicity;
implementation is straightforward and calibration-free. However, large measurement
uncertainty can arise in harsh, noisy environments where fluctuations in laser
transmission can cause errors in baseline fitting. At high pressures, broadening of the
absorption lineshape also limits the ability to resolve the baseline.
15
2.4 Wavelength Modulation Absorption Spectroscopy
Wavelength modulation spectroscopy (WMS) relies on the same spectroscopic
theory as direct absorption, although the analysis and implementation are significantly
more complex. The primary benefits of the WMS technique are:
•
Rejection of low-frequency noise produced by the test environment, e.g. vibration
or emission by shifting detection of the absorption signal to a much higher
frequency.
•
Removal of the necessity for baseline fitting as in the DA technique.
•
Increasing the minimum detectable absorbance by orders of magnitude over the
DA technique.
•
Removal of the effects of non-absorption-related laser transmission fluctuations
produced by the test environment (with 1f-normalization of WMS-2f signal).
WMS measurements have been proven to be highly accurate, sensitive, and noiseresistant in harsh environments where direct absorption can suffer from a poor signal-tonoise ratio (SNR) [57-60]. The basis of the WMS technique is the application of a highfrequency modulation to the laser injection current. The simultaneous frequency and
intensity modulation of the laser light causes harmonics of the modulation frequency to
arise upon interaction with an absorption feature. These harmonics can be isolated with a
lock-in amplifier and compared to models to infer mole fraction and temperature. The
WMS technique can be implemented in two modes:
•
Fixed-wavelength: The laser center wavelength is fixed at the transition
linecenter frequency while high-frequency modulation is applied and the 2f peak
signal is recorded. The 2f peak signal is considered for measurements since its
sensitivity to laser modulation parameters is minimized [59]. This form of WMS
is capable of very high-bandwidth measurements, and is particularly useful for
measurements involving blended spectra (common at high pressures) [59].
Typically, the laser center frequency is tuned in a small range about the linecenter
frequency to ensure that the 2f peak is resolved (the laser center frequency may
16
not be exactly at linecenter due to current/temperature controller drift, laser drift,
and pressure or Doppler shifting).
•
Scanned-wavelength: The laser wavelength is tuned over all or part of the
spectral range of the transition lineshape. Because the laser is tuned over a larger
wavelength range, the effective time response of the sensor decreases. However,
this technique allows for the complete spectral resolution of a transition for both
thermometry and Doppler-shift velocimetry.
Implementation of the scanned-
Gas
sample
Time
Lock-in
@ 1f
2f peak
height
Time
1f signal
Σ
Lock-in
@ 2f
Intensity
Detector
2f signal
wavelength WMS technique is illustrated in Figure 2.5.
1f value
@2f peak
location
Time
Figure 2.5: Implementation of wavelength-scanned WMS technique. Data is shown
for signals collected during the NASA Langley test campaign: λ=1349nm, T=990K,
P=72kPa, XH2O=0.26, L=18.7cm.
As seen above, the laser injection current drive signal consists of a high-frequency
(f ) sinusoid superimposed on a lower frequency (fslow) wavelength scan. In practice it is
preferable to use a sine wave for the low-frequency scan to avoid adding higher
harmonics of this scan frequency to the signal [61]. In the intensity vs. time plot of the
figure above, the high-frequency modulation is seen superimposed on the slow scan; the
distortion of the detected signal due to absorption is also seen as the laser frequency is
scanned through the spectral range of the transition. The detected signal is then input to a
lock-in amplifier [62,63] which isolates the harmonics at the frequencies of interest,
namely 1f and 2f. Operation of the lock-in amplifier is quite simple; the input signal is
multiplied by a reference sinusoid at the required frequency (1f or 2f for the current
17
sensor), which shifts the harmonic signals to DC.
The software lock-in can be
implemented for multiple wavelengths in real-time, with the ability to extract any number
of harmonics simultaneously. A low-pass filter is then used to isolate the harmonic
signal. Having obtained the 1f and 2f signals, calibration-free WMS can be applied by
comparing the measured signals to simulations in order to infer temperature and mole
fraction [57,58,61,64-66]. As indicated in Figure 2.5, the relevant measurements for this
analysis are the 2f peak height and the corresponding 1f value at the 2f peak location.
In the remainder of this section, the fundamental equations necessary for the
application of the 1f-normalized WMS-2f technique are presented for current-tuned
TDLs. The theory of WMS-2f has been studied and reported extensively [57,61,65-72],
but enough is reproduced here to define terms and allow the reader to understand the
details
of
the
sensor
design.
Nomenclature
follows
that
of
References
[21,40,57,61,64,65]. The instantaneous laser frequency and intensity of a current-tuned
TDL are governed by:
ν (t )=ν (t ) + a cos(2π ft )
I 0 (t ) =+
I 0 (t ) i0 cos(2π ft + ψ 1 )
(16)
(17)
In Equation 16, ν (t ) is the laser frequency [cm-1] averaged over the modulation (with time
dependence due to the slow scan), f is the modulation frequency [Hz], and a is the
modulation depth [cm-1]. In Equation 17, I 0 (t ) is the laser intensity averaged over the
modulation (again with time dependence due to the slow scan), i0 is the linear intensity
modulation amplitude, and ψ1 is the linear phase shift between intensity and frequency.
The nonlinear intensity modulation terms have been omitted as they tend to be
insignificant at the moderate modulation depths used for WMS at or below atmospheric
pressures [65]. To successfully model the WMS signal, the parameters a, i0, and ψ 1 must
be known. These parameters are specific to a given laser current, temperature, and
modulation frequency and must be measured each time these values change. Figure 2.6
illustrates the measurement technique for the laser modulation parameters.
18
I0
i0
ν
a
Figure 2.6: Intensity (top panel) and frequency (bottom panel) modulation for NEL
diode laser at 50kHz. Modified from Reference [65].
The top panel shows the intensity modulation of a DFB laser as the high-frequency
modulation (50kHz) is applied to the injection current; simultaneously, the laser
frequency modulation is shown in the bottom panel as obtained from the interference
signal produced as the laser is fed into a ring etalon. The parameters a, i0, and ψ1 are
measured as indicated in Figure 2.6. The complete details of these measurements are
given in more detail by Li et al. [65].
Equations 3, 16, and 17 can now be combined to express the transmitted intensity
for WMS:
I t (t ) =  I 0 (t ) + i0 cos(2π ft + ψ 1 )  exp [ −α (ν (t ) + a cos(2π ft )) ]
(18)
If the slow-scan time dependence is neglected, this function is even and can be expanded
using the Fourier cosine series:
19
∞
∑
exp [ −α (ν + a cos(2π ft )) ] =H k (ν , a) cos(2π kt )
(19)
k =0
1
H 0 (ν , a ) =
2π
π

exp  − Pi L

−π
∫
π

1
H k (ν , a ) = exp  − Pi L
π

−π
∫

∑ S φ (ν + a cos(ξ )) dξ
j j
(20)

j

∑ S φ (ν + a cos(ξ )) cos(kξ ) dξ
j j
j
(21)

The spectral absorbance has now been expressed as in Equation 5, where Pi is the partial
pressure of the absorbing species, Sj is the linestrength of absorption feature j, and φ j is
the lineshape of absorption feature j. Note that in Equations 20 and 21, the integration
variable is designated as ξ instead of θ as in References [40,61,64,65]. This is due to the
fact that θ appears in later equations as the crossing half-angle used in crossed-beam
Doppler-shift velocimetry. The parameters ν and I 0 are the laser frequency and intensity
averaged over the modulation at the midpoint of the slow scan as indicated in Figure 2.7.
Intensity [V]
4.5
I0
4.0
A
Frequency [cm-1]
3.5
0.6
ν
0.4
0.2
Aν
0.0
0
5
10
Time [ms]
Figure 2.7: Intensity (top panel) and frequency (bottom panel) modulation of slowscan signal at 250Hz for NEL diode laser. High-frequency modulation is 255kHz.
20
High-frequency modulation in the frequency vs. time signal has been omitted for
clarity.
The top panel shows the intensity modulation of the WMS laser signal (no absorption);
modulation of 255kHz has been superimposed on the slow scan. The bottom panel
shows the corresponding modulation of slow-scan laser frequency averaged over the
modulation. The parameters A and Aν refer to the slow-scan intensity and frequency
modulation amplitudes, respectively. Criteria for selecting the various WMS parameters
presented in this section are summarized in Table 2.1.
Table 2.1: Selection criteria for WMS parameters.
Parameter
Selection criteria
A, Aν
Lineshape spectral resolution, Doppler
shifting
fslow
Sensor bandwidth
i0 , a
Modulation index
f
Noise characteristics of environment,
compatibility with frequency multiplexing
The amplitude of the slow-scan modulation is primarily determined by the
required spectral resolution of the absorption lineshape. If only the WMS-2f peak value
is of interest (as in fixed-wavelength WMS), the slow scan can be modulated in only a
small wavelength range around the linecenter. However for Doppler-shift measurements,
it is desirable to resolve the entire lineshape; hence a larger slow-scan amplitude is
necessary. The slow-scan amplitude must also be large enough to capture frequencyshifted lineshapes due to bulk velocity of the flow; this Doppler shift can range from 10-5
cm-1 in subsonic flow to >10-1cm-1 in hypersonic flow.
Selection of the slow-scan
modulation frequency is determined by the rate at which the sensor is to produce
measurements (note that the sensor bandwidth is actually 2fslow for sinusoidal modulation
since the laser scans through the absorption feature on both the up-scan and down-scan of
21
the sine wave). The properties of the test environment must be considered to ensure that
the sensor bandwidth is appropriate for the temporal scale of the phenomena present in
the system.
The high-frequency modulation amplitude (modulation depth, a) determines the
modulation index, which governs the curvature and amplitude of the WMS signals
(discussed in the next chapter). The frequency of this modulation should be significantly
higher than the characteristic noise frequency of the test environment in order to benefit
from the noise-rejection property of the WMS technique. If frequency multiplexing of
multiple lasers is to be used, the modulation frequencies should also be selected to
minimize cross-talk of the harmonics (see Section 5.1).
The signal for transmitted intensity passes through a software lock-in amplifier,
which consists of a mixer and a low-pass filter. The mixer multiplies the detected signal
by two sinusoids of equal and arbitrary phase, producing an X- and Y-component:
X 2 f=
GI 0
2
i0


 H 2 + 2 ( H1 + H 3 ) cosψ 1 


GI  i

Y2 f =
− 0  0 ( H1 − H 3 ) sinψ 1 
2 2

(22)
(23)
where G, the detector gain, now appears in these equations. This technique for extracting
the harmonic signal is insensitive to the phase between the input signal and the reference
sinusoids applied in the lock-in amplifier. The 2f signal is given by the root-sum-square
of the two components:
=
S2 f
X 22 f + Y22f
(24)
In calibration-free WMS, the 1f signal is used to remove the detector gain and average
laser power [21,40,57,61,64,65]. Following the same procedure, the 1f signal can be
calculated:
22
X1 f =
GI 0
2


H2 

 H1 + i0  H 0 +
 cosψ 1 
2




GI  
H
Y1 f =
− 0 i0  H 0 − 2
2  
2
=
R1 f
 sin ψ 

1


X 22 f + Y22f
(25)
(26)
(27)
The 1f-normalized 2f signal is now described by Equations 20-27, and the necessary
parameters can be divided into two classes: laser modulation parameters a, i0, and ψ1,
and spectroscopic parameters Sj and φ j .
The linestrength is solely a function of
temperature, while the lineshape depends on broadening coefficients, which have both a
pressure and temperature dependence.
TDLAS measurements with WMS require
accurate knowledge of both the spectroscopic and laser modulation parameters for the
sensor.
2.5 Temperature Measurement Methodology
The current sensor measures density by coupling a 1f-normalized WMS-2f
temperature measurement with a facility pressure measurement. The ideal gas law is then
applied to obtain density. The 1f-normalized WMS-2f signal can be modeled once the
laser modulation and spectroscopic parameters described in the previous section have
been measured. The temperature dependence of this signal is embedded in the Hi terms
of Equations 20 and 21. As described in Section 2.1, the linestrength is solely a function
of temperature, while the lineshape function, most commonly modeled with the Voigt
profile, requires knowledge of the Doppler- and pressure-broadened half widths. The
Doppler contribution to the line width is a function of temperature and physical constants
and does not need to be measured experimentally. The pressure-broadened contribution
to the linewidth depends on broadening coefficients which must be measured (if not
already known) as a function of temperature and composition.
23
The simulation used for the current temperature measurements is based on a
model initiated by Li et al. [65], which was thoroughly tested with H2O up to pressures of
30atm and temperatures of 900K [61,73]. The model was further improved by Rieker et
al. [61,73] to model the WMS signal beyond the optically thin limit (absorbance < 0.05).
This model incorporates Equations 20-27 to calculate the 1f-normalized 2f signal, and
temperature is inferred by comparing the measured values (for the ratio of WMS-2f/1f
signals for the two targeted transitions) with computed values. This technique has been
demonstrated to measure temperature in the reflected shock region of a shock tube within
1% of the theoretical value using H2O absorption [57], and within 0.5% using CO2
absorption [58], as well as flame temperature within 1.5% of a thermocouple reading
[74]. The model used for this work was modified to include an improved approximation
to the Voigt function [75,76].
2.6 Density Measurement Methodology
Density can be obtained with either DA or WMS techniques. Previous TDL
mass-flux sensors have relied on the direct absorption method for density measurements
[10,12,22,25,26,77]. This leaves the sensor susceptible to the shortcomings of the DA
technique mentioned in Section 2.3.
By implementing the WMS temperature
measurement technique, the sensor density measurement benefits from both noiserejection and increased SNR. Here the density measurement relies on a temperature and
pressure measurement; pressure measurements are obtained with fast time response
(20Hz) using pressure transducers installed in the NASA Langley facility. Pressure and
temperature are used in conjunction with the ideal gas law to determine density, ρ:
P = ρRT
(28)
Here P is the pressure in Pa, R is the universal gas constant for the gas mixture in J/kgK,
and T is the temperature in K.
24
Assumption of ideal gas behavior can be justified by examining the
compressibility factor, Z, of the test gas.
As the compressibility factor of a gas
approaches unity, the more closely the gas is described by ideal gas behavior. The
compressibility factor is a function of the reduced pressure and temperature, Pr and Tr,
and Z near unity is achieved for most gases, including air, when Pr <0.1 or Tr>2 [78,79].
For the conditions at the NASA Langley DCSCTF, the values of Pr and Tr (0.02 and 7.5,
respectively) easily satisfy these conditions. Hence the ideal gas law can be applied to
determine density from pressure and temperature with negligible error.
2.7 Velocity Measurement Methodology
Diode laser absorption measurements of velocity rely on the Doppler-shift effect.
If a component of flow velocity exists parallel to a beam path, an absorption feature will
experience a frequency shift of its linecenter, Δν [cm-1], given by:
∆ν ν o = U parallel c
(29)
This Doppler shift is dependent on the unshifted linecenter frequency νo [cm-1], the speed
of light c [m/s], and the component of bulk velocity parallel to the beam path Uparallel
[m/s]. A crossed-beam setup as shown in Figure 2.8a is typically used to obtain the
relative frequency shift. Because absorption is a line-of-sight measurement, the velocity
determined using this technique is not defined at a specific point; the measurement is a
spatial average of the velocity within the plane encompassed by the two beams. This
leads to the realization that nonuniformity in the flow-field velocity distribution can
influence the velocity measured from Doppler-shifted absorption lineshapes. Further
discussion of this effect, as well as the ramifications of nonuniformity in other flow
properties is found in Chapter 4.
25
Δν
0.4
Air flow
velocity, U
Unormal
2θ
Uparallel
Absorbance
0.3
0.2
0.1
0.0
-0.4
b)
a)
Upstream-pointing
beam
Downstream-pointing
beam
-0.2
0.0
0.2
0.4
Frequency [cm-1]
Figure 2.8:
a) Schematic of crossed-beam configuration for Doppler-shift
velocimetry. b) Simulated frequency shift for direct absorption lineshapes with
λ=1349nm, 2θ = 90o, U = 1600m/s, T = 915K, P = 0.68atm, XH2O = 0.26, L = 18.7cm.
The crossing half-angle θ can now be used to recover the axial flow velocity U, as
seen in the following equation:
∆ν ν o = 2sinθ ⋅ U c
(30)
Here the frequency shift is directly proportional to the sine of the crossing half-angle.
Hence by maximizing the crossing angle, the frequency shift between the absorption
features in Figure 2.8b is also maximized. This causes an increase in the minimum
velocity that can be resolved and makes frequency-shift detection less susceptible to
noise.
However, spatial constraints at most ground-test facilities typically limit the
crossing angle to no more than 90o.
Previous TDL measurements have applied Doppler-shift velocimetry using direct
absorption of water vapor [12,26,41], potassium [41], O2 [10,11], and NO [25,77].
Sensing of velocity via O2 [22,23,27,80] has shown that WMS-2f can provide an
improvement in measurement precision and resolution.
The current work extends
Doppler-shift velocimetry to the WMS-2f/1f technique, taking advantage of
improvements in SNR and noise-rejection capability as discussed in the following
chapter. The superiority of WMS-2f/1f velocity sensing over the WMS-2f technique is
discussed further in Appendix B.
26
Resolution of the velocity measurement is dependent on the linecenter frequency,
crossing angle, and the smallest frequency shift that can be measured. For a constant
sample rate and scan rate, the frequency-shift detection limit increases with laser scan
amplitude (Aν) since the laser must scan farther in frequency between data points. These
larger scan amplitudes are necessary to resolve the lineshape of pressure-broadened and
Doppler-shifted features. The resolution of the 2f/1f lineshape for a sensor sampling at 5
MHz with a slow-scan frequency of 250Hz and scan range of 0.35cm-1 (typical width of a
high-temperature H2O absorption feature) is 7 (10)-5cm-1. Assuming near-IR diode laser
absorption with a typical linecenter frequency ~7400cm-1, a frequency-shift detection
limit of 7 (10)-5cm-1, and a crossing angle of 90o, a single-sweep velocity resolution of
2m/s is obtained, which is roughly 0.1% uncertainty for a 1500m/s flow and suitable for
high-speed test environments. This theoretical resolution for the sensor is applicable in
the limit of identical lineshapes measured on the upstream- and downstream-pointing
beams which are not distorted by flow nonuniformities, noise, or laser transmission/gas
condition fluctuations. By fitting the lineshape and making additional Doppler-shift
measurements between data points, the velocity resolution can be improved to better than
1m/s as required for a low-speed validation experiment.
27
28
Chapter 3: 1f-Normalized Wavelength
Modulation Spectroscopy with 2fDetection
The benefits of the 1f-normalized WMS-2f technique have been successfully
exploited for TDL measurements in harsh environments for many years. However, study
of this technique has typically been focused on the optically thin limit (absorbance < 5%).
In this section, the behavior of the 1f-normalized WMS-2f (WMS-2f/1f ) lineshape is
investigated for varying optical thickness and modulation index, with particular emphasis
on the regime of large absorbance which has not previously been thoroughly analyzed.
With a better understanding of the behavior of the WMS-2f/1f signal, simple guidelines
are developed to optimize the lineshape for velocity measurement.
3.1 Theory and Background
Obtaining the WMS-2f/1f signal is quite straightforward; the lock-in amplifier
outputs of Equations 24 and 27 are simply divided to produce the WMS-2f/1f lineshape.
Before proceeding, an important parameter must be introduced – the modulation index m:
m = a ∆ν HWHM
(31)
Here ΔνHWHM is the lineshape half width at half-maximum. The modulation index is a
measure of the laser frequency modulation relative to the width of the lineshape, and in a
following section the 2f/1f lineshape is shown to be a strong function of this parameter.
The WMS signals are sensitive to the curvature of the absorption lineshape. In
the limit of low modulation indices (derivative spectroscopy), the harmonics closely
29
approximate the derivatives of the absorption lineshape [81-83].
The cause of this
behavior can be traced to Equations 22-27, which show that the WMS-kf (k=1, 2, 3…)
signal is strongly dependent on harmonic Hk, and a weaker function of the Hk-1 and Hk+1
harmonics.
As the modulation index is reduced, i0 simultaneously decreases (this
parameter is linearly proportional to modulation depth for current-tuned TDLs [60,65]),
and the contribution of the Hk-1 and Hk+1 harmonics to the WMS signal is diminished.
Hence the WMS-kf signal becomes dominated by the Hkth harmonic, which is
proportional to the kth derivative of the absorption lineshape [69]. Absorbance is plotted
Absorbance
with its first and second derivatives in Figure 3.1.
a)
0.15
0.10
0.05
c)
2nd derivative of absorbance
(absolute value)
b)
1st derivative of
absorbance
0.00
0.001
0.000
-0.001
3.0x10-5
2.0x10-5
1.0x10-5
0.0
7454.10
7454.25
7454.40
7454.55
7454.70
-1
Frequency [cm ]
XH2O=0.25, and L=18.8cm. a) Absorbance. b) 1st derivative of absorbance.
c) Absolute value of 2nd derivative of absorbance.
30
The above plot also illustrates the behavior of an idealized diode laser, in which
there is no intensity change as the wavelength is tuned. In a real TDL the laser intensity
and frequency are tuned simultaneously, which causes the first harmonic (1f ) to reside on
a non-zero background:
R1 f 0 =
1
GI 0 i0
2
(32)
This is in fact the 1f signal in the absence of absorption, obtained by evaluating Equations
24-26 while recognizing that H0=1 and Hk=0 in the case of zero absorption. However for
a diode laser where wavelength and intensity tuning are independent, 1f normalization is
not possible since the 1f signal resides on a zero background. This is because the linear
intensity modulation amplitude, i0, would be zero in the absence of intensity tuning.
It is useful to begin analysis of the WMS-2f/1f lineshape by qualitatively
examining the nature of the 2f and 1f signals. Figure 3.2 displays simulations of the
WMS signals for a current-tuned TDL wavelength-scanned over an isolated water vapor
transition at 1341nm.
31
a)
Absorbance
0.15
0.10
0.05
b)
Simulated 1f signal
0.00
0.10
0.08
0.06
c)
Simulated 2f signal
0.04
0.02
0.01
d)
Simulated 2f/1f signal
0.00
0.4
0.3
0.2
0.1
0.0
7454.10
7454.25
7454.40
7454.55
7454.70
-1
Frequency [cm ]
XH2O=0.25, and L=18.8cm. a) Absorbance. b) WMS-1f lineshape. c) WMS-2f
lineshape. d) WMS-2f/1f lineshape. Modulation index for WMS simulations is 1.6.
Absorption linecenter frequency indicated by dashed line.
Comparing Figures 3.1b and 3.2b, it is clear that the WMS-1f signal indeed
reflects the 1st derivative of the absorption lineshape. As mentioned previously, the 1f
signal resides on a non-zero background, a value to which it asymptotes at frequencies
farther from the absorption linecenter.
Comparison of the 2f signal with the absolute value of the second derivative of
absorbance (Figures 3.1c and 3.2c) also illustrates qualitative agreement. The 2f signal is
always positive because it is the root-sum-square (RSS) of the lock-in outputs. It is also
seen that the 2f peak coincides with the peak in absorbance, and that the zero crossings
32
occur at roughly the same location as the maximum and minimum of the 1f signal. Note
that the asymmetry seen in the WMS-2f signal is due to the coupling of frequency and
intensity modulation in diode lasers as described in References [60,84].
The WMS-2f/1f signal of Figure 3.2d appears similar to the 2f signal, but displays
asymmetry resulting from division by the asymmetric 1f signal. Of particular importance
is the fact that normalization of the 2f signal with the 1f signal causes an order of
magnitude increase in signal amplitude. This is a result of the sharp downward slope of
the 1f signal between its maximum and minimum; the following sections will explore
how absorbance and modulation index can be adjusted to exploit and optimize this
behavior. A final point to note is that the WMS-2f/1f peak does not occur at the same
frequency as the WMS-2f peak. This effect is exacerbated by an increase in absorbance,
as will be shown in the following section.
Previous TDL measurements of velocity have used either direct absorption
[10,12,25,26,41,77] or WMS-2f [22,23,27,80]. The current sensing technique further
improves velocimetry precision and resolution by normalizing the WMS-2f signal with
the WMS-1f signal. Referring to Equations 22-27, it is seen that the 1f-normalized
WMS-2f signal is independent of detector gain and average laser intensity.
Such
normalization has been demonstrated to improve the stability of optical sensors through
resistance to transmitted laser intensity fluctuations from non-absorption-related losses
[57,60,61,64-66]. This feature of the WMS-2f/1f signal is of great benefit for velocity
sensing, where the ability to resolve Doppler shifts requires sensitive detection of the
transition linecenter.
In addition to rejecting fluctuations in laser transmission, the WMS-2f/1f signal
can be sensitized for velocity measurement by adjusting the modulation depth to optimize
the 2f/1f lineshape for varying degrees of optical depth. Detection of the Doppler shift
from the difference of transition linecenters is improved when the lineshapes are tall and
narrow, as may be accomplished by allowing strong absorption and by adjusting the
modulation index. When probing absorption transitions with absorbances of >10%, the
first harmonic of the laser transmitted intensity (1f signal) becomes significantly distorted
33
by the absorption lineshape. As mentioned previously, the 1f signal reflects the first
derivative of the absorption lineshape, and grows taller and sharper as absorption
increases. In the desired case of large absorption, normalization of the WMS-2f signal by
the 1f signal can be used to generate a tall, sharply rising feature that is ideal for Dopplershift detection.
3.2 Influence of Optical Depth
WMS measurements of temperature often take advantage of an approximation to
Equation 3 which can be made in the limit of small absorption (typically absorbance <
0.05) [57,64]. By linearizing the exponential of Equation 3, the following relation is
obtained:
I t ,ν
I 0,ν
= 1 − αν
(33)
This brings about a corresponding simplification in the formulation of Equations 20 and
21 for the harmonics of the WMS signal:
=
H 0 (ν , a )
=
H
k (ν , a )
− Pi L
π
π
− Pi L
2π
∫π ∑ S φ (ν + a cos(ξ )) dξ
(34)
∫π ∑ S φ (ν + a cos(ξ )) ⋅ cos(kξ ) dξ
(35)
j j
−
j
π
j j
−
j
With all other equations unchanged, it is seen that dividing the WMS signals for two
absorption features removes the direct dependence on partial pressure and path length:
34
(WMS − 2 f /1 f )λ
(WMS − 2 f /1 f )λ
1
=
2
S1 f [φ1 (T , P,ν 1 ) ]
S2 f [φ2 (T , P,ν 2 ) ]
(36)
The linestrength is a function of temperature, while the lineshape function is a weak
function of temperature and a complex function of pressure. Hence the two-line WMS2f/1f ratio approximates a function of temperature if the transitions are selected such that
the lineshape functions have weak or similar temperature dependences. Operating in the
optically thin regime simplifies WMS model and the necessary calculations, while
removing direct dependence on pressure, mole fraction, and path length.
Although this property is attractive, the WMS-2f/1f signals for non-optically thin
conditions can still be simulated very accurately if the gas pressure and composition are
well known [61,73]. This enables application of the WMS-2f/1f technique to the regime
of large absorbance, where dramatic changes to the WMS-2f/1f lineshape are seen; this
behavior can subsequently be exploited to improve the measurement of frequency shift
for velocity sensing. An additional benefit to using transitions with large absorbance is
an increase in SNR.
Figure 3.3 illustrates the WMS-1f, WMS-2f, and WMS-2f/1f signals for varying
degrees of optical depth. The driving factor for the dramatic increase in the WMS-2f/1f
amplitude is the change in the 1f signal as absorbance increases.
The increase in
amplitude is also accomplished without broadening the lineshape (for the current case
where absorbance is increased by increasing path length), a feature which makes the
WMS-2f/1f signal attractive for Doppler-shift sensing.
35
c)
Simulated 1f signal
Simulated 2f signal
b)
a)
Absorbance=0.03
Absorbance=0.15
Absorbance=0.5
Absorbance=1
0.20
0.16
0.12
0.08
0.04
0.15
0.10
0.05
0.00
2.5
2.0
1.5
1.0
0.5
0.0
7454.10
7454.25
7454.40
7454.55
Frequency [cm-1]
7454.70
Figure 3.3: Simulated WMS signals for varying absorbance (or optical depth).
Same conditions as those for Figure 3.2 are used, and absorbance is varied by
changing path length. Modulation index m=2.2. a) WMS-1f lineshape. b) WMS-2f
lineshape. c) WMS-2f/1f lineshape.
The extra inflection point in Figure 3.3a that appears for absorbance > 0.5 is an
artifact of the lock-in amplifier output for the WMS-1f signal. The X1f and Y1f signals
from Equations 25 and 26 which compose the WMS-1f lineshape are plotted in Figure
3.4. As can be seen in the left panel (Figure 3.4a), the shape of the 1f signal is dominated
by the X1f component. As absorbance increases, the X1f lineshape crosses zero; this
results in the inflection point when the lock-in amplifier squares the X- and Ycomponents to form the WMS-1f signal (see Equation 27). The same effect can occur at
lower absorbances if the modulation index is sufficiently low – lower modulation index
36
results in a lower i0, which moves the X1f signal closer to zero. This property of the 1f
0.15
0.080
0.10
0.075
Simulated Y1f signal
Simulated X1f signal
signal has been verified experimentally, and is correctly modeled by simulation.
0.05
0.00
-0.05
-0.10
-0.15
-0.20
Absorbance=0.03
Absorbance=0.15
Absorbance=0.5
Absorbance=1
-0.25
7454.10 7454.25 7454.40 7454.55 7454.70
0.065
0.060
0.055
0.050
Absorbance=0.03
Absorbance=0.15
Absorbance=0.5
Absorbance=1
0.045
0.040
7454.10 7454.25 7454.40 7454.55 7454.70
Frequency [cm-1]
a)
0.070
b)
Frequency [cm-1]
Figure 3.4: Simulation of lock-in amplifier outputs for WMS-1f signals in Figure
3.3: a) X1f . b) Y1f.
It should be noted that the even derivatives (2nd, 4th, 6th, etc.) of the absorption
lineshape are symmetric, while the odd derivatives are all asymmetric.
The
corresponding harmonic signals reflect this property – the X1f signal (dominated by the
H1 harmonic) is asymmetric, while the Y1f signal (composed of the H0 and H2 harmonics)
is symmetric.
The analysis in this section indicates that large absorbance can significantly
increase the amplitude of the WMS-2f/1f signal. In conjunction, the slope of the central
peak dramatically steepens as absorbance increases; the next section further examines the
behavior of the WMS-2f/1f signal in response to modulation depth.
3.3 Influence of Modulation Depth
Previous work [27,56-58,64,65] has often used values of the modulation index
m~2.2 where the WMS-2f signal is a maximum, as shown in Figure 3.5a. This value was
calculated and experimentally verified for Lorentzian, Gaussian, and Voigt profiles by
Reid and Labrie [69]. However, the 2f/1f amplitude has not previously been examined as
37
a function of modulation index; as seen in Figure 3.5b, the WMS-2f/1f peak is maximized
for values of the modulation index m~1. The simulations produced in Figure 3.5 are for
an isolated transition at 1341nm – in practice, the presence of neighboring lines can cause
both the peak 2f and 2f/1f values to shift to slightly different modulation indices. The
2f/1f lineshape is sensitive to the curvature of an absorption feature; hence the specific
modulation index at which the 2f/1f amplitude is maximized can vary slightly with
different transitions and amount of absorption.
However, the previously mentioned
effects are minor; simulations for a wide range of transitions (1300nm to 1490nm) and
degrees of absorbance (0.01 to 2) show that the maximum 2f/1f amplitude consistently
remains within the range m=0.9–1, quite different from traditional use of WMS-2f for
1.0
1.0
0.8
0.8
0.6
0.4
0.2
0.0
0.0
a)
Normalized 2f/1f
peak amplitude
Normalized 2f peak amplitude
species detection where m~2.2 is desired.
0.6
0.4
0.2
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
0.0
Modulation index
0.4
b)
0.8
1.2
1.6
2.0
2.4
2.8
Modulation index
Figure 3.5: Normalized amplitudes of: a) WMS-2f signal versus modulation index.
b) 1f-normalized WMS-2f signal versus modulation index. Simulation is for H2O
transition at 1341.5nm with absorbance = 15%.
When m~2.2, not only is the WMS-2f signal a maximum value, but the WMS-2f
signal is least sensitive to the lineshape function or variations in m. Similarly when m~1
the 1f-normalized WMS-2f signal minimizes its sensitivity to these variations; e.g., for a
change in the modulation index from 0.9-1.1 the 2f/1f signal amplitude changes by less
than 1%. However, it should be noted that the range of values for which the WMS-2f/1f
signal plateaus is much narrower than for the WMS-2f signal.
38
When the total absorption is greater than ~10%, the WMS-2f/1f lineshape narrows
and increases in amplitude for m~1. The behavior of the WMS-1f, WMS-2f, and WMS2f/1f lineshape with varying modulation index is illustrated in Figure 3.6.
b)
Simulated 2f signal
a)
Simulated 1f signal
0.12
0.10
0.08
0.06
0.04
0.02
0.025
m=0.5
m=0.9
m=1.6
m=2.2
0.020
0.015
0.010
0.005
c)
0.000
0.4
0.3
0.2
0.1
0.0
7454.10
7454.25
7454.40
7454.55
Frequency [cm-1]
7454.70
Figure 3.6: Simulations of WMS signals with varying modulation index: a) WMS1f. b) WMS-2f. c) WMS-2f/1f. Same conditions as Figure 3.2 are used with
absorbance = 15%.
It can be seen that the 2f/1f lineshape at high absorbance is optimized for velocity
sensing by use of a modulation index~1. Optimization of the modulation index causes
the 2f/1f lineshape to increase in amplitude; this improvement is a result of the steepening
of the 1f signal in Figure 3.6a balanced by sufficient strength of the 2f signal in Figure
3.6b. Although the 1f slope is found to be maximized for an m between 0.5 and 0.9, it
can be seen that the 2f signal strength drops too sharply in this range to form a suitable
2f/1f signal. For m~1, the 2f amplitude is still roughly 60% of its value at m=2.2 – hence
39
the signal level is of similar strength. However, as m decreases below 0.5, low signal
levels may limit velocity resolution.
While the 2f signal is maximized as m approaches 2.2, it is also seen that the
feature becomes much broader – a result of modulation broadening as described in
References [70,85].
This broadening is undesirable for sensitive resolution of the
Doppler shift (for velocity detection) and can increase the distortion in the lineshape
resulting from neighboring transitions; in contrast, use of a low modulation index results
in narrow WMS-2f/1f lineshapes.
The current simulations assume that the slow-scan midpoint laser intensity ( I 0 ) is
constant at all points along the lineshape. Thus the intensity variation upon which the
high-frequency modulation is superimposed has been neglected. A more detailed model
for the scanned WMS-2f/1f waveform including intensity modulation by the slow scan is
currently being developed. 1 Initial comparisons between the two models show small
differences in the 2f/1f away from line center, though variation with absorbance and
modulation index as shown above is unchanged.
Previous work by Lyle et al. [22] and Philippe and Hanson [27] demonstrated that
WMS-2f velocimetry offered improved signal-to-noise ratio (SNR) compared to direct
absorption; here we find that by using an m~1 and selecting transitions with absorbance >
10%, the 1f-normalized WMS-2f approach can further improve velocity resolution. Later
in this work, this improvement is demonstrated through velocity measurements
conducted in quiescent air (Appendix B), a low-speed wind tunnel at Stanford (Chapter
6), and a supersonic wind tunnel at NASA Langley (Chapter 7).
1
Strand, C. L. 2010. Private communication.
40
Chapter 4: Line-of-Sight Measurements
in Nonuniform Flow Fields
Absorption spectroscopy measurements are path-integrated, i.e. the temperature,
pressure, velocity, and composition at each point along the beam path are incorporated
into the detected absorption feature. In uniform flow fields, the gas properties measured
from detected lineshapes faithfully represent the conditions of the test gas. However in
the presence of flow nonuniformity, the detected signal can become distorted, skewing
the resulting measurements. This chapter addresses the effects of nonuniformity in the
test gas on LOS absorption measurements by using CFD solutions to simulate pathintegrated lineshapes; this allows for nonuniformity effects to be quantified and enables
the development of guidelines for desensitizing LOS measurements to flow
nonuniformity.
4.1 Nonuniformity in Non-Reacting Flow Fields
Line-of-sight laser absorption sensors have been successfully deployed in a wide
variety of environments, and are particularly attractive because they are noninvasive,
easily implemented, and highly sensitive to gas parameters. These sensors enable the
measurement of flow properties such as velocity and temperature, which is essential for
the operation of ground-test facilities, assessing the performance of aeroengine models
and components, and validating the accuracy of computational fluid dynamics solutions.
Velocimetry and thermometry have been performed with high accuracy using both direct
absorption and wavelength modulation spectroscopy in a variety of environments
including shock tubes [26,27,58,64,77,80], full-scale engine models [10,23], and
supersonic ground test facilities [12,25,56]. However, because the absorption signal is a
path-integrated measurement, the detected lineshape is influenced by the pressure,
41
temperature, velocity, and composition profiles existing along the laser beam path. These
nonuniformities can cause the LOS temperature and velocity measurements to deviate
from the values of interest in the bulk flow. Hence analysis is necessary to quantify the
influence of flow nonuniformity on LOS measurements and to develop guidelines to
minimize these effects.
Distortion in the detected absorption lineshape is a function of the degree of
nonuniformity and the pressure and temperature dependence of the selected transition.
Distortion of the lineshape can shift the apparent transition line center, producing an error
in the measured Doppler shift; similarly, distortion from nonuniformity can cause
changes in the amplitude of the detected signals, hence affecting temperature and
concentration measurements.
Temperature effects on LOS measurements have been studied extensively in
flames [86,87]. Based on this analysis, a profile fitting method for temperature was
developed [88,89], which involves probing multiple lines with different temperature
dependences and using least squares fitting to obtain an appropriate temperature profile.
The disadvantage of this method is the necessity for multiple lasers and the
computational expense of processing the data.
A simpler technique to address
nonuniformity effects on LOS measurements is to analyze lineshapes simulated from
CFD solutions [61,90]. For simple geometries and well-characterized flow conditions,
CFD is a straightforward and accurate method to model the spatially resolved properties
of the flow. By applying the equations that model the laser transmitted intensity (see next
section), the lineshapes produced by nonuniform flow can be simulated; this provides a
simple method to quantify the effects of nonuniformity on a LOS measurement. Velocity
nonuniformity effects were investigated in previous work using O2 absorption by Lyle, et
al. [23] who demonstrated that at low velocities, the distortion to the detected lineshape
caused by boundary layers is nearly negligible. Knowing the fraction of the beam path
passing through stagnant regions of absorption, a simple linear correction can be applied
to remove the effects of the low-velocity regions [10,23].
42
This technique was
demonstrated at subsonic velocities by simulations assuming simple step-function
changes in velocity. However at high velocities, the larger Doppler shift results in more
noticeable distortion in the lineshape. Actual flows also possess continuous gradients in
velocity, temperature, pressure, and mole fraction that are poorly described by a simple
step function.
Flow nonuniformity can result from a wide variety of factors, e.g. changes in
channel geometry, boundary-layer separation, flow obstructions, and wall heat transfer.
Nonuniformity discussed in this section will be restricted to well-mixed, non-reacting
flow; the composition of the test gas is considered spatially uniform and unchanging in
time (frozen composition). Furthermore, the flow is assumed to be free from shock
structures since the discontinuity of flow properties across shocks is not easily addressed
with respect to a LOS measurement.
Hence the primary types of nonuniformity
discussed here will be thermal and velocity boundary layers.
4.2 Modeling WMS Lineshapes in Nonuniform Flow
To properly assess the effects of nonuniformity on LOS measurements, accurate
simulations of the WMS lineshape must first be produced. This requires modification of
the governing equations for the WMS lineshape introduced in Section 2.4 to include the
influence of spatially nonuniform flow conditions.
From Equation 29 it can be seen that lineshapes along the beam path may
experience slightly different frequency shifts caused by nonuniformity in the axial
velocity, U, along the line of sight. To simulate the effects of flow nonuniformity,
Equations 20 and 21 are modified to allow absorbance to vary as a function of x, the
distance along the beam path (more detail in Reference [21]); temperature, velocity,
pressure, and composition gradients are now incorporated into the x-dependence of
absorbance:
43
1
2π
H 0 (ν=
, a)
H k (ν =
, a)
1
π
∫π exp −α (ν +
π

−
∫π exp −α (ν +
π

−
)
∆ν ( x) + a cos(ξ )  d ξ

2
∆ν ( x) + a cos(ξ )
2
) cos(kξ ) dξ
(37)
(38)
The relative frequency shift, Δν (as defined in Equation 30), has now been included to
indicate that the absorbance may be frequency-shifted due to velocity along the beam
path (relative frequency shift is divided by two since these equations consider absorption
on a single beam). The sign of Δν is positive for a beam directed downstream and
negative for a beam directed upstream; the frequency shift is again a function of x,
indicating that different velocities at points along the beam path will cause different
magnitudes of frequency shift. The above equations coupled with Equations 22-27 and
30 now completely define the path-integrated WMS-2f/1f lineshape allowing for
temperature, pressure, mole fraction, and velocity nonuniformities along the laser line of
sight. As described in the next section, these equations will be used to simulate WMS
lineshapes in a nonuniform flow.
4.3 Nonuniformity Analysis for NASA Langley
DCSCTF
A CFD solution was used to simulate lineshapes for lines of sight through
nonuniform flow in the DCSCTF isolator used for mass-flux sensor demonstration
measurements. The CFD solution provides temperature, pressure, density, and uvwvelocities in three dimensions.
Hence this data can be used to calculate the path-
integrated values measured by a TDLAS sensor on a specific LOS; these TDLAS lines of
sight can then be translated in the flow field. Figure 4.1a shows the sensor mounted to
stages to translate the sensor LOS. The setup can be configured to translate either
vertically or horizontally across the duct.
44
Nozzle
Upstream
pointing beam
Downstream
pointing beam
Y
X
Z
b)
Vertical
translation
2.88”
5.21”
Horizontal
translation
Y
X
Z
c)
a)
Upstream
pointing beam
Downstream
pointing beam
Figure 4.1: a) NASA DCSCTF isolator section with TDLAS mass-flux sensor
configured for vertical translation. b) CFD geometry for DCSCTF isolator
(symmetry about vertical axis is assumed) with vertical translation configuration
shown. c) CFD geometry for DCSCTF isolator with horizontal translation
configuration shown.
In the vertical translation configuration of Figure 4.1b, the lasers cross in a horizontal x-z
plane, which was then translated vertically (y-axis) across the duct. Similarly for the
horizontal translation configuration of Figure 4.1c, the lasers cross in a vertical x-y plane
and were translated horizontally (z-axis) across the duct. Because the sensor collects
measurements as it translates across the duct, planes of CFD data (outlined in black)
encompassing all laser lines of sight (indicated by the red dashed arrows of Figure 4.1b
and Figure 4.1c) can be used to evaluate the influence of nonuniformities at various
locations in the duct. Spatial resolution was limited by the finite beam size of the laser;
hence the CFD data, which was produced on a very fine spatial grid, was averaged over
the beam diameter (approximately 1mm). The CFD solution for pressure along the laser
LOS for the vertical translation configuration is displayed in Figure 4.2a. The planes of
data for temperature, velocity, and pressure were extracted along the diagonal laser path
indicated by the red arrows shown in Figure 4.1b.
45
1
0.5
0
-0.5
-1
7
8
9
10
11
Velocity [m/s] Pressure [Pa] Temperature [K]
Vertical distance from centerline [in]
static pressure: 78000 79800 81600
1.5
1200
1120
1040
960
84000
80000
76000
1600
1200
800
400
0
Distance along beam path [in]
a)
0
4
8
12
16
Distance along beam path [cm]
b)
Figure 4.2: a) CFD pressure data along laser LOS in vertical translation
configuration (units are Pa). b) Temperature, pressure, and velocity data along
LOS at the vertical center of duct.
The thin black box in Figure 4.2a outlines the 1mm region of the slice that was
used to determine the CFD-predicted conditions along the laser LOS in Figure 4.2b. The
variation of temperature, pressure, and axial velocity is plotted as a function of distance
along the downstream-pointing beam for the sensor in the vertical translation
configuration. These data were used with the equations defined in the previous section to
compute the path-integrated lineshape for each LOS.
The process was repeated at
various vertical positions in order to compare with measurements taken using the TDLAS
sensor. The path-integrated WMS lineshapes of Figure 4.3 were simulated using the
CFD data of Figure 4.2b. The 1341nm transition (E”=1962.51cm-1) with a modulation
index m=0.9 is considered in this analysis. In the vertical translation configuration, the
path-integrated absorbance is roughly 0.16. A significant frequency shift can be seen
between the lineshapes produced on the downstream- and upstream-pointing beams
(illustrated in Figure 4.1b and Figure 4.1c).
46
Downstream-pointing beam
Upstream-pointing beam
0.4
0.3
0.2
Δν
0.1
0.0
7454.2
7454.4
7454.6
-1
Frequency [cm ]
Figure 4.3: Frequency-shifted path-integrated WMS-2f/1f lineshapes simulated
from CFD data. Frequency shift corresponds to a 1600m/s core flow.
The frequency shift can be measured at various points along the lineshape;
however, to develop a high-speed, robust velocity detection algorithm, only the data in
the laser frequency-scan from the central peak to the two adjacent valleys was
considered. Ideally, the velocities measured on either the high- or low-frequency face of
the lineshape would be identical. However, the presence of nonuniformities in the beam
path can distort the lineshape, causing slight differences in these measured frequency
shifts.
Figure 4.4a shows the variation of velocity inferred from path-integrated
lineshapes as a function of boundary-layer (BL) thickness, where the thickness of the
boundary layer was defined as the distance to the point at which the velocity reached
99% of the free stream value. In this analysis the same pressure, temperature, and mole
fraction gradients were used for all boundary-layer thicknesses. We will first consider
the top two curves in Figure 4.4a (BL=0.9cm thick), which are produced with the data in
Figure 4.2b. It is clear that the simulated path-integrated velocity measurement is lower
than the core velocity shown in the lower plot of Figure 4.2b (1600m/s). This is to be
expected since the measurement is obtained from a path-integrated lineshape, produced
as the laser beam travels through two low-velocity boundary layers and the core flow.
47
Indeed, when the previously described measurement technique was applied to lineshapes
simulated with no boundary layers, the core velocity was recovered at all measurement
points along the lineshape. Intuitively, this suggests that the velocity inferred from LOS
measurements should decrease as boundary-layer thickness increases as illustrated in
High frequency face
Low frequency face
Measured velocity [m/s]
1580
BL=0.9 cm
1560
BL=1.8 cm
1540
BL=2.7 cm
1520
1500
BL=3.6 cm
0.0
a)
0.2
0.4
0.6
0.8
Position along lineshape
LOS measured velocity
difference from core value [%]
Figure 4.4b.
1.0
-1
-2
-3
-4
-5
-6
-7
5
b)
10
15
20
25
30
35
40
45
BL thickness/path length [%]
Figure 4.4: a) Measured velocities from path-integrated lineshapes with varying
boundary-layer thickness. The position along lineshape refers to the location on the
lineshape used for Doppler-shift measurement, with 0 corresponding to the valley
and 1 corresponding to the central peak.
b) Mean
difference
between
measured velocity of Figure 4.4a and core velocity versus combined boundary-layer
thickness as percentage of an 18.7cm path length.
It should be noted that in addition to an overall decrease in measured velocity as
the boundary-layer thickness increases, the difference in velocity measured at various
points along the lineshape also increases (moving along abscissa of Figure 4.4a). This is
due to increased distortion in the lineshape as the low-velocity boundary layers become a
greater percentage of the path length. This distortion also contributes to the increasing
discrepancy between velocities measured on the high- and low-frequency faces as
boundary-layer thickness increases.
Figure 4.4b shows the mean deviation of the path-integrated measurement from
the core velocity as a function of the combined boundary-layer thickness. The abscissa
of Figure 4.4b is computed as the percentage of the beam path along the 18.7cm laser
48
LOS that passes through the combined boundary layers. In the extreme case where
roughly 40% of the laser LOS is contained in the boundary layers, only a 6% decrease in
the path-integrated velocity measurement is predicted. For the DCSCTF isolator, the
CFD solution predicts that 10% of the path length is contained in the boundary layers,
and a decrease of less than 2% in the path-integrated velocity measurement is expected.
It is clear that for the current transition and modulation index, the sensitivity of the
TDLAS measurement to nonuniformities is quite low. Optimal line selection and optimal
choice of modulation index can minimize the TDLAS measurement sensitivity to
nonuniformities as will be discussed in the following sections.
It is also seen that the decrease in the path-integrated velocity measurement is
roughly linear with the boundary-layer thickness. This indicates that the path-averaged
velocity measurement can be corrected to recover the core velocity. For example, with
10% of the beam path passing through boundary layers, the simulated path-integrated
velocity measurement is roughly 1.5% lower than the core value, and the TDLAS
measurement can be adjusted accordingly. In Chapter 7, this analysis of path-integrated
lineshapes simulated with the CFD solution is used to correct velocity measurements in
the NASA Langley DCSCTF to within 0.25% of the facility-predicted value for the
direct-coupled flow.
4.4 Case Studies of LOS Measurements in
Nonuniform Flow
Having investigated the expected role of nonuniformity for the NASA Langley
DCSCTF, the next goal is to proceed with a more general analysis which can lead to the
development of broad guidelines to minimize the effects of nonuniformity. Analysis was
performed for two ground-test facilities: the T2 free-piston shock facility at Mach 10 and
the NASA HIFiRE Direct-Connect Rig (HDCR) isolator at Mach 2.2. For both cases
analyzed, a crossed-beam configuration with a 90o crossing angle was assumed, and the
49
WMS-2f/1f technique was again used. It is also assumed that the static pressure and gas
composition is constant along the beam path; the effects of pressure and composition
gradients can easily be integrated into a more comprehensive analysis in the future.
These studies allow for the investigation of nonuniformity effects in both the supersonic
and hypersonic regime, where errors can be significant.
4.4.1
Line Selection for Nonuniform Flow
The sensitivity of spectroscopic transitions to flow nonuniformities is an
important consideration in the design of an optical diagnostic. In general it is desirable to
select lines that have strong absorbance at the core flow conditions and weak absorbance
at conditions in the boundary layer; appropriate temperature dependence of the transition
linestrength is the primary selection criterion for obtaining this behavior. As mentioned
previously, the linestrength is a function of the lower-state energy of the absorption
transition and the temperature (see Equation 6). The dependence of the linestrength on
the molecular partition function is shown in Equation 7.
Of interest is the lower-state energy at which linestrength is maximized for a
given temperature. This can be derived as in Reference [87] by taking the derivative of
the linestrength function with respect to temperature:
1 dS hcE " 1 d (TQ )
=
−
S dT
kT 2 TQ dT
(39)
The energy-temperature curve is formed by setting the left side of Equation 39 equal to
zero:
50
E (T ) =
k T d (TQ )
hc Q dT
(40)
This equation defines the lower-state energy that maximizes transition linestrength at a
given temperature. Inserting Equation 7 into Equation 40, the energy-temperature curve
for water vapor can be determined as shown in Figure 4.5.
Lower state energy [cm-1]
8000
7000
dS
>0
dT
6000
5000
4000
3000
dS
<0
dT
2000
1000
0
1000
2000
3000
Temperature [K]
Figure 4.5: Energy-temperature curve for water vapor.
At a given temperature, transitions with a lower-state energy above E(T) will have
linestrengths that increase as temperature increases; similarly, the linestrength will
decrease with increasing temperature for transitions with E” below E(T). For internal
supersonic flow, the boundary layers are typically at a higher temperature than the core
flow due to the stagnation condition at the surfaces of the walls. Hence it is desirable to
choose a transition with linestrength that decreases as temperature increases, minimizing
the contribution of the hot boundary layers to the total absorption. The selection process
can be optimized by considering the ratio of linestrengths at the core temperature and at
the boundary-layer temperature:
51
R=
S (Tcore )
(41)
S (TBL )
To maximize sensitivity to the conditions in the core flow, a transition should be selected
for which R is maximized, i.e. the linestrength at the core temperature is much larger than
linestrength at the boundary layer temperature. This criterion will be applied to the
studies performed in the following sections.
4.4.2
Nonuniformity Analysis of NASA HDCR Isolator
The goal of the NASA HIFiRE program is to investigate phenomena related to
hypersonic flight through experimentation [91,92].
In support of flight tests, CFD
solutions for flow components were performed to examine the flow conditions within
model components. In this section, the effects of nonuniformity on a LOS measurement
in the HDCR isolator (used to support HIFiRE flight tests) are examined. The flow
through the isolator is air at Mach 2.2; a water vapor mole fraction of 25% is assumed
(typical of vitiated flows), facilitating the use of H2O absorption features. The beams are
crossed in the horizontal plane, and the conditions along the beam path are displayed in
Figure 4.6 and Table 4.1.
52
2400
Velocity
Temperature
Temperature [K]
Velocity [m/s]
2000
1600
1200
800
400
0
0
2
4
6
8
10
Distance along beam path [cm]
NASA HDCR isolator.
Table 4.1: Gas conditions along laser LOS for NASA HDCR isolator.
Free
stream
Boundary
layer
Temperature
[K]
Velocity
[m/s]
Pressure
[kPa]
H2O
mole
fraction
Path
length
[cm]
846
1363
88
0.25
9.84
variable
variable
88
0.25
0.16
The boundary layer in the isolator is extremely thin – roughly 1.6mm; hence the
effects of nonuniformity on the LOS measurement are expected to be quite small.
However, the effects of laser modulation and proper line selection can still be
investigated. Using the conditions shown above, Equation 41 was used to select two
lines for the nonuniformity analysis:
•
Optimal choice: A line at 1365.6nm (E”=95.2cm-1) was selected to
maximize the ratio of linestrength at the core conditions to linestrength
in the boundary layer. Because the linestrength of this transition at the
53
core temperature is roughly 20 times higher than its linestrength at the
boundary layer temperature (~2000K), nonuniformity effects on LOS
measurements were minimized.
•
A line at 1487nm (E”=4436cm-1) was selected to
Poor choice:
minimize the ratio in Equation 41; this results in a much higher
linestrength at the boundary layer temperature than at the core
temperature,
and
clearly
illustrates
the
unwanted
effects
of
nonuniformity.
For situations where the boundary layers are cooler than the core flow, the
opposite linestrength temperature dependence would be desirable, although the same
selection procedure would be applied. The absorbances for the 1365.6nm and 1487nm
lines are 8% and 80% respectively at the current conditions. Lineshapes tend to broaden
as absorbance increases; this has a detrimental effect on LOS measurements since this
causes increased distortion in the lineshape resulting from absorbance occurring near the
unshifted linecenter (produced by the low-velocity boundary layers). Hence there is
limited benefit to selecting transitions with high absorbance, although optimization of the
modulation index can be used to significantly narrow the lineshape. The effects of flow
nonuniformity on velocity measurements are now examined for both lines.
High-frequency face
Low-frequency face
1358
1356
1354
1352
1350
0.0
a)
1355
1360
0.2
0.4
0.6
0.8
1345
1340
1335
1330
0.0
1.0
b)
High-frequency face
Low-frequency face
1350
0.2
0.4
0.6
0.8
1.0
Figure 4.7: Measured velocities from path-integrated lineshapes for: a) 1365.6nm
line. b) 1487nm line. Modulation index is 0.9. The position along lineshape refers
54
to the location on the lineshape used for Doppler-shift measurement, with 0
For the optimal line choice in Figure 4.7a, it is seen that the LOS velocity
measurement is lower than the core value by only 7m/s in a 1363m/s flow (0.5%
difference) whereas the line selected in Figure 4.7b gives an average error of 22m/s
(1.6%). Measurements on both the high- and low-frequency faces of the lineshapes
match closely, indicating that little distortion caused by nonuniform flow is present in the
lineshape. As expected, the LOS measurements faithfully reflect the core properties due
to the thin boundary layer, even in a situation where the transition is not chosen properly.
Measured velocities for both lines are shown for a modulation index of 2.2 below.
1355
High-frequency face
Low-frequency face
1358
1356
1354
1352
1350
0.0
a)
1360
0.2
0.4
0.6
0.8
1345
1340
1335
1330
0.0
1.0
b)
High-frequency face
Low-frequency face
1350
0.2
0.4
0.6
0.8
1.0
The measured velocities for a modulation index of 2.2 are roughly the same as for
m=0.9. However, for the poorly selected line, using m=2.2 does slightly lower the
measured velocity, though not by an amount significant at supersonic conditions.
However, this is a trend that will become more evident at conditions with thicker
boundary layers where nonuniformity is more significant.
55
Temperatures inferred from the 1f-normalized WMS-2f peak values of pathintegrated WMS lineshapes are shown in Figure 4.9. Again, because the boundary layers
are thin, the LOS measurements are very close to the core value.
However, the
measurements performed using the optimized line choice (low E”) do match the core
value most closely.
The temperature and velocity comparisons show that properly
selecting the temperature dependence of the transitions can reduce the influence of flow
nonuniformity on LOS measurements.
The next section proceeds to analyze path-
integrated lineshapes under hypersonic conditions, where nonuniformity effects are more
Measured temperature [K]
severe.
High E", m=0.9
High E", m=2.2
Low E", m=0.9
Low E", m=2.2
900
880
860
840
Core temperature = 846K
820
800
780
760
Figure 4.9: Temperatures measured from path-integrated WMS lineshapes. High
E” refers to 1487nm line, low E” refers to 1365.6nm line.
4.4.3
Nonuniformity Analysis of T2 Free-Piston Facility
Measurements of the thermal and velocity boundary layers over a flat plate were
performed by O’Byrne et al. [93] in the T2 Free-Piston Shock Tunnel Facility [94] at the
Australian National University.
This provided the necessary data to investigate
nonuniformity in a Mach 10 flow, where distortion from nonuniform velocity is more
evident. The flat-plate boundary-layer data was mirrored about the axial dimension to
56
simulate flow through a 4cm wide duct as would be seen in an engine model (e.g. a
scramjet isolator). The conditions along the laser beam path are summarized below.
3000
Velocity
Temperature
2000
Temperature [K]
Velocity [m/s]
2500
1500
1000
500
0
0
1
2
3
4
Distance along beam [cm]
T2 shock tunnel.
Table 4.2: Gas conditions along laser LOS for T2 shock tunnel.
Free
stream
Boundary
layer
Temperature
[K]
Velocity
[m/s]
Pressure
[kPa]
H2O
mole
fraction
Path
length
[cm]
362
3107
2.4
0.25
3.62
variable
variable
2.4
0.25
0.19
The conditions above were produced using a shock in 98.9% N2 and 1.1% O2; for
this analysis, the test gas assumed is 25% H2O (to enable water vapor absorption
measurements) with air as the balance. Following the line selection procedure outlined in
the previous section, the same two lines chosen previously (1365.6nm and 1487nm) were
found to be suitable for nonuniformity analysis at the current conditions. Path-integrated
57
lineshapes were simulated from the data in Figure 4.10, and a comparison of the
measured velocities is shown in Figure 4.11.
3108
3106
3104
3102
3100
0.0
a)
0.2
0.4
0.6
0.8
High-frequency face
Low-frequency face
1860
High-frequency face
Low-frequency face
3110
1840
1820
1800
1780
1760
0.0
1.0
b)
0.2
0.4
0.6
0.8
1.0
It is clear from these results that proper line selection is essential; measurements
using the optimized line choice (Figure 4.11a) precisely yield the core velocity, and are
unaffected by the thick boundary layers (~10% of the beam path). However, velocity
measurements using the poorly selected line are roughly 44% lower than the core value
(see Figure 4.11b). This is a result of the 1487nm line absorbing strongly in the lowvelocity boundary layers and skewing the LOS velocity measurement.
58
1840
High-frequency face
Low-frequency face
3108
3106
3104
3102
3100
0.0
a)
3110
0.2
0.4
0.6
0.8
High-frequency face
Low-frequency face
1820
1800
1780
1760
0.0
1.0
b)
0.2
0.4
0.6
0.8
1.0
As shown in Figure 4.12, it is again evident that using a modulation index of 0.9
yields LOS measurements closer to the core value. Velocity measurements using m=2.2
as shown above result in measurements that are roughly 20m/s (1%) lower than those
using m=0.9 for the high E” line. This is due to the narrowing of the lineshape as the
modulation index is lowered, reducing the influence of distortions resulting from the lowvelocity boundary layers near the transition linecenter frequency.
59
Measured temperature [K]
540
520
500
480
460
440
420
400
380
Core temperature = 362K
360
340
High E", m=0.9
High E", m=2.2
Low E", m=0.9
Low E", m=2.2
Figure 4.13: Temperatures measured from path-integrated WMS lineshapes. High
E” refers to 1487nm line, low E” refers to 1365.6nm line.
The temperatures inferred from the 1f-normalized WMS-2f peak values of pathintegrated WMS lineshapes are shown in Figure 4.13. There is now a clear discrepancy
between temperature measured from the poorly selected line and the core temperature;
the measured temperature ranges from 140K – 160K higher than the core value. This is
because the high E” line absorbs heavily in the high-temperature boundary layer. The
temperature measured with the optimized line matches the core temperature within 4%.
These results demonstrate that by properly selecting the transition lower-state energy, the
sensitivity of LOS measurements to temperature and velocity nonuniformity can be
dramatically reduced.
4.5 Sensor Design to Minimize Nonuniformity Effects
The analysis in the previous section demonstrates that lines can be chosen to
improve the accuracy of LOS measurements in highly nonuniform flows. The primary
factor in selecting lines is the temperature dependence of the linestrength; the goal is to
minimize absorption in the boundary layers while maximizing absorption in the core
region. For WMS lineshapes, the modulation index can be optimized to further reduce
60
the influence of nonuniform flow; the criteria for selecting lines to minimize
nonuniformity effects on LOS measurements are summarized below:
• Maximize ratio of linestrength at the core temperature to linestrength at the
boundary layer temperature. This minimizes the effects of absorption in the
boundary layer on the path-integrated lineshape.
The benefit of proper line
selection was demonstrated at both supersonic and hypersonic conditions to
improve the sensitivity of the temperature and velocity measurements to the
conditions in the core flow.
• Use optimized modulation index~1. Lowering the modulation index narrows
the lineshape, reducing the influence of absorption in the low-velocity boundary
layer which occurs near the unshifted linecenter frequency. This improves the
accuracy of both the LOS velocity and temperature measurement; as described in
the previous chapter, the precision of velocity measurements is also improved at
lower modulation indices.
61
62
Chapter 5: Sensor Design and
Experimental Methodology
In this section, the theory and techniques introduced in the previous chapters are
incorporated into the design of the sensor. The fundamentals behind the sensor are first
addressed, i.e. selection of suitable absorption transitions for the target conditions and the
supporting spectroscopic measurements that were performed. Also addressed in this
chapter is the proper selection and design of the sensor hardware for deployment in the
harsh environment of the NASA Langley facility. The work presented in this section sets
the foundation for the field measurements performed in the following chapters.
5.1 Sensor Architecture
The details of the sensor design are shown in Figure 5.1. Two lasers at λ1 =
1349nm and λ2 = 1341.5nm were modulated at f1 (190kHz) and f2 (255kHz) and slowly
scanned (250Hz) with a sine wave. Selection of the two laser wavelengths is discussed
in the following section. Light from the fiber-coupled polarization-maintaining 2 lasers
was combined onto a single fiber, and then the two beams were split and directed
upstream and downstream in the flow. The beams were collimated at a crossing angle of
2θ=90o through the test section and captured with detectors. The WMS signals from
multiple lasers can be demultiplexed by their modulation frequency, which allowed the
use of a single detector for each beam [95,96]. The signals from both beams were
collected on upstream and downstream detectors and separated into signals at f1, f2, 2f1,
2
The use of polarization-maintaining lasers and optical hardware is shown to
significantly reduce the susceptibility of the optical train to noise from vibrations and
fiber bending. These properties are discussed further in Appendix A.
63
and 2f2 using a software lock-in amplifier. The selection of the proper modulation
frequencies, f1 and f2, was based on minimization of crosstalk between harmonics in
frequency space. Specifically, it is desirable that the harmonics of interest (1f1, 2f1, 1f2,
2f2) are sufficiently isolated from each other and from higher harmonics (3f1, 3f2, 4f1, 4f2,
etc.); analysis of the relative widths/strengths of the harmonics in frequency space can
assist in the proper choice of modulation frequencies. A more detailed analysis of the
selection process is given in Reference [61]. An additional advantage of frequency
multiplexing is the ability for simultaneous measurement of both velocity and static
temperature corresponding to either beam.
N2 purged
Detectors
U from Doppler shift
T from line ratio
ρ from ideal gas law
2θ
Lasers and detectors translate
along horizontal and vertical
slot windows in duct
Laser #1 @ 1349 nm
Analog filter
DAQ Computer
Laser multiplexer/
splitter
Laser #2 @ 1341.5 nm
Sinusoid @ f1
Laser Temperature/
Current Controller
Sinusoid @ f2
Figure 5.1: Two-laser frequency-multiplexed WMS sensor for mass flux at H2O
wavelengths λ 1 and λ 2 (~1349 and 1341.5nm). The two lasers are combined on a
single fiber and then split to be directed upstream and downstream in the
supersonic flow with a crossing angle 2θ. Velocity is determined from the relative
Doppler shifts of the absorption lineshape, and gas temperature from the ratio of
the two absorption signals.
64
An illustration of the sensor data flow is shown in Figure 5.2. Signals acquired
from the detectors were digitized and passed through a software lock-in, which extracted
the 1f and 2f signals at the two wavelengths.
The WMS-2f/1f signals at both
wavelengths, combined with spectroscopic and laser modulation parameters and a facility
pressure measurement, were used to infer temperature as modeled by the equations in
Section 2.4. Simultaneously, the WMS-2f/1f signal at λ2 = 1341nm was input to the
Doppler-shift measurement algorithm to obtain velocity.
Temperature was then
converted to density via the ideal gas law and combined with the velocity measurement to
obtain mass flux.
2f /1f signal
Δν
Lock-in
amplifier
Doppler shift
measurement
2f , 1f
λ2
WMS  2 f / 1 f 
WMS  2 f / 1 f 
1
2
WMS peak ratio
2f, 1f
λ1
Frequency
Velocity
Mass Flux
T
Ideal gas
law
Density
Temperature
Spectroscopic
parameters:
S, γair, γself
Modulation
parameters:
a, i0, ψ1
Facility
pressure
measurement
Figure 5.2: Schematic of data flow for WMS-based TDLAS mass-flux sensor.
Temperature is measured from WMS signals for both wavelengths and velocity is
simultaneously measured from the relative Doppler shift of an absorption feature.
Temperature and pressure are used to determine density, and coupled with the
velocity measurement to determine mass flux.
During field measurements, data was recorded and post-processed; real-time
operation was not feasible due to the rapid collection of data and the computational
65
expense of the processing algorithm.
However, future iterations of the sensor may
include modifications to streamline the data processing scheme for real-time operation.
5.2 Line Selection and Spectroscopy
Proper selection of absorption transitions lies at the heart of any TDLAS sensor;
here the criteria for selecting lines for the NASA Langley mass-flux sensor are reviewed.
These design rules are targeted toward temperature and Doppler-shift velocity
measurements based on absorption spectroscopy in high-temperature supersonic flows.
A list of 2632 candidate water vapor transitions between 6800cm-1 and 7460cm-1
(1340nm and 1470nm) where telecom diode lasers are readily available was selected
from HITRAN 2008 [53] based on a requirement of linestrength greater than (10)-4
cm-2atm-1. The target supersonic test facility has a gas temperature of ~1000K, pressure
of 72kPa, H2O mole fraction of 25%, and a path length of 10.5cm (horizontal translation
configuration) or 18.7cm (vertical translation configuration). For illustrations of the two
translation configurations refer to Figure 4.1. These gas conditions were used to optimize
the line selection:
1) Absorbance greater than 0.1 was required for the facility conditions. This
allows for implementation of the 2f/1f lineshape optimization for velocity
measurement as described in Chapter 3.
In addition, this absorbance level
guarantees strong SNR for absorption measurements. This reduced the number of
candidate lines to 202.
2) Difference in lower-state energies of the two lines was maximized as described
in Reference [54] for temperature sensitivity over the expected temperature range
in the supersonic test facility. This reduced the number of candidate lines to 10.
3) Minimum separation of the line centers of 0.3cm-1 from the nearest neighbor
was required to ensure sufficient isolation and minimize distortion of Dopplershifted features. This reduced the number of candidate lines to 2.
66
Based on these criteria, two H2O lines at λ1=1348.86nm (E1”=1006.12cm-1) and
λ2=1341.45nm (E2”=1962.51cm-1) were selected. Although spectroscopic data for these
transitions is listed in the HITRAN database, these values can differ significantly from
actual measurements. The HITRAN lower-state energies are generally calculated to a
high degree of accuracy if the line assignment is correct; however, linestrengths,
pressure-broadening coefficients, and exponents for pressure-broadening temperature
dependence often need to be measured to improve accuracy for quantitative sensing
applications.
The linestrengths and air- and self-broadening coefficients (γair and γself) were
measured by wavelength-scanned direct absorption in a high-uniformity heated cell at
Stanford described in Reference [55]; the experimental setup for these experiments is
reproduced in the figure below.
Figure 5.3: Experimental setup for measurement of linestrength and pressurebroadening coefficients in Stanford heated cell [55].
The exponents for self-broadening (Nself) and air-broadening (Nair) temperature
dependence as defined in the equations below were also measured.
67
T
2γ self (T ) = 2γ self (To ) o
T



T
2γ air (T ) = 2γ air (To ) o
T



N self
(42)
N air
(43)
The reference temperature, To, is customarily defined to be 296K.
As shown in Figure 5.3, the scanned-wavelength direct absorption technique was
used, with the laser injection current being driven by a linear ramp. The central zone of
the cell was filled with a known pressure of test gas; for linestrength and self-broadening
measurements, pure water vapor was used, while an air-water vapor mixture was used for
air-broadening measurements. Temperature of the central zone was measured with three
equally spaced type-K thermocouples (Omega) with an accuracy of 0.75% of the reading.
Pressure was measured with a 1000Torr MKS Baratron pressure transducer accurate to
0.12% of the reading. The gas temperature was allowed to equilibrate at each set point
until the three thermocouple readings were within 1K agreement.
Attenuation of the laser transmission due to H2O absorption was monitored with
detectors, and the regions of the beam path external to the cell were purged with nitrogen
to remove ambient water vapor absorption. Direct absorption measurements were taken
at fixed temperatures as the pressure of test gas was varied. Data measured for the
1349nm line are shown in Figure 5.4.
68
Linear fit
Measured
0.03
S(400K)=2.094 cm-2atm-1
0.02
0.8
a)
Collisional width (FWHM) [cm-1]
Integrated Absorbance [cm-1]
0.04
1.0
1.2
1.4
1.6
1.8
2.0
2.2
P*X*L [atm cm]
b)
0.016
0.014
Linear fit
Measured
2γself(400K)=0.48 cm-1atm-1
0.012
0.010
0.010
0.015
0.020
0.025
0.030
Pressure [atm]
Figure 5.4:
a) Measurement of linestrength at 400K for 1349nm line.
b) Measurement of self-broadening coefficient (FWHM) at 400K for 1349nm line.
From the integrated absorbance at various pressures, the linestrength at a
particular temperature can be measured (see Equation 8) from the slope of the line plotted
in Figure 5.4a. Similarly, by measuring the collisional width at varying pressures, the
pressure-broadening coefficient at a given temperature can be determined from the slope
of the line in Figure 5.4b using Equation 12. The experimental method outlined in
Reference [55] was applied to both linestrength and broadening coefficient
measurements, with each point representing the best fit to 150 direct absorption scans.
69
a)
b)
Figure 5.5: a) Measured linestrength versus temperature for 1341nm and 1349nm
lines. b) Measured air-broadening coefficient (HWHM) versus temperature for
1349nm line. Best fits from HITRAN database also shown for comparison.
Figure 5.5 shows measurements of the linestrength and air-broadening coefficient
as a function of temperature; the broadening coefficient temperature dependence
exponents can be determined by performing a power fit to the curve in Figure 5.5b. Best
fits based on values from the HITRAN [53] database are also shown.
Measured
spectroscopic data are presented in Table 5.1 and Table 5.2 and compared with values
from the HITRAN database.
Table 5.1: Linestrengths and self-broadening coefficients (HWHM) at 296K.
Smeasured
cm-2/atm
SHITRAN
cm-2/atm
γself, measured
cm-1/atm
γself, HITRAN
cm-1/atm
measured
1348.86nm
1.20 (10)-2
1.28 (10)-2
0.299
0.34
0.71
1341.44nm
1.73 (10)-4*
1.86 (10)-4
0.198
0.25
0.56
Line
*measured by Liu et al. [55]
70
Nself,,
Table 5.2: Air-broadening coefficients (HWHM) at 296 K.
Line
γair, measured
cm-1/atm
γair, HITRAN
cm-1/atm
Nair, measured
Nair, HITRAN
1348.86nm
6.21 (10)-2
6.30 (10)-2
0.57
0.49
1341.44nm
3.23 (10)-2
3.18 (10)-2
-0.16
-0.16
As seen in the above tables, the current measurements can differ from the values
listed in HITRAN by up to 14%. The measurement uncertainty for the current values is
less than 3%. These values provide the database needed to simulate the 1f-normalized 2f
signal and are used for temperature validation in the Stanford high-uniformity furnace
described in the following chapter. The absorbances for the two selected lines at the
expected facility conditions are simulated in Figure 5.6.
0.4
Absorbance
0.3
0.2
0.18
Absorbance
Horizontal translation
configuration
Vertical translation
configuration
0.1
0.0
7413.0
7413.7
Horizontal translation
configuration
Vertical translation
configuration
0.12
0.06
0.00
7453.6
7414.4
7454.3
7455.0
Frequency [cm-1]
Frequency [cm-1]
Figure 5.6: Simulated absorbances for 1349nm (left panel) and 1341.5nm (right
panel) lines. Spectroscopic data from Tables 5.1 and 5.2 are used. Conditions are
P=72kPa, T=990K, XH2O=0.26, L=18.7cm (vertical translation) or L=10.35cm
(horizontal translation).
As seen in the above figure, strong absorbance is expected for both lines in the
vertical and horizontal translation configurations. This allows for optimization of the
WMS-2f/1f signal as described in Chapter 3.
71
Good separation from neighboring
transitions is also seen, improving the ability to make Doppler-shift measurements. In
the following chapter, the newly measured spectroscopic database is used to validate the
sensor temperature measurement prior to deployment at the NASA Langley test facility.
5.3 Experimental Hardware
This section describes the selection of the lasers, optics, and optomechanics
incorporated in the sensor. Lasers and optics were required to deliver tightly collimated
beams with adequate optical power through the test section; robust design of the sensor
optomechanical hardware was necessary to maintain alignment in the harsh, vibrating
environment of the DCSCTF. Angled optical mounts were necessary to pitch the laser
beams through the 45o slots in the test section, and modifications were required to
accommodate the purge fittings. The size and weight of the assembled hardware was
also constrained by the weight limit of the translation stages and the physical access
available around the numerous facility cooling lines and pressure transducer wires.
5.3.1
Lasers, Fiber Optics, and Detectors
The lasers used in the sensor are fiber-coupled polarization-maintaining
Distributed Feedback (DFB) diode lasers manufactured by NEL (NLK1B5EAAA). The
laser wavelengths are 1348.8nm (30mW) and 1341.5nm (20mW). DFB lasers [97-99]
fall under the class of edge-emitting lasers such as Distributed Bragg Reflector (DBR),
and Fabry-Perot (FP); these lasers are fabricated by horizontally stacking a series of ptype and n-type semiconductor layers.
72
Bragg grating
p-type layers
metal electrodes
n-type layer
n substrate
active region
Figure 5.7: Schematic of a DFB diode laser.
As shown in the figure above, a Bragg grating is etched into the surface of the
active layer. This grating acts as the wavelength selection mechanism for the laser; as the
grating expands due to thermal or electrical heating, the wavelength of constructively
amplified light in the active region changes. DFB lasers have long been used in the
telecommunications industry [100-102], and are attractive for optical sensing due to their
reliable single-mode operation, high optical power, and fast tuning characteristics
[24,61,64,103,104]. Additionally, DFB lasers are spectrally narrow and free from modehopping behavior, which are some of the drawbacks of FP and DBR lasers. These lasers
are ideal for accessing the targeted transitions and accommodating the rapid injection
current modulation necessary for WMS measurements.
Two 35m polarization-maintaining single-mode fibers manufactured by Oz Optics
(PMJ-3A-3A-1300-7/125-3-35-1) were used to deliver light from the lasers into the test
facility. Single-mode fibers have small diameter cores and restrict light transmission to a
single propagation mode; this avoids the problem of modal noise (manifested as a speckle
pattern in the transmitted light) caused by the propagation of multiple incoherent modes
within multi-mode fibers [105]. In addition, the small core size results in a smaller beam
diameter at the output with less divergence.
73
~5-10 μm
Jacket
θ
Core, ncore
Cladding, ncladding
Figure 5.8: Transmission of light in a step-index single-mode fiber optic waveguide.
Core enlarged for illustration.
The schematic above shows the propagation of light in a step-index fiber optic
waveguide. Here θ is the acceptance angle for an incoming ray to be transmitted in the
waveguide; as illustrated in Figure 5.8, total internal reflection of the light ray is achieved
due to the difference in the indices of refraction between the core and cladding materials.
Snell’s Law governs the angle at which light is bent (refracted) when moving between
media with different indices of refraction:
n1 sin θ1 = n2 sin θ 2
(44)
Here θ1 is the incidence angle and n1 is the index of refraction for medium 1; θ2 is the
refracted angle, and n2 is the index of refraction for medium 2. When a light ray is
incident on the interface between media 1 and 2 at an angle greater than the critical angle
(with respect to the boundary normal), light is totally internally reflected and propagates
along the axis of the waveguide. The critical angle, θc, can be calculated easily from
Equation 44 by recognizing that θ2=90o at the onset of total internal reflection:
74
n 
θc = sin −1 2 
 n1 
(45)
This phenomenon occurs for rays moving from a medium of higher index refraction to a
medium with a lower index.
A 2x2 50/50 polarization-maintaining coupler (Canadian Instrumentation and
Research, Ltd. 954P) was used to combine and split the optical power from the two
lasers. A schematic of the coupler is shown in Figure 5.9.
A
1
2
Index-matching
liquid
Polished fiber
halves
B
Core
separation
Figure 5.9: Schematic of 2x2 evanescent wave 50/50 coupler. Inset shows crosssection of coupler.
Power from each of the lasers enters the coupler through inputs A and B. The
optical power from the two inputs is mixed, then split 50/50 into outputs 1 and 2;
nominally there is 50% of the optical power from the wavelength in input A and 50%
from that in input B in each of the outputs. The coupler used for the current work
operates using the evanescent wave phenomenon; optical contact between the cores of
two fibers allows for laser power to be shared between the two waveguides. The amount
of energy transferred is a function of the interaction length and core separation distance
[106,107]. The coupler is manufactured by polishing the cladding of the fiber until the
75
core is exposed and bringing the cores into optical contact with a thin layer of indexmatching liquid in between. The red circles in Figure 5.9 are the stress-inducing rods
found in polarization-maintaining PANDA fibers (discussed further in Appendix A). As
shown in the inset, the stress-inducing rod is removed on the half of the fiber that is
polished away.
Various methods for combining and splitting optical power in fibers exist.
Conventional free-space coupling methods typically involve partially reflecting mirrors
or thin films/plates to split the input beam; these methods are reviewed more thoroughly
in Reference [108]. Major drawbacks include susceptibility to etalons, complex setup,
and high sensitivity to alignment. Considering the rigors of shipping and assembling
equipment during a field campaign, free-space couplers were not a viable option. The
primary fiber-based techniques are fusing or polishing (evanescent wave). Fiber-based
coupling has the advantage of providing a compact, simple method for mixing and
splitting light that is easily manufactured and implemented. Fused-fiber couplers are
made by twisting bare fibers and heating until the fibers are fused together. This method
is much easier to implement than the polishing technique; however, the advantage of the
evanescent wave coupling technique is that the fiber cores remain intact, unlike fusedfiber couplers [109], resulting in reduced cross-coupling between polarization modes.
Evanescent wave couplers also have lower insertion and excess losses (0.005dB and
0.05dB, respectively) than fused-fiber couplers [110]. Insertion loss refers to the total
loss of optical power resulting from insertion of the coupler; excess loss is the optical loss
within the coupler.
Two PM laser attenuators (Oz Optics BB-500-11-2300/1550-7/125-P-40-3A3A3-1) were used to match the powers of the two lasers prior to coupling and transmission
to the test environment. By doing this, the laser signals occupied roughly the same
dynamic range and experienced the same degree of bit noise from digitization. PM fiber
mating sleeves (Thorlabs ADAFC2-PMN) were used to connect fiber components.
These connectors are made from a single piece of material, unlike typical fiber
76
connectors that are manufactured in two pieces and screwed together. PM connectors are
manufactured with stricter tolerances in order to ensure that the polarization axes of the
input and output fiber components are closely aligned.
Large area InGaAs detectors (Sciencetech IGA-030-H) were used to obtain the
transmitted laser signals. The detector has a 3MHz bandwidth, 0.1μs rise time, and 7mm2
active area. The high bandwidth guaranteed that modulation on the order of hundreds of
kHz could be recorded without aliasing. Also, the large active area resisted loss of signal
due to beam wandering during a run since the detector was mounted on the heavily
vibrating test section.
5.3.2
Optomechanical Components
The pitch and catch optical components were carefully selected to maintain
alignment of the laser beams through the test section during facility operation. The pitch
and catch assemblies are shown in Figure 5.10. The pitch assembly in Figure 5.10a
consists of a fiber-coupled collimation lens (Thorlabs F240APC-SP1345), a kinematic
mount (Thorlabs KC1-T), and an angled beam tube. The aspheric 3 fiber-coupled lenses
provided a small beam diameter (1.4mm) necessary to probe the boundary layer, and
were anti-reflection coated at 1345nm to maximize the output laser power. The lens
coupling was manufactured to place the fiber tip exactly at one focal length from the lens
to optimize collimation. A fixture was drilled in the beam tube to allow for nitrogen
purging to remove ambient water vapor. The mounts are very rigid, and the adjustment
knobs could be locked in place after alignment; this guaranteed that the beams would
remain within the 3-mm wide slots in the isolator walls.
The mirror mount (Thorlabs KCB1) for the catch assembly shown in Figure 5.10b
allowed the mirror, beam tube, and detector to be integrated into a single component.
3
Aspheric lenses are used to reduce the effects of spherical aberration in lenses, in which
rays far from the lens centerline are focused to slightly different locations than rays near
the center. This results in improper collimation of a transmitted beam; aspheric lenses,
which have closer to ideal surface curvatures, are an excellent solution to this problem.
77
The mirror mount turned the captured beam by 90o, allowing for adjustment of pitch and
yaw, and focused the beam onto the detector. The angled beam tube was fabricated to
terminate within 1mm of the window surface, and the cavity within the mount was
purged with nitrogen to remove ambient water vapor from the beam path. One-inch focal
length aluminum-coated spherical concave mirrors (Thorlabs CM254-025-G01) were
used to focus the captured beams. These mirrors provide very high reflectivity without
undesirable chromatic aberration which can be introduced by a focusing lens.
The
detector was placed at the focal point of the mirror; this design, along with the large
active area of the detectors, prevented loss of signal during testing, even with heavy
vibration in the test section.
Beam tube
Beam tube
Purge fitting
Purge fitting
Detector
Fiber-coupled
collimation lens
Focusing mirror
b)
a)
Figure 5.10: TDLAS sensor optomechanical components: a) Pitch assembly.
b) Catch assembly. Red dashed lines indicate window surface.
5.3.3
Translation Stages
Two translation stages (Zaber T-LSR 150B) were used to translate the sensor
pitch and catch systems for spatially resolved measurements. The stages served as the
platforms on which the pitch and catch optics were mounted, and it was necessary that
they provide a stable, level surface during testing. The primary selection criteria were:
78
• Appropriate size and weight for integration with the NASA Langley facility
hardware. Also sufficient length to allow travel across entire height and width of
test section.
• Sufficiently high operating temperature to survive close proximity to hot test
section (~600K outer wall temperatures).
• High rigidity to resist facility vibration and maintain alignment.
• Stepper motor to provide smooth, repeatable motion.
• Backlash reduction to ensure repeatability of linear motion.
• Motor step size sufficiently small to achieve spatial translation on the order of
millimeters.
• Capability for remote operation and integration with TDL software control.
• Sufficient speed and torque to translate TDL sensor across duct during a 20
second run.
150mm
travel
Computer
control
data cable
201mm
Mounting
holes
Translation
stage link
cable
Figure 5.11: Zaber T-LSR 150B translation stage.
79
65mm
43mm
The selected stages (one unit shown in Figure 5.11) performed reliably both in the
lab and during the course of testing at NASA Langley. The stages offered 150mm of
linear travel, and could be linked together using the translation stage link cable to move
simultaneously. Control was facilitated through Labview, and the stages interfaced with
the computer through a serial connection. The translation platform also included a grid
of bolt holes for convenient mounting of the optomechanical components detailed in the
previous section.
Laser light
Detector signals
Mounted
fiber-coupled
lens
a)
Focusing
mirror
Catch optics
Detector
b)
Figure 5.12: Fully assembled TDLAS mass-flux sensor mounted on NASA Langley
wind tunnel: a) Pitch assembly. b) Catch assembly.
Figure 5.12 shows the assembled optomechanics of the TDLAS sensor mounted
on the NASA Langley test facility. Mounting plates angled at 90o were fastened to the
translation stage platform to create a mounting surface perpendicular to the test-section
wall. As seen in the above figure, the optomechanical components of the sensor are
compact and require minimal assembly and alignment. The components were easily
locked in place and were able to maintain alignment of the laser beams through the 3mmwide slots in the isolator section during testing.
5.3.4
Sensor Control and Data Acquisition System
Three data acquisition (DAQ) cards (National Instruments PXI-6115) were used
to generate the voltage signals to the laser controller and acquire and digitize incoming
80
voltage signals from the detectors. The cards have 12-bit resolution, and the dynamic
range can be adjusted to match the signal to be recorded. The maximum acquisition rate
is 10MHz/channel; the maximum output rate is 4MHz for a single channel or 2.5MHz for
dual channels. The DAQ cards were installed in a National Instruments PXIe-1062Q
chassis, and each card was connected to a National Instruments BNC-2110 connector
block to output and acquire voltage signals. The chassis provided a rugged, portable
housing for the DAQ cards, and interfaced with the computer using a single PXI
connection. Signal generation, data acquisition, and operation of the translation stages
were facilitated through the computer with the Labview software interface.
Laser current
& temperature
controller
Laser 1 current drive signal @f1
Detector signals
PXI chassis
DAQ computer
Connector
blocks
Test section
Detector signals
Figure 5.13: Signal flow between computer and DAQ system. Computer is used to
generate laser current modulation waveforms; voltage signals are produced by the
DAQ cards and sent to the laser controller which modulates laser injection current.
Detector signals are digitized by DAQ cards and sent to computer for storage.
Figure 5.13 illustrates the operation of the sensor DAQ system. The laser drive
signals were produced using the computer, allowing for the slow-scan and modulation
81
frequencies and amplitudes to quickly and easily be adjusted.
These signals were
transmitted to the DAQ cards in the PXI chassis, which produced the voltage outputs sent
to the laser current controller. The two drive signals were output using different cards to
minimize crosstalk between the outputs on a single card. The detected voltage signals
were then transmitted back to the DAQ cards, which digitized and transmitted the data to
the computer for storage.
Figure 5.14: Generation of laser drive signals. Slow scan shown on left, complete
WMS laser drive signals shown on right. Amplitudes are in volts.
The laser drive signals used for testing at NASA Langley are shown above.
Beginning with a slow-scan frequency of 250Hz and amplitude of 0.17V, the two laser
drive signals were formed by superimposing two different high-frequency modulations.
Laser 1 (1349nm) was modulated at 190kHz with an amplitude of 0.85V, which
corresponds to an m=2.2; Laser 2 (1341.5nm) was modulated at 255kHz with an
amplitude of 0.31V, which corresponds to an m=0.9. Each signal was then delivered to
the laser controller as indicated by the red and blue arrows in Figure 5.13. The slow-scan
and high-frequency modulation amplitudes and frequencies were adjusted as needed
through the control software.
82
Chapter 6: Temperature and Velocity
Validation Experiments at Stanford
Before deploying the sensor in a harsh, uncharacterized environment, an
important task is to validate the sensor measurements against well-known, highly
controlled conditions. This allows for a test of the sensor hardware and data processing
schemes, characterization of measurement uncertainty, and identification of any potential
problems that could arise when the sensor is deployed. With this goal in mind, two wellcharacterized facilities were selected at Stanford for validation of the sensor temperature
and velocity measurements. This chapter describes the experimental setup and the results
obtained from the validation measurements.
6.1 Validation of Temperature Measurement
6.1.1
Experimental Setup
The heated cell described in Section 5.2 provided an ideal environment for
validation of the sensor temperature measurement.
Water vapor temperature was
measured in a quartz cell placed in the center of the three-zone furnace to provide a
uniform (~1%) temperature as measured by thermocouples at the center and each end of
the cell. The slow-scan frequency was set at 2kHz and the 1349nm and 1341.5nm lasers
were modulated at f1=190kHz and f2=255kHz, respectively, with data collected at 5MHz.
Modulation frequencies were selected according to the procedure described in Section
5.1. The laser parameters i0, a, and ψ1 were measured at these settings in order to model
the 1f-normalized WMS-2f signal for a path length of 228cm (3 passes through cell) and
a pressure of 14Torr of neat water vapor. Regions external to the test cell were purged
83
with dry nitrogen to eliminate absorption from the ambient air. The experimental setup is
shown below.
Furnace
Pitch lens,
N2 purged
Detector,
N2 purged
Laser
controller
Fiber coupler
DAQ
computer
Detector signal
Figure 6.1: Experimental setup for temperature validation in 3-zone heated cell.
Single-pass setup shown; actual experiment performed for 3 passes.
Prior to data collection, the background 2f and 1f signals were recorded; the
backgrounds were then removed from the measured signals as detailed in Reference [61].
In both the heated-cell experiments and the NASA Langley test campaign, the
background signals were negligible – more than an order of magnitude lower than the
measured signals. Sources of the WMS-2f background include etalon effects in the laser
beam path (typically arising from constructive/deconstructive interference of internal
reflections in windows), nonlinear intensity modulation effects, and background
absorption outside the measurement region [61,71]. For the experiments described in this
work, great care was taken to eliminate etalons and ambient absorption; the modulation
depths used were also low enough for nonlinear intensity modulation effects to be
insignificant.
6.1.2
Results of Temperature Velocity Validation
To infer temperature, the 1f-normalized WMS-2f peak values were computed as a
function of temperature for both the 1341.5nm and 1349nm lines (following the
equations introduced in Section 2.4); the ratio of these two signals was then produced as
in Figure 6.2.
84
1f-Normalized 2f peak ratio
(1341 nm/1349 nm)
0.6
Calculated
Experimental
0.5
0.4
0.3
650 700 750 800 850 900 950 1000
Temperature [K]
Figure 6.2: Measured and calculated 1f-normalized 2f peak ratio for the high E”
line (1341nm) divided by the low E” line (1349nm).
By comparing the measured 1f-normalized WMS-2f peaks to the simulated
values, the temperature was inferred to within 1% of the thermocouple reading for
measurements from 650-1000 K, the temperature range of interest for the current sensor.
The WMS signals were recorded for 1 second at each temperature condition and
averaged. A 4th-order polynomial was fitted to the computed WMS signals and used to
convert the measured WMS signals to temperature. Results with similar accuracy can be
obtained at lower temperatures, though other transition pairs may have preferable
sensitivity in the low-temperature range. The sensor-measured temperature is compared
to the thermocouple readings in Figure 6.3.
85
WMS Sensor Temperature [K]
1000
900
Measured
Ideal
1% boundary
800
700
600
700
800
900
1000
Thermocouple Temperature [K]
Figure 6.3: Comparison of sensor- and thermocouple-measured temperatures in
Stanford heated cell.
These results show that the sensor is capable of making highly accurate
temperature measurements within the temperature range of interest. The time-resolved
scatter in the data was less than 0.5% in these experiments. The laser modulation in this
experiment was identical to that used in the DCSCTF campaign except for the higher
slow-scan frequency (2kHz vs. 250Hz). Because of the complexity of WMS-based
measurements, careful laboratory validation at the exact conditions to be used in a
measurement campaign is essential prior to deployment of the sensor in the field.
6.2 Velocity Measurement Validation in Low-Speed
Tunnel
6.2.1
Facility and Experimental Setup
The Stanford Flow Control Wind Tunnel (described in detail in Reference [111])
is used to provide highly uniform, well-known flow velocities up to 18m/s. The facility
is closed-loop and operates at atmospheric pressure with room-temperature air and
86
ambient humidity. The tunnel is 91cm high, 61cm wide, and 3.1m long; a picture of the
facility is shown in Figure 6.4 along with the pitch and catch optics and an illustration of
the beam paths.
Figure 6.4: Stanford Flow Control Wind Tunnel with mounted sensor hardware.
Beam paths through test section indicated by dark arrows.
In this experiment, significant design changes were required in order to deploy the
sensor. The walls of the tunnel are made of 1-inch thick Plexiglass, which transmits
poorly in the 1300 – 1400nm region accessible to near-infrared diode lasers. To address
this problem, it was necessary to drill holes through the top and bottom of the tunnel
(drilling through the sidewalls was not acceptable). Additionally, the crossed-beam setup
was not possible due to the presence of a conveyor belt along the bottom of the tunnel
(see Figure 6.4). This limited optical access to a small region of the tunnel; the details of
the experimental setup are shown in Figure 6.5.
87
Figure 6.5: Schematic of velocimetry validation experiment at Stanford Flow
Control Wind Tunnel.
As seen above, the two beams counter-propagate at a 60o angle; this emulates the
crossed-beam setup of Figure 2.8a. Two holes offset by 3 inches along the tunnel
centerline were drilled at a 60o angle through the top and bottom of the tunnel. The inner
surface of the tunnel was sealed with a thin sheet of plastic, and pitch and catch optics
were aligned through the holes. The pitch and catch hardware described in the previous
chapter were used; the beams were pitched through fiber-coupled collimation lenses and
caught onto 1-inch focal length mirrors which focused the light onto 3-mm diameter
InGaAs detectors (3MHz bandwidth). The pitch/catch setups on the top and bottom of
the tunnel were purged with nitrogen to remove absorption occurring in regions external
to the tunnel.
A different water vapor transition was selected for this particular experiment to
account for the low temperature (300K) and low water vapor mole fraction (1%). A
water vapor transition near 1371nm (E”=23.8cm-1) was used to obtain a signal for the
184cm path length similar to that expected from the high-temperature, humid gas in the
NASA Langley test facility (18.7cm path length, 600-1000K, 13%-25% H2O). The slowscan frequency was 250Hz, the modulation frequency was 130kHz, and the sampling rate
was 5MHz. The sensor bandwidth in this case was 500Hz; the laser wavelength was
88
scanned via a sine wave over the absorption lineshape twice per cycle. The velocity was
determined from the Doppler shift of the 2f/1f lineshape, which included more than 6000
points. Use of 2000 points over a laser frequency-scan range of 0.35cm-1 could achieve
similar velocity resolution. For subsonic velocity testing, 50 averages were used to
guarantee a measurement scatter well below 1m/s.
6.2.2
Results of Sensor Velocity Validation
The Doppler-shifted lineshape for the 1371nm transition at m=0.9 is shown in
Figure 6.6. Here it is seen that the 2f/1f amplitude is quite large; this is due to the long
beam path (184cm) that was required for this experiment.
Δν = 7 x 10-4 cm-1
WMS-2f/1f Signal
5
4
3
2
1
0
-0.03
Downstream beam
Upstream beam
-0.02
-0.01
0.00
Frequency [cm-1]
0.01
0.02
Figure 6.6: Doppler-shifted lineshapes for 1371nm transition in Stanford Flow
Control Tunnel. Shift corresponds to velocity of 18m/s.
Data were collected for m=0.9 to optimize the WMS-2f/1f signal and for m=1.7 to
demonstrate the improvement in velocity resolution due to optimizing the modulation
index. Data are presented in Figure 6.7, where the left panel shows measurements of
time-resolved velocity (50 averages, 100ms measurement time per data point), and the
right panel shows measured velocity versus tunnel set point. The tunnel set point is
adjusted by adjusting the fan speed; no measurements are taken between 16 – 17m/s as
89
the tunnel resonates at this condition. The tunnel velocity is measured with a pitot probe,
and the uncertainty was calculated by Matalanis and Eaton [111] to be 0.73% of full scale
(0.13m/s). Optimization of the modulation index improved the standard deviation of the
measurements by 50%. This was especially important at low-speed conditions where
frequency shifts are small – on the order of 10-4cm-1. With m=0.9 the measured velocity
measurements have less than a 0.5m/s difference from the tunnel set point.
a)
b)
Figure 6.7: Velocity measurements in Stanford high-uniformity tunnel: a) Timeresolved velocity measurements for modulation index of 0.9 and 1.7. b) Measured
velocity with one second resolution versus tunnel set point.
The sensor design including modulation optimization demonstrate the capability
to resolve frequency shifts less than 10-4cm-1 (the smallest shift measured was 0.97 (10)-4
cm-1, corresponding to a velocity of 2.5m/s), and provide confidence for application of
the sensor to the supersonic regime where Doppler shifts of the absorption features are
two orders-of-magnitude larger. In the following chapter, the TDLAS mass-flux sensor
is deployed in the field at the NASA Langley DCSCTF.
90
Chapter 7: Mass-Flux Measurements at
the NASA Langley Direct-Connect
Supersonic Combustion Test Facility
(DCSCTF)
The field campaign results presented in this chapter represent the capstone
measurements for the sensor designed in this thesis. The TDL sensor was deployed to
measure temperature, velocity, and mass flux in a high-enthalpy, supersonic wind tunnel
at NASA Langley. Temporally and spatially resolved measurements were tested against
CFD and facility model predictions.
Additionally, concepts such as modulation
optimization and nonuniformity analysis were applied to improve sensor measurements.
The success of the sensor at this facility proves the benefits of TDL mass-flux sensing
with WMS-2f/1f, affirms the accurate modeling of facility flow with CFD, and provides
confidence in deploying the sensor to environments where mass flux is not wellcharacterized.
7.1 Facility Overview
Vitiated ground-test facilities are often used to reproduce hypersonic flight
conditions, either by matching flight enthalpy or velocity.
A common method for
generating high-enthalpy flow is by combustion-heating the air, then expanding the flow
through a supersonic nozzle with optional O2 replenishment [112]. This technique is
employed at the DCSCTF at NASA Langley, which facilitates the testing of ramjet and
scramjet combustor components by simulating flight between Mach 4 and 7.5. Tests of
igniters [113], fuel injector geometries [114-116], and nozzle/combustor flow studies
91
[117] are routinely conducted at the DCSCTF. High stagnation enthalpy is achieved by
pre-heating with H2-O2-air combustion (O2 input rate is regulated to yield a postcombustion mole fraction similar to atmospheric concentration) and accelerating the
heated gas through a Mach 2 or Mach 2.7 converging-diverging nozzle. Additional
details regarding facility operation can be found in [118,119]; a picture of the facility is
shown in Figure 7.1 and a schematic in Figure 7.2.
Figure 7.1: Photograph of the DCSCTF at NASA Langley showing flowpath
sections as labeled.
At the far left of the photograph is the combustion heater, which operates at
stagnation pressures from 115 to 500psi and stagnation temperatures from 890 to 2110K
[120]. Flow then enters the water-cooled supersonic nozzle; TDLAS measurements were
made in a modified isolator section (described in the following section) directly behind
the nozzle. Following the isolator is the fuel injection block and combustor where
scramjet models are tested, and at the far right is the exhaust system. Because the isolator
section was not cooled, test times did not exceed 30 seconds; between runs, atmospheric
air was cycled through the test cell to cool the facility, and tests could be repeated every
15 minutes.
92
Figure 7.2: Schematic of NASA Langley DCSCTF [120].
The facility is outfitted with a Pressure Systems Inc. Electronic Scanning Pressure
system with an accuracy of 0.5% of full scale (0.2psi for 45psi scanners). The system
outputs data from 50-100Hz, and averages the data down to 20Hz. The facility input
flow rates are measured with ASME sharp-edged orifice plates with flange-mounted
pressure taps; the mass-flow measurements have an uncertainty of 3%. Based on the
uncertainty in pressure (0.5%) and the sensor temperature measurement from Section
6.1.2 (1%), the estimated uncertainty for the sensor density measurement at the DCSCTF
is 1.12%. An uncertainty analysis using the sensor density uncertainty and the sensor
velocity uncertainty from Section 6.2.2 (0.9%) yields an expected sensor mass-flux
uncertainty of 1.44%. This upper limit is a twofold improvement in the current mass-flux
uncertainty (measurement accuracy) at the DCSCTF, and measurements in the following
sections show mass-flux measurements with uncertainties of less than 1%.
The facility flow conditions are currently estimated using an inviscid 1-D
thermodynamic equilibrium solver [121-123]. Required parameters for the solver are the
input mass fluxes of oxygen, hydrogen, and air, the geometry of the nozzle, and an
93
estimated heat loss between the heater and the nozzle. The solver iterates until a solution
for the nozzle exit plane parameters is determined, assuming isentropic flow in the
nozzle. This code provides accurate values for comparison with TDL sensor results
during the measurement campaign.
The Viscous Upwind Algorithm for Complex Flow Analysis (VULCAN) [124]
CFD code developed at NASA Langley was used to compute the flow conditions in the
DCSCTF isolator.
This code has been shown to accurately model experimental
measurements of mole fraction, pitot pressure, and total temperature in a Mach 1.8
coaxial jet [125], wall pressures at the exit of a Mach 2.5 nozzle [126], and wall pressures
at the inlet and burner of a flight-tested scramjet engine [127]. Based on the stagnation
temperature and pressure in the combustion heater, nozzle and isolator geometries, and
assumed heat fluxes into the facility walls, the VULCAN code was applied to compute
the relevant flow properties within the test section, i.e. static temperature, pressure, and
axial velocity.
Previous optical diagnostics at the DCSCTF include silane-seeded laser-sheet
flow visualization at the nozzle exit, coherent anti-Stokes Raman spectroscopy (CARS)
thermometry at the nozzle exit plane [119] and in the combustor [123], OH absorption
thermometry at both the nozzle exit and in the combustor [116], and shadowgraph and
UV camera imaging for OH radical visualization in the combustor [115]. Hence the
diagnostics previously deployed have mostly involved thermometry and flow
visualization; the current TDLAS sensor adds spatially and temporally resolved massflux measurements in the facility isolator to the complement of optical diagnostics at the
DCSCTF. In the future, the TDLAS mass-flux results could be included as part of the
standard diagnostic measurements performed during tunnel operation.
7.2 Test-Section Design and Experimental Setup
Precise design of the optical test section was crucial for the successful deployment
of the TDL mass-flux sensor. Extensive modeling was performed to ensure proper
94
material selection, robust optical access design, and capability for TDL sensor
integration. The optical isolator section described in this section successfully survived
dozens of tests at the DCSCTF, where flow temperatures were on the order of 800 –
1000K for each run. Excellent optical alignment was maintained throughout each test
even in the presence of heavy vibration from the facility and spatial translation of the
sensor across several inches of the duct. This section outlines the modifications to the
isolator section of the DCSCTF to facilitate TDL measurements.
The setup and
integration of the TDL sensor with the tunnel hardware are also described in detail.
7.2.1
Scramjet Isolator Section
The isolator is an important component of a scramjet engine, consisting of a
constant area or slightly diverging section situated between the inlet and the combustor.
The flow downstream of the inlet adjusts to the high static back-pressure in the
combustor through a pre-combustion shock train that resides in the isolator. Since the
pressure rise is accomplished over a finite distance, the combustion process is isolated
from the compression occurring at the inlet [128].
The presence of the isolator
safeguards against inlet unstart, in which the pre-combustion shock train is expelled from
the inlet, causing a large decrease in mass capture by the engine. The main components
of a scramjet engine are shown in Figure 7.3.
Figure 7.3: Illustration of flow through a scramjet engine [129].
95
The DCSCTF operates with a constant area rectangular isolator upstream of the
combustor model. When the tunnel is operated with no combustion (as was the case for
the tests described in this work), flow through the isolator is uniform and shock-free.
This makes the isolator an ideal region for a line-of-sight absorption measurement.
Furthermore, the simple geometry of the isolator allows for less time-consuming CFD
modeling of the flow and facilitates the comparison between TDL measurements of gas
parameters and CFD solutions. However, modifications to the isolator section were
necessary to facilitate optical access to the flow and to enable integration with the
TDLAS mass-flux sensor.
7.2.2
Modified Isolator with Optical Access
Design of the optical isolator section was initiated from the original isolator used
at the DCSCTF. The length of the isolator was increased for the current design in order
to facilitate the crossed-beam setup necessary for the velocity measurement. The test
section was machined from a solid block of copper in order to guarantee uniform
expansion in response to the thermal load of the high-temperature test gas.
Pressure taps
Horizontal
translation
beam paths
Vertical
translation
beam paths
Figure 7.4: Modified DCSCTF isolator section for TDLAS mass-flux sensor. Beam
paths in horizontal and vertical translation configurations also indicated (red
arrows).
96
A picture of the modified DCSCTF isolator is shown in Figure 7.4 with the top
and side window mounts removed. The grey residue around the slot on the sidewall is
residual GRAFOIL sealing material that was placed between the mount and the test
section. The isolator is 17.28” long, with an internal rectangular channel that is 2.88” in
height and 5.208” in width (15 in2 area). The top, bottom, and sidewalls are all 1” thick.
The beam paths for the horizontal and vertical translation configurations are indicated
with red arrows. Two pressure taps are located on each surface at 1.4” from the leading
and trailing edges of the test section; these 8 taps provide the pressure measurements
needed to compute gas density from measured temperature.
Proper design of the windows and window mounts was another crucial task. In
addition to sealing the test section, the windows and mounts must also facilitate etalonfree transmission of laser light into and out of the test section while keeping the windows
isolated from the test gas. As mentioned previously, etalons in windows can result in
unwanted background 2f signals which are unstable and can fluctuate during testing. A
schematic of the window mount for the isolator sidewall is shown in Figure 7.5. All
dimensions are the same for the mounts on the top and bottom of the isolator, the only
difference being the length (dimension into the page). The sidewall mounts are 3.875”
long, while the top and bottom wall mounts are 6.21” long; both mounts are 2.75” wide.
97
Incident
angle, θ1
0.25”
Refracted
angle, θ2
θ2
θ2
θ2
1”
θ1
1” thick
isolator
wall
3mm
Figure 7.5: Cross-sectional view of sidewall window mount for isolator section. Ray
trace for 45o incident beam also shown.
Because of the large angle of incidence (45o), a flat window of sufficient
thickness can be designed such that all reflections within the window avoid transmission
through the test-section slots. The incident and refracted angles are labeled in Figure 7.5.
For the current design, the incident angle is 45o in order to obtain the desired crossing
angle of 90o as illustrated by the arrows in Figure 7.8a. The index of refraction for air is
n1=1 and for BK-7 glass is n2=1.5; the refracted angle θ2 within the window is calculated
from Snell’s Law (Equation 44) to be 28o. Knowing this angle and the thickness of the
window (0.25”), the horizontal distance that the beam “walks” is determined to be
3.4mm. Internal reflections also occur at the refracted angle of 28o, and are also shifted
by 3.4mm. As seen in Figure 7.5, the plenum directly under the window has been
dimensioned such that no reflections (dashed arrows) can be transmitted through the slot
in the isolator wall. This strategy avoids the design complexity needed to generate a
mount for wedged windows (the typical method to eliminate etalons), as well as the
increased cost and manufacturing time that would be required.
Two 1/8” Swagelok fixtures are inserted at the top and bottom of the mounts in
order to purge the plenum area behind the window. The pressurized plenum prevents hot
98
test gases from shooting through the slots in the walls and damaging the windows. In
addition, the region between the window and the inner wall of the test section is kept free
from unwanted absorption by water vapor in this near-stagnant gas.
7.2.3
Hardware and Experimental Setup
This section describes the integration of the TDL mass-flux sensor with the
DCSCTF. The translation stages are attached to the test section using 4 bolts, with a
ceramic spacer placed between the stage and the test section to minimize heat conduction
from the hot copper walls. Purge lines for dry, heated nitrogen were connected to each of
the two connections on the window mounts. During testing, only the four windows in
use were purged.
Figure 7.6 shows a schematic of the experimental setup during the measurement
campaign at the NASA Langley DCSCTF.
The computer, data acquisition system,
lasers, laser controller, and fiber optic hardware resided in the control room above the test
cell as shown in Figure 7.7. Light from the two lasers was multiplexed together, split
50/50, and transmitted into the test cell through two 30-meter polarization-maintaining
fibers. The fibers and translation stage control cable were routed through an access port
in the control room floor and into the test cell.
The fibers were coupled to the collimation optics attached to the translation stages
which pitched light into the test section. The transmitted light was then focused by a
mirror onto detectors (both also fixed to translation stages). The detector signals were
transmitted through 30-meter coaxial cables back to the control room and acquired with
the data acquisition system. Access to the test cell during a run was not permitted, hence
the translation stages were remotely operated with computer control. During a run,
tunnel operating conditions were monitored in real-time to ensure that the facility
properly maintained the test point.
99
Flow
Control room
(above test cell)
Test cell
2x 30 m
fiber to
test cell
Combustion
heater
2x 30 m
BNC cable to
control room
Figure 7.6: Schematic of experimental setup for TDL mass-flux measurements at
NASA Langley DCSCTF.
100
Low-pass
filters
Fiber
coupler
DAQ computer
Mounted
diode lasers
NI DAQ
chassis
Laser
attenuators
Laser controller
Figure 7.7: Experimental setup in DCSCTF control room.
The mass-flux sensor was mounted on the custom-isolator section located
between the nozzle and the fuel injectors in Figure 7.1. Optical access via slot windows
on the isolator section is shown in Figure 7.8a.
a)
b)
Figure 7.8: Mass-flux sensor installed on custom-isolator section: a) Sensor
configured to probe vertical planes of the flowpath; arrows illustrate the beampaths.
b) Sensor configured to probe horizontal planes of the flowpath.
The volume between the window and the slots was purged with heated nitrogen to
minimize water vapor in the stagnant gases in the optical path through the isolator wall.
The nitrogen was heated to 353K and delivered at 305SLPM. Measurements were taken
at various purge flow rates to investigate the effect on the TDLAS measurement; no
significant variation in the sensor velocity or temperature measurement was seen in
101
response to changing the purge flow rate. The sensor optical components were attached
to translation stages as shown in Figure 7.8b. The short optical paths external to the
isolator were purged with unheated nitrogen. The optical setup was translated on the
vertical walls, then on the horizontal walls to enable measurements in both vertical and
horizontal planes. Changing the translation configuration required the removal and remounting of both the pitch and catch translation stages. Realignment of the laser beams
was also needed, and the process could be completed within two hours.
7.3 Sensor Operation
Sensor control and data acquisition was accomplished through the Labview
software interface. The modulation signals for the laser current controller were produced
by the software. A digital pulse train was also generated by the software to synchronize
signal generation with data acquisition. Data was collected at 5MHz and stored in binary
format to reduce file size.
The TDL mass-flux sensor was operated in two modes:
• Temporally resolved measurements were taken at a fixed position within the
duct to monitor facility conditions during the entire run.
The sensor was
translated to the measurement position prior to testing. Data acquisition began at
combustion heater ignition and continued until flow was stopped; this enabled
the sensor to capture transients at facility startup and shutdown.
• Spatially resolved measurements were taken at ten locations as the sensor was
translated either horizontally or vertically across the full height or width of the
duct during a single run.
The spatial increments are shown in Figure 7.9.
Smaller increments were used near the walls of the test section to enable finer
resolution of the boundary layer.
102
3mm
increments
12mm
increments
3mm
increments
3mm
increments
24mm
increments
3mm
increments
Figure 7.9: Measurement locations for spatially resolved data acquisition.
Translation directions are indicated with blue arrows, locations indicated with
yellow markers. Flow is into the page.
In translation mode, the control software was triggered using a digital pulse supplied by
the facility. The pulse was generated at the beginning of tunnel test time, signaling the
TDLAS control software to initiate the measurement routine. The translation stage was
sent a command to move into position, after which data was acquired for one second and
stored to disk. Once acquisition was complete, the sensor automatically moved to the
next measurement position and the procedure was repeated.
7.4 Measurements of Velocity, Temperature, and Mass
Flux
During testing of the TDLAS mass-flux sensor, a Mach 2.65 nozzle was used to
simulate Mach 6 and 7 flight enthalpies, producing the nominal test conditions
summarized in Table 7.1.
These conditions were computed using the facility 1-D
thermodynamic equilibrium solver and varied slightly from run to run.
103
Table 7.1: Nozzle exit plane conditions for Mach 6 and 7 set points at NASA Langley
DCSCTF.
Flight enthalpy
Static pressure
[kPa]
Static temperature
[K]
Water mole
fraction
Nozzle exit
velocity
[m/s]
Mach 6
72
714
0.19
1440
Mach 7
72
935
0.25
1630
For a 45o pitching angle through the test section, the path length was 18.71cm in
the vertical translation configuration and 10.35cm in the horizontal translation
configuration (see Figure 7.4).
0.2
0.0
a)
0.4
2f/1f amplitude
2f/1f amplitude
0.4
0
5
10
15
0.2
0.0
-0.2
20
b)
Time [ms]
0.0
0.2
Frequency [cm-1]
Figure 7.10: Signals collected for 1341.5nm laser in the vertical translation
configuration with beams crossing in the center horizontal plane during NASA
Langley DCSCTF measurement campaign: a) Time-resolved WMS-2f/1f signals for
both beams. b) Measured WMS lineshapes vs. frequency for both beams.
Measured signals during the DCSCTF campaign are shown in Figure 7.10. As
expected, the selected transitions provided high SNR at both facility set points and for
both the horizontal and vertical translation configuration. The sensor hardware functioned
as designed, collecting strong transmitted intensity signals despite heavy vibration and
sensor translation during testing. As shown in Figure 7.10b, the central peaks of the
104
WMS-2f/1f lineshapes are clearly resolved and free from interference from neighboring
transitions.
7.4.1
Temporally Resolved Velocity Measurements
Figure 7.11 shows the time-resolved (50Hz) velocity measured in the center of the
channel with the sensor configured to probe the horizontal plane and a modulation index
m=0.9. Figure 7.11a shows the data without boundary-layer correction while Figure
7.11b includes this correction. After the initial start-up transient of the tunnel (caused by
a surge of flow after the hydrogen and oxygen supply valves open), the sensor
measurement without the BL correction was in good agreement with the velocity
computed from the facility predictive code described earlier. The first plateau in velocity
from 2.5 to 5 seconds corresponds to an H2 and O2 mass-flow rate of roughly 80% of the
operating condition. The CFD solution for the isolator at the Mach 7 condition predicted
the boundary-layer thickness to be roughly 9mm.
The uncorrected velocity
measurements shown in Figure 7.11a are roughly 1.7% lower than the facility-predicted
value; Figure 7.11b shows the data of Figure 7.11a with the boundary-layer correction,
and the improvement in agreement between measured and facility-predicted velocities.
105
1800
Velocity [m/s]
Velocity [m/s]
1800
Predicted velocity = 1630 m/s
1650
1500
1500
1350
1350
0
a)
Predicted velocity = 1630 m/s
1650
5
10
15
20
0
25
5
b)
Time [sec]
10
15
20
25
Time [sec]
Figure 7.11: Time-resolved velocity in the middle of the channel, horizontal plane:
a) no correction b) with correction for nonuniformity along LOS.
By correcting for the presence of boundary layers, the difference between the
sensor-measured velocity and the predicted velocity is reduced by more than a factor of
6, bringing the agreement to within 0.25% in a 1630m/s flow. Because of the necessity
for accurate measurement of mass flux, this improvement in accuracy by accounting for
nonuniformity along the LOS is quite significant.
It should be noted that the BL
correction relies only secondarily on the CFD solution. The CFD analysis is used to
quantify the effect that boundary-layer thickness has on a LOS measurement; the sensor’s
spatially resolved measurements yield a value for BL thickness and indicate the
corresponding magnitude of the velocity correction to be applied.
7.4.2
Temporally Resolved Temperature Measurements
Static temperature was determined simultaneously with velocity during all runs.
Both laser wavelengths were multiplexed onto the upstream and downstream beams, and
temperature was determined by comparing the measured 1f-normalized WMS-2f peak
values with simulations for both beam paths. The 1349nm laser was modulated at m=2.2
and the 1341nm laser at m=0.9 for velocimetry.
As described in References
[40,61,64,65], the WMS-2f signal is maximized at m=2.2 and hence changes slowly in
106
response to perturbations such as flow nonuniformity; while only the 1349nm laser was
modulated at m=2.2, this mitigated the influence of nonuniformity on the temperature
measurement. The temperature measurements were not corrected since the influence of
temperature nonuniformity as predicted by the CFD analysis was relatively insignificant.
Time-resolved temperature data are plotted in Figure 7.12 with the Mach 7 flight
condition on the left and the Mach 6 flight condition on the right. These data were
measured at the center of the flow for a horizontal plane at Mach 7 and a vertical plane
for Mach 6. The temperatures for the downstream- and upstream-pointing beams are in
excellent agreement as expected. The 1-σ standard deviation of the average temperature
after the startup transient is ~10K for both conditions. The gas temperature predicted by
the facility model is also in excellent agreement with the measured data after the startup
transient. More measurements are required to determine if the slow variation in gas
temperature is a real facility effect or a measurement artifact, although the gradual rise in
temperature during the run could reflect the change in wall losses as the test-section
temperature increases. In Figure 7.12b, the fluctuations in temperature are a result of the
facility being unable to steadily maintain the Mach 6 flight condition (the nozzle used is
designed for the Mach 7 condition). Again the temperature data dramatically show the
magnitude and duration of facility startup.
107
Downstream
Upstream
1100
900
Downstream
Upstream
Temperature [K]
Temperature [K]
Predicted temperature = 992 K
1000
900
800
5
a)
10
15
20
25
30
700
600
500
35
Time [sec]
b)
Predicted temperature = 762 K
800
5
10
15
20
25
30
35
Time [sec]
Figure 7.12: Gas temperature for downstream- and upstream-pointing beams: a) In
the center horizontal plane for the Mach 7 flight condition. b) In the center vertical
plane for the Mach 6 flight condition. Facility model value also shown.
7.4.3
Temporally Resolved Mass-Flux Measurements
The velocity data (with boundary-layer correction) and temperature data were
combined with facility pressure measurements to determine the mass flux as the product
of velocity and density. For these data the λ1~1349nm laser was modulated at m=2.2 and
λ2~1341nm was modulated at m=0.9. The time-resolved mass flux is shown in Figure
7.13, measured in the center horizontal plane for the Mach 7 flight condition in the left
panel (Figure 7.13a), and in the center vertical plane for the Mach 6 flight condition in
the right panel (Figure 7.13b).
The data for mass flux from the downstream- and
upstream-pointing beams are nearly identical, as expected from the excellent agreement
in the temperature data in Figure 7.12. There is also close agreement between the
measured values and those predicted from the facility model; however, deviations occur
near the beginning of the test due to the startup transient and toward the end of the test as
the input gas mass flows decreased. The decrease in the measured mass flux is primarily
caused by a decrease in the O2 mass-flow rate supplied to the facility. The TDLAS
measurements confirm that the mass flux was nearly constant during a run and
108
demonstrate the sensor’s ability to detect slight deviations in mass flux caused by
changes in the input mass-flow rates.
500
600
Mass flux [kg/m2s]
450
Mass flux [kg/m2s]
Downstream
Upstream
Downstream
Upstream
400
Predicted value = 391 kg/m2s
350
300
250
200
150
a)
500
Predicted value = 475 kg/m2s
400
300
200
5
10
15
20
25
30
35
5
b)
Time [sec]
10
15
20
25
30
35
Time [sec]
Figure 7.13: Mass flux using temperatures taken with downstream- and upstreampointing beams and BL-corrected velocity: a) In the center horizontal plane for the
Mach 7 flight condition. b) In the center vertical plane for the Mach 6 flight
condition. Facility model value also shown.
7.4.4
Spatially Resolved Velocity Measurements
The sensor was also translated during a test across the channel for spatially
resolved measurements; a scan of vertical planes from the left to the right sidewall of the
channel (looking downstream) is shown in Figure 7.14a and a scan of horizontal planes
from top to bottom is shown in Figure 7.14b. The sensor was first positioned within 0.5
mm of the wall at its starting position (top wall for vertical translation, left sidewall for
horizontal translation) and measurements were taken at ten points as the sensor was
translated across the full height or width of the channel during a single tunnel run. At
each point in Figure 7.14, the sensor measurements were averaged for one second, and
the error bars shown are the 1-σ standard deviations of these average values. The total
time for translation and data acquisition was 13 seconds. The optical alignment was
degraded near the walls of the channel, where vibrations can block the edge of the laser
beam; this reduced the signal-to-noise ratio of the transmitted intensity and produced a
corresponding increase in the observed standard deviation shown in the error bars. The
109
spatially resolved CFD velocity data were path-integrated along the sensor beam path,
Distance from centerline [mm]
and the resulting values are plotted in Figure 7.14 for comparison.
TDLAS measurement
CFD path-integrated solution
1750
Velocity [m/s]
1500
1250
1000
750
500
250
0
a)
-60
-40
-20
0
20
40
30
20
10
TDLAS measurement
CFD path-integrated
solution
0
-10
-20
-30
0
60
b)
Distance from Centerline [mm]
250 500 750 1000 1250 1500 1750
Velocity [m/s]
Figure 7.14: Spatially resolved velocity (no correction applied) plotted from: a) Left
to right of channel (facing downstream) in vertical planes. b) Top to bottom of
channel in horizontal planes. Solid data points indicate measurements taken during
facility startup transient.
Overall there is good agreement between the CFD path-integrated solution and
the measured values. The first three TDLAS measurements (solid data points in Figure
7.14a and Figure 7.14b) tend to be higher due to the startup transient seen in Figure 7.11.
In the vertical scan direction, the boundary-layer thickness predicted by the CFD (~9mm)
is confirmed by the TDLAS measurements. For the horizontal scan in Figure 7.14a, the
boundary layer-thickness may be under-predicted by the CFD simulation, although the
TDLAS measurements agree closely in the core flow. These data demonstrate that the
sensor has the capability to make precise, accurate, spatially resolved velocity
measurements in the high-speed, high-temperature flow of the DCSCTF at NASA
Langley.
7.4.5
Spatially Resolved Mass-Flux Measurements
Temperature and velocity data collected at various points within the duct were
processed to produce the spatially resolved mass-flux measurements in Figure 7.15. The
110
sensor measurements are in good agreement with the CFD solution; again the three
outliers at the far left of Figure 7.15a and top of Figure 7.15b are a result of increased
mass flow during the startup transient.
As mentioned previously, optical alignment
tended to be poorer near the edges of the slot windows, resulting in the higher standard
deviations seen in the sensor measurements near the walls.
Overall, the sensor
measurements show that there is good spatial uniformity within the test section and prove
that the CFD solution correctly models the DCSCTF flow conditions.
Mass flux [kg/m2s]
400
300
200
100
0
a)
Downstream
Upstream
CFD solution
-60
-40
-20
0
20
40
30
20
10
Downstream
Upstream
CFD solution
0
-10
-20
-30
0
60
b)
50 100 150 200 250 300 350 400
Mass flux [kg/m2s]
Figure 7.15 Spatially resolved mass flux (no correction applied) at Mach 7 condition
plotted from: a) Left to right of channel (facing downstream) in vertical planes.
b) Top to bottom of channel in horizontal planes.
111
112
Chapter 8: Summary and Future Work
8.1 Summary of Thesis
A mass-flux sensor based on TDLAS of water vapor at 1.4 microns was designed,
constructed, and tested under precisely controlled conditions at Stanford prior to
deployment in a supersonic flow facility at NASA Langley. Mass flux, the product of
velocity and density, was measured based on the combination of velocity and temperature
measurements. Velocity was measured from the relative Doppler shift of an absorption
transition for beams directed upstream and downstream in the flow. Temperature was
measured from the ratio of two absorption signals and used to determine density from the
ideal gas law when coupled with a facility pressure measurement. A new strategy to
improve TDLAS velocity resolution by optimizing the modulation index for 1fnormalized WMS-2f measurements was described here for the first time.
This
normalization accounted for non-absorption losses in the transmitted laser intensity, and
thus reduced noise from vibration and beam steering. The current analysis represents the
first study of the behavior of the WMS-2f/1f lineshape in response to modulation index
and absorbance changes; the lessons learned were applied to generate tall, narrow WMS2f/1f lineshapes that were optimal for Doppler-shift velocimetry.
Line-selection criteria for the sensor design were stated and the needed
spectroscopic database was measured.
The measurement scheme was validated in
controlled laboratory environments: measurements within 1% of a thermocouple reading
were performed in a heated cell at elevated temperatures, and velocity measurements
within ±0.5m/s of the tunnel set point were obtained in a low-speed high-uniformity wind
tunnel. By using newly developed guidelines for optimization of the 2f/1f lineshape, the
velocity measurement precision was increased by 50% over measurements taken with a
non-optimized modulation index. These results demonstrated the potential of TDLAS
113
sensing for accurate mass-flux measurements in ground-test facilities, even at low
velocities.
An analysis of the effects of nonuniformity in temperature, pressure, mole
fraction, and velocity on the WMS-2f/1f lineshape was presented for the first time.
Because TDLAS is a path-integrated technique, there is a need to understand and
quantify the effects of flow nonuniformity on LOS measurements. By incorporating a
CFD solution for the flow within the DCSCTF isolator section, path-integrated WMS2f/1f lineshapes were produced, accounting for nonuniform conditions along the laser
LOS.
A correction to recover the core velocity from the path-integrated velocity as a
function of boundary-layer thickness was developed.
Temperature and velocity
nonuniformity effects on LOS measurements were thoroughly studied in both supersonic
and hypersonic conditions; this analysis led to the development of design rules to
minimize the influence of nonuniformity on LOS absorption measurements.
Having proven the accuracy and precision of the TDLAS mass-flux sensor under
controlled conditions, the sensor was then deployed for spatially and temporally resolved
mass-flux measurements in a high-speed, high-temperature flow in the DCSCTF at
NASA Langley. Measurements at NASA were made in a custom-isolator section with
optical access. The isolator was designed to facilitate optical measurements in vertical
and horizontal planes, and windows and window mounts were designed to eliminate
etalon interference and enable purging. Measurements of mass flux, temperature, and
velocity were found to be in close agreement with both the facility predictive code and
CFD solutions. The improvement in velocity precision afforded by the optimized WMS2f/1f technique was again confirmed, with standard deviations of less than 1% in a 1630
m/s flow. The TDLAS velocity measurement was then corrected using the previously
conducted CFD nonuniformity analysis to within 0.25% of the value predicted by the
facility code. Temperature measurements were made with high precision (10K standard
deviation in a 990K flow), and agreement with the predicted value was also within 1%.
Mass-flux measurements had similar precision (standard deviation less than 1% of full
scale) and accuracy (within 1% of predicted value). Finally, spatially resolved mass-flux
114
measurements were shown to be in good agreement with the CFD solution,
demonstrating the sensor’s capability to make accurate measurements with spatial
resolution on the order of a beam diameter (1-2mm). These results demonstrate the
potential of TDLAS sensing for accurate mass-flux measurements in ground-test facilities
and the potential for improving line-of-sight TDL measurements in nonuniform flow
fields.
8.2 Future Research
8.2.1
Improvements to TDLAS Mass-Flux Sensor
A number of paths for future research stem from the work presented in this thesis.
Building on the demonstration of the TDLAS mass-flux sensor’s accuracy in a highenthalpy supersonic flow, the sensor can confidently be deployed to measure mass
capture in a test environment where the mass flux is not well-known, such as a model
inlet or at a different ground-test facility. Some improvements to the next-generation
sensor include:
•
Adapt the data processing algorithm to measure mass flux in real-time. This
would allow the sensor to be deployed as part of a typical diagnostics package
during operation of ground-test facilities or in-flight testing. This would require a
64-bit operating system to enable processing of larger data sets, or a decrease in
the sampling rate to reduce input data set size.
•
Reduce dwell time at data acquisition locations during spatially resolved
measurements. The spatial resolution of the sensor can be improved by allowing
for more measurement points to be probed during a run. Data showed that
velocity, temperature, and mass flux during the 1-second measurement time were
fairly constant, and hence the need for averaging was minimal. Reducing the
measurement time by a factor of 25 to 40ms would still allow for 10
measurements to be taken at a single location.
115
At this rate, many more
measurement locations could be probed, covering the span of the duct with a finer
spatial resolution.
•
Adapt sensor to target other absorbing species in atmospheric or combusting
conditions. Water vapor is found in large quantities in combustion-driven flows;
hence TDLAS based on H2O is more feasible in combustion-driven ground-test
facilities and engine exhaust gases.
However, water vapor is not present in
significant amounts in the atmosphere and the relative humidity tends to vary with
both altitude and weather conditions. TDLAS of O2 has been proven for massflux measurement previously [10,22,23,27,80]; adaptation of the current sensor
architecture to target O2 would be straightforward.
In environments where
hydrocarbon combustion is present, the sensor can be adapted to target species
such as CO2 and CO. High-accuracy measurements using O2 [22,23,27,80] and
CO2 [58,130,131] have demonstrated that the WMS technique can easily be
applied to different absorbing species. The signal levels for transitions in the 2.7
μm CO2 band and O2 760nm band are also comparable to those in the H2O 1.3 μm
band, guaranteeing good SNR for TDL sensing.
•
Use 16-bit DAQ or increase sampling rate. This would improve the minimum
velocity resolution and enhance the ability to detect small frequency shifts.
However, the size of each set of recorded data would increase, resulting in longer
data processing times. Finer resolution is especially desirable for low-velocity
subsonic measurements.
8.2.2
Pressure and Composition Nonuniformity Analysis
The most significant sources of error in LOS measurements are temperature and
velocity nonuniformity along the beam path; however, pressure and composition
fluctuations often occur, and can also affect the accuracy of LOS measurements.
Nonuniform pressure can cause broadening and pressure-shifting of the detected
lineshape that is not predicted by a model assuming uniform flow. This can skew the
temperature measurement, and the distortion induced in the lineshape by nonuniform
116
pressure can also affect the measurement of velocity.
Similar effects result from
composition nonuniformity, in which the broadening parameters and amplitude of a
lineshape can become distorted. The same approach applied in Chapter 4 can be used to
assess the effects of nonuniform pressure and composition, with the goal of quantifying
the relative significance of nonuniformity in temperature, velocity, pressure, and
composition. Clearly each test environment will have unique flow characteristics, and a
complete analysis of the various nonuniformities listed above will aid in the development
of line-selection criteria suitable for a specific application.
8.2.3
Investigation of Higher-Order WMS Harmonics
The WMS technique can also be extended to higher harmonics beyond the 1f and
2f. The use of a software lock-in allows for multiple harmonics to quickly and easily be
extracted from the detected signal. While there is a decrease in signal level [66,132] as
higher harmonics are used, there is an improved insensitivity to noise (shifting detection
to higher frequencies improves isolation from environmental noise). The ratio of any pair
of WMS-kf signals (k=1, 2, 3…) also results in the removal of the dependence on
detector gain and transmitted intensity; the pair of harmonics used for the ratio can be
tailored to yield the optimal lineshape for the sensor application. Several higher WMS
harmonics are plotted in Figure 8.1.
117
b)
Simulated 3f signal
Simulated 4f signal
a)
0.015
0.010
0.005
0.000
0.010
0.005
c)
Simulated 5f signal
0.000
0.006
0.004
0.002
d)
Simulated 6f signal
0.000
0.003
0.002
0.001
0.000
7454.2
7454.4
7454.6
Frequency [cm-1]
XH2O=0.25, and L=18.8cm. a) WMS-3f lineshape. b) WMS-4f lineshape. c) WMS-5f
lineshape. d) WMS-6f lineshape. Modulation index is 2.2.
The number of inflection points increases along with the order of the harmonic.
As before, the most desirable lineshapes are narrow with high amplitude; this improves
the SNR and precision of the velocity measurement. However, because higher harmonics
have multiple peaks, there is now the opportunity for more frequency-shift measurements
to be made. As seen in Figure 8.2, the ratio of the 4f and 2f harmonics produces a
lineshape with two narrow, large-amplitude peaks. This essentially doubles the number
of possible measurements that can be made over the 2f/1f ratio.
118
2.4
2.0
1.6
1.2
0.8
0.4
0.0
7454.25
7454.50
7454.75
-1
Frequency [cm ]
Figure 8.2: Simulation of WMS-4f/2f signal for same conditions as Figure 8.1.
Further study is necessary to determine the modulation indices at which the
various harmonic ratios are optimized; experimentation is also required to find the proper
combination of harmonics yielding a lineshape that is optimized for Doppler-shift
velocity sensing. Frequency-shift measurements are also possible using the X and Y
lock-in outputs. As seen in Equations 22, 23, 25, and 26, the X and Y components both
have direct dependence on detector gain and transmitted intensity. Hence a ratio formed
with these signals will have the same noise suppression characteristics as a ratio of WMS
harmonics. This may reduce the complexity of the resulting lineshape and allow for
faster data processing times.
8.2.4
Single-Beam Mass-Flux Sensing
Simplification of the optical access to the test section is another area of
improvement for the current sensor, as well as TDLAS sensing in general. Reduction of
the number of access ports eliminates potential disturbances to the flow, simplifies
fabrication, and reduces hardware costs. The current sensor uses two crossed beams,
requiring eight angled slots through the test section and eight slot windows and mounts
(two on each of the sidewalls and two on each of the top and bottom walls). The
experimental setup could potentially be simplified by passing one angled beam through
119
the test section, retroreflecting the beam off the far wall, and detecting the retroreflected
beam. This reduces the necessary optical access from eight windows to two (one on a
sidewall and one on the top or bottom wall). Laser retroreflectors are compact, and can
be installed in a small groove cut into the internal channel, minimizing disturbance of the
flow; however, cleaning of the retroreflector surface may be required periodically. The
experimental setup for such a technique is shown below.
Laser,
pitch lens
Focusing mirror,
detector
Retroreflector
Figure 8.3: Experimental setup for single-beam TDLAS mass-flux sensor. Inset
shows basic principle of retroreflector operation.
The data processing for this experiment would be largely unchanged; absorption
resulting from the original beam would experience an equal and opposite frequency shift
with respect to absorption resulting from the retroreflected beam. However, since the
lineshapes are now captured on the same detector, they may blend together in the
frequency range between the transitions. This would reduce the usable area for Dopplershift measurements, but may be worth the reduction in experimental complexity and
hardware cost. Additional work is necessary to determine the appropriate modulation
parameters and spectroscopic requirements for making such a measurement.
120
Appendix A: Polarization-Maintaining
Hardware
The development of polarization-maintaining capability in fiber optics dates back
to the late 1970’s, although the use of PM optical hardware in sensors has only recently
been adopted.
PM fiber technology is highly important in the telecommunications
industry for coherent optical communications [133,134], optical fiber devices [135], and
active transmission lines [136]; hence there has been significant effort to improve the
reliability, cost-effectiveness, and performance of PM technology since its inception.
The benefits of PM technology can be leveraged to enhance the sensitivity and precision
of TDLAS mass-flux sensing; in particular, velocity measurements can be improved
significantly when the detected signals are free from temporal intensity fluctuations that
can be introduced by standard fiber optics.
Here the principles of polarization-
maintaining fiber optics are investigated, and the benefits of PM hardware for TDLAS
velocity measurements are demonstrated.
A.1 Background and Theory
A fundamental property of an electromagnetic wave such as light is its
polarization, i.e. the orientation of the wave’s oscillations. Electromagnetic radiation is a
transverse wave: the direction of oscillation is perpendicular to the direction of wave
propagation.
Light is composed of many individual waves that can have different
directions of oscillation and relative phase shifts; the oscillation of the vector sum of
these individual waves describes the polarization state of the overall wave.
Electromagnetic waves composed of many random polarizations can always be resolved
into orthogonal components; various types of polarization are illustrated in Figure A.1.
121
x
x
x
z
z
y
y
a)
z
y
b)
c)
Figure A.1: Illustration of electromagnetic wave propagation for: a) Linear
polarization. b) Circular polarization. c) Elliptical polarization. Direction of
electric field vector is indicated by arrows.
The electric field vector of a linearly polarized wave oscillates in a single plane as shown
in Figure A.1a. If the wave is composed of components with equal amplitude and 90o
phase shift oscillating in orthogonal planes, circularly polarized light is produced as
displayed in Figure A.1b. Circular polarization is actually a special case of elliptical
polarization (Figure A.1c), where the wave is composed of orthogonal components of
arbitrary phase shift and amplitude. As light propagates in a waveguide such as an
optical fiber, the polarization typically becomes elliptical since cross-coupling between
polarization modes frequently occurs.
A.2 Polarization-Maintaining Fibers
Polarization-maintaining fibers are capable of restricting the polarization of light
transmission to a single plane. Typical single-mode fibers allow for transmission of light
in two degenerate orthogonal modes [137,138]; coupling between these two polarization
modes causes the transmitted light to become elliptically polarized.
Because the
propagation characteristics of these modes are very similar, transfer of energy between
modes occurs frequently.
The degree of coupling between polarization modes is
primarily a function of the mechanical and thermal stresses applied along the fiber
(bending, twisting, tension, or heat) [109,139].
Cross-coupling of energy between
transmission modes results in polarization noise, which is manifested as intensity
fluctuations at the fiber output.
122
Polarization-maintaining capability is achieved by introducing a strong stressinduced birefringence within the fiber; birefringence refers to the property of an
anisotropic material in which the index of refraction depends on the polarization state of
the incident light. To some degree, geometrical birefringence also exists within the fiber
due to the core being slightly non-circular, although this effect is much less significant
than stress-induced birefringence [140]. Because of the large difference in the indices of
refraction between the two polarization modes of the fiber, the relative phase of any light
that is cross-coupled between the two modes rapidly drifts away. Hence cross-coupling
becomes a highly inefficient process, and typical thermal or mechanical stresses on PM
fibers do not induce coupling between modes.
Various techniques exist for generating stress-induced birefringence in fibers, the
most common of which is to introduce stress applying parts (SAP) made of a different
material during the fiber drawing process. Since the thermal expansion coefficients of
the SAP’s (typically made of glass) and fiber core are different, a highly directional stress
field is introduced in the fiber. The stress field is a function of the difference in thermal
expansion coefficients between core and cladding materials and the separation of the
SAP’s from the core. Some common types of PM fibers are shown in Figure A.2.
Core
a)
Cladding
Stress rods
b)
c)
Figure A.2: Various types of polarization-maintaining fiber:
b) Elliptical cladding. c) Bow-tie.
a) PANDA.
Many other configurations exist to maintain polarization within a fiber [109];
however, the most popular type of PM fiber is the PANDA configuration shown in
123
Figure A.2a. In this type of fiber, the fiber core is sandwiched between two stressinducing rods; the bow-tie configuration in Figure A.2c operates using the same
principle.
External stress
x (slow axis)
y (fast axis)
nx = ny
Core
Cladding
a)
External stress
x (slow axis)
y (fast axis)
nx > ny
Core
Cladding
b)
Figure A.3: Illustration of polarization for light transmitted in: a) Standard singlemode fiber. b) PM single-mode fiber. Arrows indicate direction of electric field
vector. Relative size of internal fiber components not drawn to scale.
Figure A.3 illustrates the mechanism through which polarization is maintained in
a PM fiber. In a standard single-mode fiber, the indices of refraction in the x and y
directions (nx and ny) are identical; hence cross-coupling of light between the two
degenerate modes is easily induced upon application of external stress, e.g. vibrations or
fiber bending. The indices of refraction are related by the following equation:
124

nx  ny  C  x   y

(46)
Here it is shown that the difference in refractive indices along the slow (nx) and fast (ny)
axes of the fiber are a function of the orthogonal stress components in the fiber, σx and σy.
The constant C is a function of the material properties used in the fiber. As mentioned
previously, the PM fiber fabrication process induces a highly directional stress field in the
fiber which generates a large difference in refractive indices nx and ny. In contrast,
standard fibers are nominally isotropic, and hence nx is the same as ny. Thus vibrations,
bending, and thermal gradients cannot efficiently induce polarization mode crosscoupling because the large intrinsic birefringence exceeds that produced by external
stresses.
This effect should be distinguished from bend losses, which occur when the fiber
is bent such that light rays encounter the core-cladding interface at less than the critical
angle and leak into the cladding. This typically occurs only for severe bends in the fiber
as shown in the figure below.
Core, ncore
Cladding, ncladding
Figure A.4: Illustration of bend loss in a fiber. Bend is exaggerated for display
purposes.
While PM fibers are not immune to bend losses, the impregnated stress members
make the fiber more rigid and resistant to bends. Exposure to heat has a similar effect to
bending by changing the local index of refraction; this can allow some of the transmitted
125
light to leak into the cladding. During field measurements it is important to carefully
route the optical fibers such that severe bends and exposure to thermal stresses are
minimized.
Typical diode lasers produce light with polarization parallel to the diode junction.
However, due to spontaneous emission, some light can be emitted with random
polarization (usually only significant near the laser threshold current). The polarization
extinction ratio (PER) of a diode is the ratio of its parallel polarization component to its
perpendicular component, and is typically 1000:1 for an edge-emitting laser operating
near maximum power [141].
Hence light is almost completely emitted in one
polarization state, but must be fiber-coupled properly to prevent cross-coupling between
polarizations.
Coupling a diode laser into a PM fiber pigtail makes the laser fully
polarization-maintaining; this process is fairly simple, and hence the cost of a PM diode
laser is not significantly greater than a conventional diode laser.
To maintain a single polarization state at the output of an experimental setup, all
components of the optical train must be polarization-maintaining. PM fibers restrict
cross-coupling of light between transmission modes; however if the input light is already
elliptically polarized, the PM fiber will transmit this polarization state to the output.
Hence any component that is fiber-coupled must also be polarization-maintaining, and
care must be taken to properly align the polarization axes when launching light into a
fiber.
In order to compare the performance of PM and non-PM fiber components, a
simple laboratory experiment to investigate the zero-velocity sensitivity of the sensor was
performed (illustrated in Figure A.5). Light from a single laser was split and both beams
were directed through a 2-foot long isolation tube; the tube removed the effect of any
drafts present in the room that could affect the velocity measurement. The velocity was
then measured based on the Doppler shift between absorption features detected on the
two beams. Ideally these velocity measurements would continuously measure zero in
quiescent room air. However, intensity fluctuations introduced by polarization changes
in the non-PM fiber components were responsible for errors in the velocity measurement.
126
Detectors
2’ isolation pipe
Laser
Laser splitter
DAQ Computer
Sinusoid @ f1 = 130kHz
Slow scan frequency = 250Hz
Laser Temperature/
Current Controller
a)
10
8
6
4
2
0
-2
-4
-6
-8
-10
2f/1f Velocity [m/s]
2f/1f Velocity [m/s]
Figure A.5: Experimental setup for zero-velocity measurements. A single laser is
split into two beams and passed through the isolation pipe. The beams are focused
with mirrors onto detectors to monitor absorption of atmospheric water vapor, and
velocity is measured from the frequency shift between absorption features measured
on either beam.
2 m/s
0
10
20
30
40
50
Time [ms]
b)
10
8
6
4
2
0
-2
-4
-6
-8
-10
0.75 m/s
0
10
20
30
40
50
Time [ms]
Figure A.6: Comparison of zero-velocity measurements using 1349nm transition at
atmospheric pressure with ambient water vapor and L=68.6cm. Left panel shows
velocity measurements taken with a non-PM laser; right panel shows measurements
with a PM laser.
127
As seen in Figure A.6, velocity precision was improved through the use of a
completely polarization-maintaining optical train; when a non-PM laser was introduced
to the system, the precision of the measurements was degraded. More than a factor of
two improvement in the velocity precision was obtained when using PM components.
The non-PM laser uses standard single-mode fiber coupling instead of the polarizationmaintaining fiber pigtail; hence polarization noise is introduced at the light source and
propagates through the optical train. These results demonstrate the ability of PM fiber
components to resist random cross-coupling of optical power in a controlled laboratory
setting; even more significant benefits are expected in the field where strong mechanical
vibrations are present.
128
Appendix B: Velocity-Measurement
Technique
The development of an efficient, sensitive algorithm for Doppler-shift detection is
an essential component of the sensor design. Velocities on the order of 1m/s produce
frequency shifts of only ~0.5 (10)-4cm-1 for H2O transitions in the 1.4 μm region. Hence
the frequency-shift detection technique must be capable of high resolution, but not so
computationally intensive that the reduction of large sets of data is excessively timeconsuming.
The majority of previous TDLAS velocity sensors have relied on measurements
of the linecenter frequency shift based on either direct absorption [10,11,25,26,41,77] or
WMS-2f [27,80]. The drawback to this method is that the frequency-shift detection
becomes a single-point measurement, disregarding measurements that could be obtained
from the remainder of the lineshape.
Increasing the number of Doppler-shift
measurement points allows for averaging and reduces sensitivity to random noise in the
signals. However, it should be recognized that some portions of the lineshape provide
higher quality measurements than others; the regions near the base and wings of the
WMS-2f1f signal have low SNR and should be avoided. The algorithm for WMS-2f/1f
Doppler-shift measurement in this work builds on the procedure initiated by Lyle et al.
[22,23] for velocity measurements based on WMS-2f signals obtained from O2
absorption.
129
0.06
Beam 1
Beam 2
2f velocity [m/s]
2f signal
0.05
0.04
0.03
0.02
0.01
0.00
1.0
1.5
a)
2.0
2.5
3.0
b)
Time [ms]
1.2
Beam 1
Beam 2
2f/1f velocity [m/s]
2f/1f signal
1.0
0.8
0.6
0.4
0.2
3.6
c)
3.8
4.0
4.2
4.4
4.6
Time [ms]
d)
10
8
6
4
2
0
-2
-4
-6
-8
-10
0.75 m/s
0
10
8
6
4
2
0
-2
-4
-6
-8
-10
20
40
60
80
100
Time [ms]
0.5 m/s
0
20
40
60
80
100
Time [ms]
Figure B.1: Comparison of zero-velocity measurements using WMS-2f and WMS2f/1f at atmospheric pressure with ambient water vapor and L=68.6cm: a) 2f
lineshapes for 1371nm line. b) Measured velocity from 2f signals. Panels c) and d)
show the corresponding results for WMS-2f/1f.
Before proceeding, it is useful to first demonstrate the advantage of WMS-2f/1f
over WMS-2f for velocity sensing. The same zero-velocity measurement experiment as
described in Appendix A was performed using the setup in Figure A.5. Zero-velocity
measurements were taken for the 1371nm line (used for the low-speed wind tunnel
validation in Section 6.2) by measuring the Doppler shift between lineshapes detected on
the two beams. PM components were used in this experiment. The first point to note is
the significant amplitude difference between the 2f signals on the two beams (Figure
B.1a), while the 2f/1f signals are nearly identical (Figure B.1c).
This reflects the
independence of the 2f/1f signal from detector gain and incident intensity. Thus the 2f/1f
signals require a smaller scaling factor to match the amplitudes, with less chance for the
130
lineshape curvature to become distorted during the normalization process. As will be
discussed later, Doppler-shift measurements require lineshapes that are the same
amplitude (ideally the lineshapes would be identical). Thus using the 2f/1f signal reduces
the degree of normalization needed to match the amplitudes of the two detected
lineshapes. Normalization of the lineshapes can introduce error to the measurement if the
curvatures of the lineshapes are not identical. Comparing Figure B.1b and Figure B.1d, it
is seen that the precision of the WMS-2f/1f velocity measurement is improved by 50%
over measurements using the WMS-2f signal. Note that the 2f/1f velocity measurement
precision in Figure B.1 is superior to the precision in Figure A.6 due to the much larger
absorbance of the 1371nm line in comparison to the 1349nm line. The higher absorbance
improves both the SNR and the optimization of the 2f/1f lineshape.
For the current data analysis, Doppler-shift measurements were considered for the
central WMS-2f/1f peak as illustrated in Figure B.2. The central peak of the lineshape
was isolated by identifying the two adjacent local minima (see Figure B.2b).
131
0.3
0.2
0.1
7454.4
7454.6
-1
b)
Frequency [cm ]
1.0
Low-frequency face
High-frequency face
0.1
0.0
7454.2
a)
Low-frequency face
High-frequency face
0.3
0.0
7454.2
0.2
7454.4
Normalized 2f/1f
0.4
0.4
7454.6
-1
Frequency [cm ]
0.8
0.6
0.4
0.2
0.0
7454.400
c)
7454.475
7454.550
Frequency [cm-1]
Figure B.2: Illustration of Doppler-shift measurement regions on WMS-2f/1f
lineshape: a) WMS-2f/1f signals for 1341nm line on upstream- and downstreampointing beams. T=990K, P=72kPa, XH2O=0.26, L=18.7cm, m=0.9. b) Doppler-shift
measurement regions highlighted in blue and green. c) Normalized Doppler-shift
measurement regions.
The lineshapes were then divided into two segments: from valley to central peak on the
low-frequency side of the lineshape (low-frequency face in Figure B.2b), and from
central peak to valley on the high-frequency side (high-frequency face in Figure B.2b).
As shown in Figure B.2c, these segments were then scaled such that the valley
corresponded to an amplitude of zero and the peak corresponded to one. Frequency shifts
can be measured by comparing the two high-frequency faces or the two low-frequency
faces; the current algorithm considers the frequency shift at 100 points along both pairs of
normalized 2f/1f segments and averages the measurements. The velocity-measurement
algorithm is illustrated in Figure B.3.
132
0.4
Lock-in
amplifier
@ 2f, 1f
2f/1f amplitude
Intensity [V]
Detected signals
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
0.00
Etalon transfer
function
0.2
0.0
0.02
0.04
0
5
15
20
1.0
Low-frequency face
High-frequency face
0.8
Δν
0.6
Δν
0.4
0.4
2f/1f amplitude
2000
1800
1600
1400
1200
1000
800
600
400
200
0
10
Time [ms]
Normalized 2f/1f
Velocity [m/s]
Time [s]
0.2
0.2
0
10
20
Time [s]
Convert to velocity
and average
30
0.0
-0.10
-0.05
0.00
0.05
0.0
-0.2
0.10
0.0
0.2
Frequency [cm-1]
-1
Frequency [cm ]
Divide and normalize peak,
measure shifts
Figure B.3: Illustration of velocity measurement algorithm for WMS-2f/1f
lineshapes. The 2f and 1f signals are obtained from detected signals using a lock-in
amplifier and converted to the frequency domain using the etalon transfer function.
The central peak of the WMS-2f/1f lineshape is then divided in two halves,
normalized, and frequency shifts are measured and converted to velocity.
The first step in the velocity-measurement algorithm is to input the detector
signals (intensity vs. time) to the lock-in amplifier.
A digital filter of appropriate
bandwidth is then used to selectively pass the frequency content about the lock-in
frequency. This produces 2f and 1f signals as a function of time, which can directly be
ratioed to produce the 2f/1f signals vs. time as shown in Figure B.3. The laser frequency
is determined as before by passing the laser through a fiber-coupled ring etalon; the
etalon transfer function is used to convert the laser signal from the time to frequency
domain.
As described previously, the central peak on both the downstream- and
upstream-pointing beams was then isolated and normalized between 0 and 1. Testing
showed that measurements had the best SNR and precision at locations greater than the
half-maximum of the central peak. Individual measurements along the high- and lowfrequency faces were averaged to produce a single Doppler-shift value for the lineshape.
133
The presence of nonuniformities in the beam path can distort the absorption
feature and cause slight differences in the measured frequency shifts at different locations
on the lineshape. Mismatch between the upstream and downstream lineshapes can also
result from bit noise, slight perturbations in the gas conditions along the LOS, changes in
laser beam transmission, unequal detector gain, and uneven splitting in the coupler [108].
The latter three factors have less of an effect on the WMS-2f/1f signal as shown in Figure
B.1. Because detector gain and intensity fluctuations are removed for the WMS-2f/1f
signal, the WMS-2f/1f zero-velocity measurement has less scatter (~50% reduction) than
the WMS-2f measurements.
Once the frequency shift was measured, Equation 30 was
used to convert the shift to velocity. Temporal averaging could be applied as necessary
to improve measurement precision.
This measurement scheme was proven to accurately measure velocities as low as
2m/s and as high as 1630m/s, corresponding to frequency shifts that ranged from (10)-4
cm-1 to 5.5 (10)-2 cm-1. The data processing speed was limited by the opening and closing
of the input data sets; since the data recorded for a single run was on the order of 1
gigabyte, it was necessary to divide the data into many smaller subsets to avoid
exceeding the computer’s available memory. Each subset of data was then opened,
processed, closed, and velocities were written to an output file. The time required to
convert raw data to velocity data was insignificant compared with the time necessary for
opening and closing the input files and writing the velocity data to disk. In the future, a
64-bit operating system may enable the data processing computer to handle larger data
sets. Alternatively, the sampling rate could be reduced, especially for high-velocity
testing where lower velocity resolution is acceptable.
This may allow for faster
processing of data, with the eventual goal of a sensor capable of real-time measurements.
134
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