Investigation of TDLAS measurements in a scramjet engine

An investigation of the viability of tunable diode laser absorption spectroscopy for use as aflow measurement device in a scramjet engine was completed.. The fundamental mass capture mea

Investigation of TDLAS Measurements

in a Scramjet Engine

A thesis submitted to the Graduate School

of the University of Cincinnati

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in the Department of Aerospace Engineering

of the College of Engineering

by Dominic L Barone B.S University of Cincinnati, June 2008

May 21, 2010

An investigation of the viability of tunable diode laser absorption spectroscopy for use as aflow measurement device in a scramjet engine was completed First, the effects on TDLASmeasurements across a temperature jump that is common in scramjet combustor flow-pathswas studied using a flat flame burner designed with four independently fueled quadrants.Rigorous thermocouple mapping of the burner was performed and a discussion of multi-thermocouple radiation correction techniques is presented

The fundamental mass capture measurements (temperature, water number density, sure, and velocity) were then made in the isolator section of a direct-connect scramjet engineand compared to a scramjet performance analysis code Post-combustion measurements(temperature and water number density) were measured in the exhaust section of the modelengine The results of the measurements and an in-depth discussion of analysis routines used

pres-in the processpres-ing of raw absorption measurements is presented

Finally, I would like to thank my parents, family and friends for supporting me in all of

my endeavors, whatever they may be; I wouldn’t be where I am today without them

1.1 Problem Statement 2

1.2 Scope 3

1.3 Objectives 4

1.4 Approach 4

2 Absorption Spectroscopy 6 2.1 Properties of the Water Molecule 7

2.2 Beer-Lambert Law 10

2.3 The Line Shape Function 11

2.4 Etalons 13

3 TDLAS System & Analysis 15 3.1 TDLAS System 15

3.2 Data Processing 18

3.2.1 Raw Signal 18

3.2.2 Frequency Determination 18

3.3 Absorption Measurement 19

3.3.1 Direct Area Integration 19

3.3.2 Line Fitting 22

3.4 TDLAS Measurements 24

3.4.1 Two Line Thermometry 24

3.4.2 Boltzmann Plot Analysis 26

3.4.3 Velocity Measurement 27

3.4.4 Pressure 28

3.5 Averaging 29

4 Flat Flame Burner Experiment 31 4.1 Flat Flame Quadrant Burner 32

4.2 Thermocouple Measurements 33

4.2.1 Thermocouple Heat Loss 33

4.2.2 Multi-Thermocouple Radiation Correction 34

4.2.3 Methodology 40

4.3 Thermocouple Results 43

4.4 TDLAS Setup 44

4.5 TDLAS Results 47

5 Research Cell 22 51 5.1 Isolator Measurements 52

5.1.1 Experimental Setup 53

5.1.2 Temperature and Density 54

5.1.3 Pressure 55

5.1.4 Velocity 60

5.2 Combustor Measurements 61

5.2.1 Experimental Setup 61

5.2.2 Combustor Results 64

5.2.3 Signal Quality and Averaging 66

6 Conclusions 74

6.1 Summary 74

6.2 Future Work 75

A Spectroscopic Constants 80 B MATLAB Programs 81 B.1 Shell Script 81

B.2 Main Program 85

B.3 Functions 91

B.3.1 Frequency Determination 91

B.3.2 Absorbance Calculation 94

B.3.3 Voigt Fitting 95

B.3.4 Direct Integration Routine 100

B.3.5 Area Calculation 102

B.3.6 Boltzmann Plot Calculations 103

List of Figures

1.1 Transmission of radiation through the atmosphere 2

2.1 Vibrational degrees of freedom for water 7

2.2 Harmonic oscillator model 8

2.3 NIR Absorbance of water 9

2.4 Beer’s Law 10

2.5 The Voigt lineshape 13

3.1 TDLAS System 16

3.2 Frequency determination 20

3.3 Signal processing 21

3.4 Area calculation methods 23

3.5 Two line thermometry 25

3.6 Boltzmann plot 27

3.7 Velocity measurement 28

4.1 Quadrant flat flame burner 32

4.2 Nusselt number model effects on radiation correction 37

4.3 Nusselt number model comparison 38

4.4 Emissivity Determination 39

4.5 Thermocouple measurement setup for mapping the quadrant burner 41

4.6 Thermocouple point map 42

4.7 Radiation correction using extrapolation of two and three points 44

4.8 Thermocouple temperature map of the quadrant burner 45

4.9 TDLAS setup for the quadrant burner 46

4.10 TDLAS flat flame burner setup 47

4.11 Quadrant burner TDLAS results 48

4.12 TDLAS and thermocouple comparison 49

5.1 Research Cell 22 schematic 52

5.2 RC-22 isolator experimental setup 54

5.3 Isolator temperature-density map 56

5.4 QPERF Comparison 56

5.5 Isolator pressure fluctuation 59

5.6 Isolator Mach number 60

5.7 RC-22 combustor experimental setup 62

5.8 Exhaust measurements 65

5.9 BW Voigt fit 70

5.10 BQ Voigt fit 70

5.11 BQ Direct Integration 71

5.12 BQ Averaging 71

5.13 BW direct integration 72

5.14 Direct integration with equal averaging over 10 points, Run BW φ = 0.3 − 0.1 72 5.15 Averaging Comparison 73

List of Tables

4.1 Operating Conditions 43

5.1 Isolator Temperature Results 57

5.2 Isolator H2O Density Results 57

5.3 Isolator Pressure Results 58

A.1 Constants used for TDLAS analysis 80

~n Velocity vector (m/s)

A Absorption area (cm−1)

A Area (cm2)

Amp Amplitude

b Pressure Broadening Coefficient (cm−1/atm)

cp Specific heat under constant pressure (kJ/kg · K)

E00 Lower-state energy (cm−1)

h Convection heat transfer coefficient (W/m2 · K)

I Signal Intensity (unit independent)

P r Prandtl’s Number (unitless)

Q(T ) Total partition function

Re Reynold’s Number (unitless)

S Absorption Cross Section (cm−1/molecule · cm−2 at standard 296K)

Chapter 1

Introduction

During the last few decades, a great deal of research, development, and flight demonstration

of air breathing hypersonic vehicles has been completed A critical challenge for hypersonicvehicles is to extend the engine operability limits In order to design a propulsion systemcapable of hypersonic flight, a detailed understanding of the flow physics associated withdifferent regions of the combustion system over a range of operating conditions is needed

To a large extent the net heat release and thrust achieved in a scramjet combustor

is governed by the effectiveness of the fuel injection, mixing and flame holding Pushingthe limits of the combustor Mach number operability envelope while maintaining minimalcombustor length requires significant improvement in the fuel-air mixing rate and flameholding Understanding how these phenomena are affecting the system is paramount toimproving scramjet performance

The harsh scramjet environment has limited the use of in-stream probes for pressure,velocity, temperature and species measurements to the inflow and outflow locations of theengine; typically only wall measurements of pressure, temperature and heat flux, are rou-tinely made throughout the entire engine The experimental information acquired from theselocations can be used to quantify the overall performance of the tested scramjets, but theycan not be easily or directly used to improve the state of the art combustion performance

Figure 1.1: Transmission of radiation through the atmosphere Adapted from Rohde[1]

knowledge In-stream experimental data (temperatures, pressures, species, and velocities)within the flow field of the scramjets are needed to advance our understanding of the fuel-airmixing and combustion processes in scramjet combustors Additionally, in-stream data can

be useful for validating results obtained using computational fluid dynamics (CFD)

Many laser based non-intrusive probes have been developed for combustion diagnostics[2, 3].This research proposed to use tunable diode laser absorption spectroscopy (TDLAS) for

H2O species and velocity measurements in scramjet combustion environments The choice

of TDLAS probe for this project is based on: (1) TDLAS has the capability to measure theconcentration of species of interest (H2O, O2, and many others), temperature and velocity,(2) TDLAS can have very fast response time and the system is very compact, (3) TDLAS

is very robust and is currently been used in many harsh environments (with heat, dust,vibrations, etc.), such as gas-, coal-, and waste-fired power plants, and (4) AFRL has recentlydemonstrated its capability in measuring temperature, water number density and velocity

in a scramjet isolator[4]

The goal of the current TDLAS research is to produce an unobtrusive measurementtechnique for temperature, density, velocity and possibly pressure in a scramjet engine Thisresearch could lead into an all optical measurement of thrust in an engine Several differentanalysis techniques are being used to validate the TDLAS data in measuring temperature

of the flame

Previous scramjet TDLAS work has mainly dealt with measurements in the isolator,which provides a clean uniform flow, ideal for TDLAS The goal of this work is to show thatthe TDLAS technique can be used in the combustion and exhaust region of a scramjet

This thesis investigated the accuracy and precision of tunable diode laser absorption troscopy for use as a flow measurement device in a scramjet engine The TDLAS systemused was verified and the ability to make average measurements over a temperature gradi-ent was proven using a flat flame burner Mass capture measurements (temperature, waternumber density, pressure, and velocity) were then made in the isolator section of a modelscramjet engine and compared to a scramjet performance analysis code Post-combustionmeasurements (temperature and water number density) were then measured in the exhaustsection of the model engine An in-depth discussion of analysis routines used in the process-ing of raw absorption measurements is presented along with careful accounting of associatederrors

spec-1.3 Objectives

In this thesis, the following objectives needed to be accomplished in order to evaluate theutility of TDLAS for use in a scramjet engine:

i Create a program capable of automatically processing and analyzing the large amount

of data produced by high-speed TDLAS data collection

ii Complete mapping and understanding of the quadrant flat flame burner being used forTDLAS verification

iii Verify the ability of TDLAS system to measure a temperature step that may be present

in a scramjet combustor flow-path

iv Show the viability of TDLAS as an in-situ measurement technique for a scramjet engine

in both the isolator and post-combustor regions

v Investigate the accuracy and precision of TDLAS for scramjet measurements

To complete the objectives of this thesis a complete understanding of the physics behindlaser absorption spectroscopy was needed Chapter 2 presents a brief overview of absorptionspectroscopy and the theory pertinent to making TDLAS measurements

Analysis of TDLAS data requires significant effort The data needs to be processedfrom its raw waveforms into useable absorption spectra Then the shape of each absorptionfeature in the spectra need to be analyzed in order to make a meaningful measurement.Not only does this process take time but the raw waveforms from TDLAS system can be asignificant amount of data The creation of an automated program that can analyze spectrawith minimal amount of input was required Chapter 3 is a review of the data processingand analysis techniques used

In order to verify the ability TDLAS to measurement a temperature step quadrant flatflame was used for a bench-top comparison Intensive thermocouple measurements weredone on the burner to provide the best possible baseline at various conditions TDLASmeasurements were then made and compared with the thermocouple measurements and theresults are presented in Chapter 4.

Due to the limitations of a flat flame burner to produce a wide range of temperaturesand pressures for validation of TDLAS, further baseline measurements were made in theisolator of a direct connect scramjet test engine The isolator measurements also allowedfor measurements of velocity The TDLAS measurements were then applied to the exhaustregion of scramjet to measure the products of combustion Chapter 5 contains the results ofthe isolator and combustor experiments

Chapter 2

Absorption Spectroscopy

Spectroscopy is defined as the study of the interaction between radiation and matter based onwavelength or frequency[5] The behavior of matter interacting with radiation can be stud-ied as a function of the wavelength or frequency of the radiation, referred to as a spectrum,which is useful in determining properties of the matter being studied There are three mainspectroscopic measurement classes: 1) absorption spectroscopy which uses the properties of

a molecule or atom’s ability to absorb radiation over a given range in the electromagneticspectrum; 2) emission spectroscopy which uses the molecule or atom’s radiative properties,

or its ability to emit radiation when excited from an outside source; and 3) scattering troscopy which measures how radiation is scattered at different wavelengths, angles andpolarizations For this work, absorption is the method of spectroscopy that will be used.Absorption is of particular interest because the absorption features can be isolated andmeasured using laser spectroscopy Due to their abundance in the telecommunication indus-try, diode lasers have become very precise, inexpensive instruments compared to other types

spec-of lasers available for spectroscopy A diode laser is a laser in which the cavity is built on

a semiconductor similar to a light emitting diode (LED) For this experiment, distributedfeedback (DFB) lasers where used where the output wavelength can be adjusted by varyingthe electric current and temperature of the a diode, thus introducing a tunable diode laser

ν2 1595 cm-1Bend

ν3 3756 cm-1Anti-symmetric stretch

Figure 2.1: Vibrational degrees of freedom for water

A diode laser is capable of tuning through a narrow range of frequencies (typically 1-5 cm−1)very quickly allowing for measurements of multiple absorption features with a single laser.Diode lasers are also very small allowing for easy transportation and setup along with thepromise of flight capabilities

2.1 Properties of the Water Molecule

Water is of particular interest in a scramjet engine because it is abundant in the atmosphereand it is a product of combustion During flight, incoming water from the atmosphere can bemeasured in the isolator; water is also produced in the engine which can then be measureddownstream as an indicator of combustion efficiency The differences temperature, pressureand velocity of the water measured in the isolator and exhaust by the laser system can beused to determine the thrust produced by the engine

In order to make TDLAS measurements we need to understand the properties of thewater molecule Water has nine degrees of freedom based on the thermodynamic principlethat molecules have three degrees of freedom for each atom in the molecule For water, thereare three translational, three rotational and three vibrational degrees of freedom, shown in

Figure 2.2: Harmonic oscillator model from Hollas[6]

figure 2.1 The three translational stages are simply the molecule’s ability to move in thethree ordinate directions common to three-dimensional space The three rotational degrees

of freedom are taken as the ability to rotate about the center of mass of the molecule inthe three ordinate directions, and the three vibrational modes are a result of the molecularbonds moving relative to each other, by stretching and bending

Each degree of freedom represents the characteristic modes of the molecule which can becombined to describe the overall motion of the molecule For a molecule to change vibrational

or rotational states it must move from a low energy state E0 to an upper energy state of E1

or vice versa The transition from one energy state to another happens in a discrete manneranalogous to the harmonic oscillator effect[6], a representation of which can be seen in figure2.2

The energy state of a given molecule can change through absorption, spontaneous sion and stimulated emission Absorption is the prominent process being studied and bothtypes of emission can be neglected over the range of the lasers being used in this experiment,although the water from combustion will produce spontaneous emission at other wavelengths.Figure 2.3 shows the absorption spectrum of water for the typical frequency range of tunable

emis-7000 0 7050 7100 7150 7200 7250 7300 7350 7400 7450 7500 0.05

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Wavenumber [cm ï1 ]

H 2 O Absorbance Laser Ranges

Figure 2.3: Absorbance of water over the range of interest to NIR tunable diode lasers withspecific reference to the frequency range of the lasers used in these experiments

lasers diode lasers being used in this experiment (compare with Figure 1.1)

It is important to understand how the energy state of the molecule is changing in eachabsorption feature Because these energy changes happen in a discrete fashion they can berepresented by integer values of quanta where a quanta is the amount of energy required

to produce a transition between states The vibrational state of water is represented in theHITRAN[7] database by a three digit number such as 000 where the integer value of eachdigit represents the quantum state of each mode For example 201 has 2 quanta of symmetricstretch vibration and 1 quanta of antisymmetric stretch Similar nomenclature can also beused to describe the rotational quanta of the molecule

There are several water absorption features that fall within the scanned frequency of thelasers used in this research, consisting of vibrational and rotational transitions All of thetransitions used for measurements fall in the vibrational transition from the 000 lower energystate to the 101 upper energy state and specific rotational transitions were selected based

on population density over the desired temperature range A complete list of constants usedand considered can be seen in appendix A.

As stated in the previous section, as radiation passes through a medium, absorption orstimulated emission can occur when the energy gap between two vibrational or rotationallevels is matched by the energy of the incoming photons Beer’s Law describes the resultinginteraction of the incoming radiation with an initial intensity I0 passing through a medium

of length l and it’s losses due to absorption

Figure 2.4: Control volume of unit cross sectional area and length l used for deriving Beer’s Lawfrom Bernath[5]

By considering a small distance dx through the medium, the change in intensity of lightcan be written in the following form:

where I is the radiation intensity, S0 is the line intensity of a particular transition, g(ν)represents the line-shape function, and N is the number of molecules present in the volumeslice Assuming constant gas properties across the line of sight the equation can then be

integrated over the entire length of the control volume, l, resulting in the following equation,

of temperature, pressure and velocity which is very useful and discussed in the next section

In order to understand absorption spectra we need to understand all of the mechanismsinvolved that produce the shape of an absorption feature As shown in equation 2.1 thereare three parts of the absorption feature: species density N , line strength S0, and line-shape g(ν − ν10) The line-strength and species density are directly related to the area ofthe absorption feature, and the line-shape function describes how the absorbance changeswith frequency This frequency dependence of absorption is very important, since it is afunction of many different physical properties of interest, including pressure, temperature,and velocity

Collisional (Pressure) Broadening

As molecules collide, the phase of the oscillating dipole moment is altered in a randommanner The result of this encounter is to take the infinitely narrow line shape associatedwith an infinitely long cosine wave to a line-shape function of finite width [5] This finite

width line-shape can be modeled using the Cauchy-Lorentz function with a full width at halfmaximum (FWHM) of:

∆νL = 1

Where T2 is the average time between collisions The number of collisions that occur within

a given time is directly related to the pressure so equation 2.2a can be re-written,

where b is known as the pressure broadening coefficient and is generally determined mentally

experi-Doppler Broadening

Similar to pressure broadening being caused by the collision of molecules, Doppler broadening

is the effect produced by the random motion of molecules relative to the measurement beam.From the point of view of an absorbing atom or molecule with a fixed resonance frequency,the wavelength of the incoming electromagnetic wave is changed due to the Doppler shiftcaused by the motion of the particle This effect can also be analyzed from the laboratorypoint of view, where the apparent resonance frequency of each atom or molecule is shifted.The frequency distribution associated with the random motion of the particles relative tothe beam path can be represented as a Gaussian line shape and the FWHM value is given

by Bernath[5]

∆νD = 2ν0

r2kBT ln(2)

∆νD = 7.1 × 10−7ν0

rT

The Voigt Profile

In order to determine an analytical expression for an absorption feature, the various linebroadening terms need to be taken into account The two revailing broadening terms being

Figure 2.5: The Voigt lineshape adapted from Bernath[5]

Pressure and Doppler broadening are represented by Lorentzian and Gaussian profiles spectively In order to combine these two terms we can think of a line shape with a Gaussiandistribution about ν0 caused by Doppler broadening and at each ν00 there is a Lorentziandistribution caused by the pressure broadening In mathematical terms this is simply theconvolution of the Gaussian and Lorentzian profiles, the result of which is known as theVoigt Profile shown in figure 2.5

re-Doppler Shift

The same principles that produce the Doppler broadening of the line-shape also cause ashift in the center frequency of the line-shape In determining the Doppler broadening itwas assumed that the random movement of the molecules was based solely on a gaussiandistribution about zero, meaning no bulk flow relative to the absorption path However,

if there is bulk flow relative to the path, a subsequent shift in the center frequency of theabsorption feature is observed This moves the entire line-shape along the frequency axis

When light is encapsulated between two reflected surface, an interference pattern is created.This pattern is used as the bases for the Fabry-Perot interferometer and is also the basic

laser resonating cavity[8, 9] When the two reflective surfaces of an interferometer are heldparallel it is said to be an etalon An etalon can easily be created using the two sides of aquartz plate as the reflecting surfaces, this can be very useful and obtrusive.

Etalons can be used to determine the relative frequency of a varying monochromatic lightsource such as a tunable diode laser The distance between peaks of the interference pattern,known as the free spectral range, is given by Hecht and Zajac[9] in equation 2.4

where (∆νf sr) is the distance between peaks, c is the speed of light and nfd is optical length of the etalon If a laser is tuned monotonically, such as in a sawtooth waveform, therange of the frequency scanned by the laser can then by measured using this etalon technique

path-by counting the number of peaks detected path-by the photo detector

Etalons are very useful for determining the frequency range of the diodes; however, theetalon effect can be very detrimental when unwanted In general, any polished window withparallel sides becomes an etalon This means that any laser passed through this window will

be effected In order to avoid this destructive pattern a beam can be set at an angle to theparallel surface of the window such that the etalon effect does not effect the laser path orthe window can be constructed so that one side is at an angle so the window will not etalon

It is important to consider these effects because they can be very detrimental to TDLASmeasurements

Chapter 3

TDLAS System & Analysis

There are two major parts of making TDLAS measurements, the physical measurementsystem and the data processing and analysis methods The TDLAS system was designed to

be a mobile measurement system capable of making multiple TDLAS measurements for asingle experiment Once a measurement is made, the data must be processed into a usablesignal and then analyzed to extract meaningful information

The TDLAS system was designed to be a flexible device, allowing for several different surements to be made A schematic of the system is shown in figure 3.1, including systemhardware and typical optical components Both the National Instruments (NI) control com-puter and the laser control system are housed in a movable cart, allowing for transportationbetween research cells, or to other facilities This system was designed and first used by Lind-strom et al[10] for tomographic reconstruction of the shock train in the isolator of a scramjetengine The same system was used for the experiments here, with some modifications of theoptical setup

mea-The laser signal is created by time-multiplexing three distributed feedback (DFB) diode

lasers, each operating in different spectral regions Each DFB diode laser output is regulated

by thermo-electric controllers (TEC) which maintain the appropriate temperature TheTECs are controlled using an ILX Lightwave LDC-3916 laser diode controller which is set

to maintain a given temperature and ramp the current to the laser according to incomingwaveform from the control computer

The fiber-coupled beams from the laser diodes are combined to one fiber using a 1x4Newport combiner In order to track the output of the diodes, the signal goes through a10/90 splitter with the 10% portion of the split going to a reference leg The 10% signal isthen split again using a 50/50 splitter and routed to a reference detector (Thorlabs PDA400) and an SiO2 etalon with a 2.000 ± 0.002 GHz at 1550 nm free spectral range from LosGatos Research Laboratory The remaining 90% beam from the 10/90 splitter is used for themeasurements, usually passing through a 50/50 splitter then a 1x8 splitter, resulting in up

to 16 measurement paths that are then collimated (Thorlabs F240APC-C collimator, 8mmfocal length) For each line of sight the transmitted laser power is then measured using 2mmdiameter FGA21 InGaAs photodiodes from Thorlabs

The NI control computer is made of three major components: the main computer (NIPXI-8105), three waveform generators (NI PXI-5402), and three multifunction data acqui-sition cards (NI PXI-6133) The main computer uses an Intel Core Duo 2.0 GHz processorwith 2 GB of DDR2 RAM and runs Windows XP from which an in-house LabWindowsCVIuser interface program controls the waveform generators and the data acquisition cards Thewaveform generators are used to create the sawtooth waves that control the thermo-electriccontrollers The data acquisition cards take the raw voltage from the photo detectors andconvert them into a storable digital signal Each PXI-6133 is capable of taking 2.5 millionsamples per second with 14 bit accuracy on 8 channels One channel is reserved for thereference detector and one is reserved for the etalon channel, allowing for up to 22 analoginputs from photodiodes or other information This can produce an enormous amount ofdata, 2.5 × 106(samples/s) × 14(bits/sample) × 8 channels × 3 cards ≈ 100(megabytes/second), a

hard drive raid array is implemented for this high speed data capture.

This section details the absorption data analysis processing in order to use the data formeasurements All of the data processing was done using MATLAB codes which can befound in Appendix B

The raw signal is given as a voltage from a photodetector, which is a relative measurementdue to many different factors The relative angle of the beam to the photodetector andwhere exactly the beam hits the detector affect the reported voltage Also, each beam’spower can be slightly different due to splitting and even though each photodetector’s gaincan be individually adjusted to account for this, it is not an accurate compensation In order

to adjust for the relative differences between each path, they need to be normalized to thereference signal

The diode lasers used in the TDLAS measurement are current tuned to produce a sawtoothwave in order to cover a frequency range of two to three wave-numbers This allows eachlaser to scan across several different absorption features This is very convenient, howeverthe nature of the tuning is non-linear in frequency space and needs to be accounted for This

is done by sending a reference signal through a known etalon path As described in section2.4, the relative frequency can be determined by finding the peaks or troughs of the etalonsignal Equation 3.1 defines relative frequency in wave-numbers ν − ν0 of each peak as afunction of the known etalon frequency f (2.00 GHz for the TDLAS system), peak number

n, and the speed of light c.

νi− ν0 = f · ni

The result of applying equation 3.1 to the each laser can be seen in figure 3.2

It is possible to calculate the absolute frequency ν0 by using a known line shape centerfrequency Further, the error of the frequency determination can be found by comparing thecenter frequencies of multiple line shapes relative to their known values

In order to get the raw signal into useful units of absorbance we need to use equation 2.1where I0 is the reference signal and I is the measurement path signal The absorbanceunits are then multiplied by -1 to get the familiar absorption peak instead of a valley asshown in figure 3.3 There are several methods for determining the area of an absorptionfeature for use in the TDLAS measurement Each method presents different tradeoffs inaccuracy, computational intensity and robustness, sometimes multiple techniques can beused in conjunction for better results

It is possible to simply integrate the absorption feature by estimating the baseline andusing a Trapezoidal Riemann Sum The baseline is removed first by using a one or twostep baseline removal process Specific frequency ranges are then selected for integration

to isolate absorption features Proper baseline removal is then checked by analyzing thesymmetry of the absorption feature over the selected range Once the appropriateness of thebaseline removal is confirmed, the absorption feature can then be numerically integrated.This method is very useful when the baseline of the entire frequency range cannot beestimated by a simple polynomial It is very important to select appropriate peaks that can

100 200 300 400 500 600 700 0.05

0.1 0.15 0.2 0.25

Point Number (fsamp uN samp ) ï1

Raw Signal Etalon Peaks

0 0.5 1 1.5 2 2.5

Figure 3.2: Frequency determination example; On the left is the raw etalon signal for each laserannotated with the found peaks On the right is the resulting frequency conversion function

100 200 300 400 500 600 700 0

0.5 1 1.5 2 2.5 3 3.5

Point Number

7160 7160.5

7161 7161.5

7162 0

0.05 0.1 0.15 0.2 0.25 0.3

Wavenumber [cm ï1 ]

Measurement Subtraction Result

Figure 3.3: Example of the de-multiplexed raw signals for each laser converted into absorbanceunits Each laser contains a measurement, subtraction, reference, and etalon channel The ab-sorbance of the subtraction path is taken from the measurement path, eliminating unwanted signalfrom the measurement path

be easily isolated for analysis In order for this technique to work well, the selected peaksneed to be well isolated from other nearby peaks, Figure 3.4 shows both The features at7185.597cm−1 and 7161.410cm−1 are not well suited due to the fact that there are otherabsorption features within the wings of the measured feature The features 7179.752cm−1and 7160.812cm−1 are well suited since they are well isolated.

Absorption features can be very closely estimated by a Voigt profile which is a convolution of

a Gaussian profile and a Lorentzian profile, which represent the Doppler broadening and thenatural line width respectively [11] The convolution of the Gaussian and Lorentzian curves

is a computationally intensive task, but an efficient method was introduced by Huml´ıˇcek[12] Using this knowledge, a complete spectra can be simulated by adding multiple Voigtprofiles together Due to non-linearities in the current tuning of the lasers themselves, thesawtooth wave is not exactly straight resulting in a baseline that must be accounted for Theresulting equation for the synthetic spectra is shown in equation 3.2 where ν is frequency, a

is an amplification factor, ν0 is the center frequency, and ∆Di and ∆Li are the full width athalf max for the Doppler and collisional broadening parameters respectively

This method proves to be very computationally intensive but provides the needed values

to calculate temperature, pressure, density and velocity This method also proves veryeffective in situations that contain Gaussian white noise, even with low signal to noise ratios,

or systematic errors that can be adjusted for using the baseline function This method

7184.5 7185

7185.5 7186

7186.5 7187

7185.5 7186

7186.5 7187

(b) Direct Integration

7184.5 7185

7185.5 7186

7186.5 7187

(c) Voigt Fitting

Figure 3.4: Area calculation methods

also allows for integration of peaks that are very close together and begin to blend Thismethod does prove to have some difficulties; with nonlinear optimization it is possible for theoptimization method to fall into a false minimum, resulting in an incorrect solution Thismethod will also fail when the baseline cannot be properly fit, due to some experimentalinfluence.

Once the data has been broken down into values for each spectroscopic feature, it needs

to be turned into a useful measurement This section describes all of the methods usedfor determining temperature, water number density, pressure and velocity One of the keyassumptions used in measurement techniques here is that the flow is in thermal equilibrium

A very quick and efficient way of determining the temperature of the beam path is to use

a ratio of absorption feature areas Because each individual water transition has a uniquetemperature dependence based on the Boltzmann factor associated with the lower stateenergy it is possible to determine the temperature using the ratio of two different absorptionpeak areas This process is very convenient for fast temperature determination

Figure 3.5 shows various spectra and maps of the peak ratios as a function of temperature

It is ideal to select peak ratios with high gradients over the temperature range being explored

to improve the response of the measurement and improve reliability It is also beneficial toselect one peak that does not change significantly over the temperature range For instance,using the 1045 line (little variation with temperature) with the 224 line (strong for lowtemperatures) will produce good results for temperature below 1200 K Above 1200 K, usingthe 1045 line with the 1875 line also yields good results

7184.5 7185

7185.5 7186

1 2 3 4 5 6 7 8 9 10

Temperature [K]

1045 i

1045 136 1216 224 222 1875

7179 7179.5 7180 7180.5 7181 7181.5

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Temperature [K]

Peak Ratios [Ai/A 224 ] 1045

136 1216 224 1875

7159.5 7160 7160.5 7161 7161.5 7162

0.4 0.6 0.8 1 1.2 1.4

Figure 3.5: Two line thermometry peak area On the left are representative spectra at 500 K,

1000 K, and 1500 K, notice significant changes in peak sizes On the right are various ratios forthe peaks that can be used for calculating temperatures

3.4.2 Boltzmann Plot Analysis

Boltzmann plot analysis is the basic tool for determining temperature and density usingmultiple absorption features of a given molecule The integrated area term can be plottedrelative to the initial energy state for each transition The temperature and density are foundfrom linear regression of these plotted points The following equation comes from integratingBeer’s law (Eq 2.1) over the area of the entire absorption feature and substituting theHITRAN relationship for the line strength as a function of temperature

+ ln 1 − e−hν10 /k B T

(3.3a)The stimulated emission term, e−hν10 /k B T ref
, is effectively zero for the transitions of waterover the temperature range studied here This simplifies Equation 3.3a to:

ln

A



(3.3b)Using equation 3.3b the Boltzmann plot can be created by plotting the integrated areaterm, lnSA

, on the ordinate axis and the initial energy state, E00, on theabscissa as shown in figure 3.6 The linear regression is straight forward We write:

y = ln

A

Srefe

−E 00 /k B T ref



(3.4c)The linear regression analysis is done using the weighted least squares fitting as prescribed

in Numerical Recipes[13] to solve for a0 and a1 The temperature and density are thendetermined using the following equations:

0 200 400 600 800 1000 1200 1400 1600 1800 2000 38.2

38.4 38.6 38.8 39 39.2 39.4 39.6 39.8

Figure 3.6: Example of a Boltzmann plot

where T is the temperature N is the total molecular number density The equations can bere-written:

N = e

a 0L

Q(T )Q(Tref)

to the random motion of the absorbing molecules If the mean velocity of the moleculesrelative to the beam is not zero, then the entire absorption feature will be shifted by a factorproportional to the velocity; shown in equation 3.7 where ~v is the bulk flow velocity vectorand ˆn is the normal vector of the measurement beam

ν = ν0



1 −~v · ˆnc



(3.7a)