May 2012 

NASA/CR–2012-217569 

Dual-Pump CARS Development and 

Application to Supersonic Combustion 

Gaetano Magnotti and Andrew D. Cutler 

The George Washington University, Washington, D. C. 
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May 2012 

NASA/CR–2012-217567 

Dual-Pump CARS Development and 

Application to Supersonic Combustion 

Gaetano Magnotti and Andrew D. Cutler 

The George Washington University, Washington, D. C.
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

Acknowledgments 

The authors would like to acknowledge the contributions of the many members of the 

research team that made this work possible. Deserving of credit are Paul Danehy, Sarah 

Tedder, Lloyd Wilson, Daniel Bivolaru, and Gregory Herring. Many other persons whose 

names are not mentioned here have contributed significantly, and the authors express 

their sincerest thanks. 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an 

official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics 

and Space Administration.
v 

Abstract

Successful design of hypersonic air-breathing engines requires new computational 

fluid dynamics (CFD) models for turbulence and turbulence-chemistry interaction in 

supersonic combustion. Unfortunately, not enough data are available to the modelers 

to develop and validate their codes, due to difficulties in taking measurements in such 

a harsh environment. 

Dual-pump coherent anti-Stokes Raman spectroscopy (CARS) is a non-intrusive, 

non-linear, laser-based technique that provides temporally and spatially resolved 

measurements of temperature and absolute mole fractions of N2, O2 and H2 in H2-air 

flames. A dual-pump CARS instrument has been developed to obtain measurements 

in supersonic combustion and generate databases for the CFD community. Issues that 

compromised previous attempts, such as beam steering and high irradiance 

perturbation effects, have been alleviated or avoided. Improvements in instrument 

precision and accuracy have been achieved.

An axis-symmetric supersonic combusting coaxial jet facility has been developed 

to provide a simple, yet suitable flow to CFD modelers. The facility provides a central 

jet of hot “vitiated air” simulating the hot air entering the engine of a hypersonic 

vehicle flying at Mach numbers between 5 and 7. Three different silicon carbide 

nozzles, with exit Mach number 1, 1.6 and 2, are used to provide flows with the 

effects of varying compressibility. H2 co-flow is available in order to generate a 

supersonic combusting free jet. Dual-pump CARS measurements have been obtained 

for varying values of flight and exit Mach numbers at several locations. 
vi

Approximately one million Dual-pump CARS single shots have been collected in the 

supersonic jet for varying values of flight and exit Mach numbers at several locations. 

Data have been acquired with a H2 co-flow (combustion case) or a N2 co-flow 

(mixing case). Results are presented and the effects of the compressibility and of the 

heat release are discussed.
vii

Table of Contents

Abstract ............................................................................................................................. v 

Table of Contents ........................................................................................................... vii 

List of Figures .................................................................................................................. xi 

List of Tables ................................................................................................................... xx 

List of Acronyms ............................................................................................................ xxi 

List of Symbols ............................................................................................................. xxiii 

CHAPTER 1 - Introduction ............................................................................................. 1

1.1 Hypersonic Air-Breathing Propulsion...................................................................... 1

1.2 Experimental Data for CFD Development and Validation ...................................... 4

1.3 Measurement Techniques......................................................................................... 5

1.4 CARS in Supersonic Combustion Experiments for CFD Validation at NASA 

Langley Research Center ............................................................................................. 10

1.5 Development of a Dual-Pump CARS Instrument for Supersonic Combustion 

Experiments.................................................................................................................. 15

CHAPTER 2 - Coherent Anti-Stokes Raman Spectroscopy....................................... 17

2.1 Introduction ............................................................................................................ 17

2.2 Molecular Energy States and Population Distributions ......................................... 18

2.3 Molecular Spectroscopy ......................................................................................... 23

2.4 Derivation of CARS Signal .................................................................................... 24

2.5 Lineshape Models .................................................................................................. 28

2.6 Multi-Color CARS ................................................................................................. 31
viii

CHAPTER 3 - The Dual-Pump CARS Instrument ..................................................... 36

3.1 Experimental Set-Up .............................................................................................. 37

3.1.1 The Laser Cart....................................................................................... 37

3.1.2 Combining and Collecting Optics ......................................................... 41

3.1.3 Wavelength Selection ........................................................................... 44

3.1.4 Laser Alignment.................................................................................... 46

3.2 The Data Acquisition System................................................................................. 48

3.3 Data Analysis ......................................................................................................... 51

3.3.1 Data Pre-Processing .............................................................................. 51

3.3.2 The Theoretical Library ........................................................................ 62

3.3.3 Spectral Fitting ...................................................................................... 63

CHAPTER 4 - Mitigation of Beam Steering Effects.................................................... 65

4.1 Introduction ............................................................................................................ 65

4.2 Beam Steering Mitigation Technique .................................................................... 67

4.3 Numerical Results .................................................................................................. 72

4.4 Experimental Results ............................................................................................. 75

4.4.1 Experimental Set-Up ............................................................................. 75

4.4.2 Beam Displacement Experiment........................................................... 78

4.4.3 Turbulence Effects Experiment ............................................................ 86

4.5 Modeling the Effects of Beam Spreading .............................................................. 94

CHAPTER 5 - High Irradiance Perturbation Effects ................................................. 99

5.1 Introduction ............................................................................................................ 99
ix

5.2 Background .......................................................................................................... 101

5.2.1 Stark Broadening ................................................................................ 102

5.2.2 Stimulated Raman Pumping ............................................................... 109

5.3 Experimental Set-up ............................................................................................. 114

5.4 Results and Discussion ......................................................................................... 116

CHAPTER 6 - Characterization of the Dual-Pump CARS Instrument .................. 128

6.1 Introduction .......................................................................................................... 128

6.2 The Hencken Burner Flame ................................................................................. 128

6.3 Non-Uniformities in the Hencken Burner Flame ................................................. 130

6.4 Instrument Accuracy ............................................................................................ 134

6.5 Herman Wallis Correction Factor ........................................................................ 136

6.5.1 Temperature Accuracy ........................................................................ 139

6.5.2 Lineshape Models ............................................................................... 141

6.5.3 Non-Resonant Susceptibility .............................................................. 145

6.6 Instrument Precision............................................................................................. 150

6.7 Instrument Dynamic Range.................................................................................. 156

6.8 Spatial Resolution ................................................................................................ 161

CHAPTER 7 - Laboratory-Scale Supersonic Combusting Jet ................................. 164

7.1 Description of the Facility .................................................................................... 166

7.2 Numerical Analysis .............................................................................................. 169

7.2.1 Thermal Analysis ................................................................................ 170

7.2.2 CFD Analysis ...................................................................................... 175
x 

7.3 Experimental Set-Up ............................................................................................ 179

CHAPTER 8 - DP-CARS Measurements in the Laboratory-Scale Supersonic 

Combusting Jet.............................................................................................................. 183

8.1 Introduction .......................................................................................................... 183

8.2 The Compressible Shear Layer ............................................................................ 184

8.3 DP-CARS Data Acquisition and Test Matrix ...................................................... 188

8.4 Additional Challenges in DP-CARS Data Acquisition in the Laboratory-Scale 

Supersonic Free Jet .................................................................................................... 192

8.5 Measurements at the Nozzle Exit ......................................................................... 195

8.6 Mixing Study ........................................................................................................ 202

8.6.1 Mean Values ....................................................................................... 203

8.6.2 Mole Fraction of Gases Based on their Provenance ........................... 212

8.6.3 Spreading Rate .................................................................................... 215

8.6.4 Standard Deviation and Co-Variances ................................................ 218

8.7 DP-CARS Results: Combustion Case .................................................................. 226

8.7.1 Means, Standard Deviations and Co-Variances for the Combustion Test 

Cases 226

8.7.2 Effect of Heat Release ........................................................................ 240

8.8 Discussion ............................................................................................................ 248

CHAPTER 9 - Conclusion............................................................................................ 250

9.1 Summary .............................................................................................................. 250

9.2 Future Work ......................................................................................................... 257
xi 

List of Figures

Figure 1-1: Schematic of a TBCC concept ......................................................................... 2

Figure 2-1: Vibrational population for N2 as function of the temperature ....................... 20

Figure 2-2: a) Rotational population for N2 and b) H2 for three values of 

temperature ........................................................................................................... 21

Figure 2-3: CARS energy level diagram .......................................................................... 24

Figure 2-4: Dual-pump CARS energy level diagram ....................................................... 33

Figure 3-1: Picture of the laser cart................................................................................... 37

Figure 3-2: Schematic of the optical set-up on the upper level of the laser cart ............... 39

Figure 3-3: Schematic of the combining and collecting optics......................................... 41

Figure 3-4: Theoretical dual-pump CARS spectrum (red) and experimental nonresonant signal spectrum (blue) collected in Argon ............................................. 45

Figure 3-5: Contribution from the Nd:YAG flashlamps................................................... 53

Figure 3-6: Contribution from the flame luminescence .................................................... 54

Figure 3-7: Average non-resonant spectrum in argon ...................................................... 55

Figure 3-8: Experimental spectra and theoretical fit before (a) and after (b) 

shifting the excitation profile ................................................................................ 59

Figure 4-1: Planar BOXCARS.......................................................................................... 68

Figure 4-2: Effect of “in-plane” beam motion: a) beams sectioned by the x-z

plane; b) beams sectioned by the focal plane (x-y) without beam steering, 

and c) with “in-plane” beam steering.................................................................... 70

Figure 4-3: a) No beam steering; b) effect of “out-of-plane” beam motion when 

using a round Nd:YAG beam and c) an elliptical Nd:YAG beam ....................... 71
xii 

Figure 4-4: Normalized CARS signal as function of the axis ratio of the Nd:YAG 

beam. ..................................................................................................................... 74

Figure 4-5: Images of the Nd:YAG pump beam at the “in-plane” focus, for 

different lens rotation angle. The numbers are the axis ratios .............................. 76

Figure 4-6: FWHM diameter of the Nd:YAG pump beam at the “in-plane” focus, 

as function of the lens rotation angle .................................................................... 77

Figure 4-7: Three images of the beams at the focal plane, with circular and 

elliptical configurations of the Nd:YAG............................................................... 79

Figure 4-8: Sensitivity of the CARS signal to displacement of the overlapped dye 

lasers relative to the Nd:YAG beam ..................................................................... 80

Figure 4-9: Sensitivity to “out-of-plane” beam displacement for round and 

elliptical Nd:YAG beam ....................................................................................... 81

Figure 4-10: Sensitivity to “out-of-plane” displacement for round and elliptical 

Nd:YAG beam; ..................................................................................................... 82

Figure 4-11: Sensitivity to combined “out-of-plane” and “in-plane” displacement 

for an elliptical Nd:YAG beam. ............................................................................ 83

Figure 4-12: Nd:YAG beam at the location of the beam crossing where the 

crossing point is moved by “in-plane” displacement ............................................ 84

Figure 4-13: Sensitivity to “out-of-plane” displacement for round and elliptical 

Nd:YAG beam. The signal is normalized dividing by the peak signal; 

dotted curves are obtained by numerical simulation ............................................. 85

Figure 4-14: Schematic of the helium jet used to generate beam steering ....................... 87
xiii

Figure 4-15: a) Centroid position of the narrowband dye laser with and without 

the turbulent helium jet; b) Images of the narrowband dye laser at the focal 

plane. ..................................................................................................................... 89

Figure 4-16: Histograms of the CARS signal for various axis ratios without the 

helium jet .............................................................................................................. 90

Figure 4-17: Comparison between the histograms of the CARS signal and the 

products of the laser intensities ............................................................................. 91

Figure 4-18: Histograms of the CARS signal for various axis ratios with the 

helium jet .............................................................................................................. 93

Figure 4-19: Histograms of the CARS signal computed with the helium jet, 

neglecting beam spreading .................................................................................... 95

Figure 4-20: Histograms of the CARS signal with the helium jet from experiments 

and numerical simulations including beam spreading .......................................... 97

Figure 5-1: a) Voigt (continuous) and collision broadened (dashed) N2 Q(5) 

linewidth (FWHM) as function of temperature; b) Estimated Stark shift as 

function of the total irradiance ............................................................................ 107

Figure 5-2:a) Collision-broadened and Galatry linewidth (FWHM) for three H2

rotational lines as function of temperature; b) Estimated Stark shift as 

function of the total irradiance ............................................................................ 108

Figure 5-3: a) CARS spectra in ambient air and b) in a Hencken burner flame at Φ

=0.3, narrowband dye laser irradiance varied ..................................................... 118
xiv 

Figure 5-4: Normalized peak to baseline ratio for N2 and O2 measured in a Φ=0.3 

Hencken burner flame (a) as function of the pump-Stokes irradiance 

product and (b) total irradiance ........................................................................... 121

Figure 5-5: Fit (a) temperature and (b) O2 mole fraction as function of the pumpStokes irradiance product .................................................................................... 123

Figure 5-6: CARS spectra collected in a Φ=2 Hencken burner flame with different 

irradiances for the S(5), S(6) and S(9) lines ....................................................... 125

Figure 5-7: Normalized peak to baseline ratio for H2 rotational lines measured in a 

Φ=2 Hencken burner flame as function of the pump-Stokes irradiance 

product (a) and total irradiance (b). .................................................................... 126

Figure 6-1: Hencken burner, top view ............................................................................ 129

Figure 6-2: Temperature contour plot in the vertical plane (y=0) for a) Φ=0.3 and 

b) Φ=2 ................................................................................................................. 132

Figure 6-3: Temperature contour plot in the horizontal plane (z=40 mm) for a) 

Φ=0.3 and b) Φ=2 ............................................................................................... 133

Figure 6-4: Measured (symbols) and computed (continuous black line) 

temperature as function of the equivalence ratio Φ ............................................ 134

Figure 6-5: Measured (symbols) and computed (continuous black line) mole 

fraction as function of the equivalence ratio Φ ................................................... 135

Figure 6-6: Herman-Wallis (HW) factor for N2 and O2 as function of the 

rotational quantum number J, according to the JK and TB models .................... 137

Figure 6-7: Difference in % between a) temperature and b) mole fractions 

obtained using the JK and the TB models for the HW factor ............................. 138
xv 

Figure 6-8: Measured (red circles) and computed (lines) temperature as function 

of the equivalence ratio Φ. .................................................................................. 140

Figure 6-9: O2/N2 ratio as function of the equivalence ratio Φ....................................... 141

Figure 6-10: Fit of an average of 500 single shot spectra collected in ambient air 

to a theoretical spectrum computed using the Voigt model ................................ 142

Figure 6-11: H2/N2 ratio as function of the equivalence ratio. ....................................... 143

Figure 6-12: Measured N2 mole fraction in Hencken burner, using Lundeen and 

Hahn values for the non-resonant susceptibilities .............................................. 145

Figure 6-13: Measured O2 mole fraction in Hencken burner, using Lundeen and 

Hahn values for the non-resonant susceptibilities .............................................. 146

Figure 6-14: Measured (symbols) and computed (continuous line) mole fraction 

as function of the equivalence ratio Φ. ............................................................... 149

Figure 6-15: Temperature standard deviation as a function of the measured 

average temperature. ........................................................................................... 151

Figure 6-16: Mole fraction standard deviation as a function of the equivalence 

ratio Φ ................................................................................................................. 155

Figure 6-17. Measured (symbols) and predicted (continuous line) CARS signal 

intensity in camera counts as a function of the temperature ............................... 157

Figure 6-18: CARS spectra for Φ=0.2, acquired (blue line), and numerically 

saturated (red line) .............................................................................................. 159

Figure 6-19: Error in temperature (a), N2 (b), O2 (c) for fuel lean cases as function 

of the temperature and of the ratio between the detector saturation 

threshold and the CARS signal intensity (α); d) error in N2 and H2 for fuel 
xvi

rich cases as function of the equivalence ratio when S(5) saturates the 

detector ................................................................................................................ 160

Figure 6-20: CARS spatial resolution ............................................................................. 162

Figure 7-1: Visible image of the laboratory-scale supersonic combusting free jet ........ 165

Figure 7-2: Schematic drawing of the laboratory-scale burner. Flow is left to right. ..... 167

Figure 7-3: Convective heat transfer coefficient on the combustion chamber and 

nozzle internal wall for several values of exit and flight Mach number ............. 172

Figure 7-4: Temperature distribution for Me=1.6 and Mf=6. Flow is left to right. ......... 174

Figure 7-5: Total temperature (top) and OH mass fraction (bottom) distribution 

for Me=1.6 and Mf=7 ........................................................................................... 177

Figure 7-6: Static temperature profiles at the nozzle exit ............................................... 178

Figure 7-7: Infra-red image of the supersonic combusting jet. ....................................... 181

Figure 8-1: Infra-red image of the supersonic combusting jet. Green circles are the 

measurement locations ........................................................................................ 189

Figure 8-2: Beam steering caused by turbulence in the laboratory-scale supersonic 

free jet. ................................................................................................................ 193

Figure 8-3: Comparison of numerical and experimental temperature profiles at the 

nozzle exit for 4 combinations of Me and Mf ...................................................... 199

Figure 8-4: Comparison of numerical and experimental mole fraction profiles at 

the nozzle exit for 4 combinations of Me and Mf. ............................................... 201

Figure 8-5: Average temperature and mole fractions at different heights for 

Me=1.6 and Mf=6 and 7. ...................................................................................... 205
xvii

Figure 8-6: Average temperature and mole fractions at different heights for Mf=6 

and Me=1.6 and 2. ............................................................................................... 208

Figure 8-7: Average temperature and mole fractions at different heights for fixed 

Mf=7 and, Me=0.75, 1 and 1.6. ............................................................................ 210

Figure 8-8: Normalized temperature (a) and N2 mole fraction (b) difference as 

function of the normalized z coordinate.............................................................. 211

Figure 8-9: Mole fractions of gases based of their provenance ...................................... 214

Figure 8-10: Jet diameter (δR), shear layer width based on the normalized 

temperature (δT) and on the center-jet mole fraction (δf) as function of the 

distance from the nozzle exit, expressed in nozzle diameters ............................ 216

Figure 8-11: Normalized growth rates as function of the compressibility 

parameter Π, compared to Slessor`s fitting curve ............................................... 218

Figure 8-12: Temperature and mole fractions standard deviation, and temperature, 

N2 co-variance (<T, N2>) at different heights for Me=1.6 and Mf=6 and 7 ........ 220

Figure 8-13: Temperature and mole fractions standard deviation, and temperature, 

N2 co-variance (<T, N2>) at different heights for Mf=6 and Me=1.6 and 2 ........ 223

Figure 8-14: Temperature and mole fractions standard deviation, and temperature, 

N2 co-variance (<T, N2>) at different heights for Mf=7 and Me=0.75, 1 and 

1.6........................................................................................................................ 224

Figure 8-15: Normalized standard deviation on the centerline, and normalized 

peak standard deviation as function of the distance from the nozzle exit, 

expressed in nozzle diameters ............................................................................. 225
xviii

Figure 8-16: Mean temperature and mole fractions at different heights for the 

combustion test-cases.......................................................................................... 227

Figure 8-17: Temperature and mole fractions standard deviations at different 

heights for the combustion test-cases. ................................................................ 228

Figure 8-18: Co-variances at different heights for the combustion test-cases ................ 229

Figure 8-19: <O2, H2> and <N2, H2> at different heights for the combustion testcases .................................................................................................................... 230

Figure 8-20: Mean, standard deviations and co-variances for z = 1 mm , 

combustion cases. ............................................................................................... 231

Figure 8-21: Mean, standard deviations and co-variances for z = 15 mm, 

combustion cases ................................................................................................ 233

Figure 8-22: Mean, standard deviations and co-variances for z = 35 mm, 

combustion cases. ............................................................................................... 236

Figure 8-23: Mean, standard deviations and co-variances for z = 65 mm, 

combustion cases; note change in horizontal scale from Figs. 8-16 through 

8-18 ..................................................................................................................... 238

Figure 8-24: Mean, standard deviations and co-variances for z = 100 mm, 

combustion cases. ............................................................................................... 239

Figure 8-25: Normalized mean temperature difference (a) and normalized 

temperature standard deviation on the centerline (b) as function of the 

normalized z coordinate ...................................................................................... 241

Figure 8-26: Composition by gas provenance for the combustion cases........................ 244
xix 

Figure 8-27: Composition by gas provenance for Me=1 and Mf=7. Comparison 

between mixing and combustion. ....................................................................... 245

Figure 8-28: Locations where the mole fractions of gas coming from the center jet 

are 20% and 80% of their value on the centerline for Me=1, and Mf=7 .............. 246

Figure 8-29: Histograms of temperature at x=0, z=1 mm (lower panel) and at 

x=14.7 mm, z=100 mm (upper panel) ................................................................. 247
xx 

List of Tables 

Table 7-1: Centerline values at the nozzle exit ............................................................... 179

Table 7-2: Mass flow-rates, computed and measured pressure for the 

combination of Me and Mf tested ........................................................................ 180

Table 8-1: Test cases for DP-CARS measurements ....................................................... 188

Table 8-2: Measurements and confidence intervals at the nozzle exit on the 

centerline for Me=1.6, and Mf=7, and H2 co-flow .............................................. 195

Table 8-3: Measurements and confidence intervals at the nozzle exit on the 

centerline for Me=1.6, and Mf=7, and N2 co-flow. ............................................. 198

Table 8-4: Values of the velocity ratio (λu), density ratio(λρ), convective Mach 

number Mc, and Slessor`s compressibility parameter Π for the conditions 

tested ................................................................................................................... 203
xxi 

List of Acronyms

CARS = Coherent Anti-Stokes Raman Spectroscopy 

CEA = Chemical Equilibrium Analysis 

CCD = Charge Coupled Device 

CFD = Computational Fluid Dynamics

DNS = Direct Numerical Simulation

DCSCTF = Direct-Connect Supersonic Combustion Test Facility 

FEM = Finite Element Method

FWHM = Full Width at Half Maximum

HW = Herman Wallis

JK = James-Klemperer 

IR = Infra-red 

IRS = Interferometric Rayleigh Scattering

LES = Large Eddy Simulation

MTV = Molecular Tagging Velocimetry

NASA = National Aeronautics and Space Administration

PIV = Particle Image Velocimetry

PLIF = Planar Laser Induced Fluorescence

RANS = Reynolds Averaged Navier-Stokes 

RBCC = Rocket Based Combined Cycle

SiC = Silicon Carbide

SLPM = Standard Liter Per Minute
xxii 

SRP = Stimulated Raman Pumping

TB = Tipping Bouanich 

TBCC = Turbine Based Combined Cycle 

TDLAS = Tunable Diode Laser Absorption Spectroscopy 

USED CARS = Unstable-resonator Spatially Enhanced CARS 

UV = Ultra-violet

VULCAN = Viscous Upwind Algorithm for Complex Flow Analysis 

WIDECARS = Width Increased Dual-Pump Enhanced CARS
xxiii 

List of Symbols

c = speed of light: 299,792,458 m/s

g = state degeneracy

h = convection heat transfer coefficient, W/(m2 K)

h = Planck`s constant: 6.626 10-34 J s

 = Planck`s constant/2π

k = Boltzmann’s constant, 1.381 × 10-23 m

2 kg s-2 K-1 

k

→

 = wave vector

Δk = phase mismatch

l = CARS probe volume length, mm 

m = molecular mass

 magnetic (orientational) quantum number

r = narrowband dye laser FWHM at its focal plane, μm

p = pressure, atm 

q = heat flux per unit area, W/m2 

u = velocity, m/s

v = vibrational quantum number

xi = mole fraction of the ith species 

Rz = Rayleigh range, mm

A = mole fraction of the gas coming from ambient air

Bv = rotational constant, cm

-1 

BD = beam displacement 
xxiv 

C = mole fraction of the gas coming from the co-flow 

D = beam spreading coefficient 

Do = optical diffusion coefficient, m2

/s

Dv = centrifugal distortion constant, cm-1 

E



 = electric field, N C-1 

Ee = electronic energy, J 

Er = rotational energy, J 

Ev = vibrational energy, J 

F = fractional strength of a sub-level

J = rotational quantum number

I = laser irradiance, GW/cm2

ITotal = sum of the average irradiance of all laser beams, GW/cm2

Mc = convective Mach number

Me = exit Mach number

Mf = flight (enthalpy) Mach number 

N = total number density, m-3

P = laser power, W 

P



 = induced polarization A2s

2

/m

T = temperature, K

Tw = wall temperature, K

Taw = adiabatic wall temperature, K

TKE = turbulent kinetic energy, m2

/s2 

V = mole fraction of the gas coming from the center-jet 
xxv 

α = crossing angle 

αe = vibration-rotation interaction coefficient, cm-1

β = Galatry narrowing parameter, cm-1/atm

δr = jet radius based on the temperature profile 

δT = shear layer width based on the temperature profile

δV = shear layer width based on the center-jet mole fraction

ε0 = vacuum permittivity, 8.854 10-12 F m-1

λρ = density ratio

λp = pressure ratio 

μ0 = vacuum permeability, 4π V s A-1 m

-1 

ρ = density, kg/m3

σ = 1⁄2 of the e-2 beam diameter, μm

 standard deviation

N τ ∆ = stimulated Raman pumping characteristic time, s

υv = vibrational bandhead, cm-1 

χ

(n) = nth order susceptibility

χ CARS = CARS susceptibility

χ NR = non-resonant third order susceptibility 

ω = circular frequency, cm-1 

ωe = vibrational frequency, cm-1 

ωexe, ωeye, ωeze= anharmonic vibrational constants, cm-1 

ωS = Stokes circular frequency, cm-1 

ωp = pump circular frequency, cm-1 
xxvi 

ω1 = frequency of the Nd:YAG laser, cm-1 

ω2 = frequency of the narrowband dye laser, cm-1 

ω3 = frequency of the broadband dye laser, cm-1 

Δj = fractional population difference 

Δk = phase mismatch

∆ν Stark = Stark shift, cm-1

Γ = linewidth, cm-1

∂σ

∂Ω = differential Raman cross section, m2

/sr

Π = compressibility parameter

Φ = equivalence ratio
1 

CHAPTER 1 - Introduction

1.1 Hypersonic Air-Breathing Propulsion 

Hypersonic air-breathing propulsion is extremely attractive for a wide range of 

applications including long range missiles, high speed military and commercial 

aircraft, and access to space. Research has been ongoing in USA and Europe for the 

last 50 years, yet several technological challenges need to be overcome to build a 

hypersonic airbreathing vehicle. [1-4] 

The fastest manned aircraft propelled by an air-breathing engine is the SR-71 

Blackbird with a top speed of Mach 3.2. Higher velocities cannot be reached with 

turbojet engines because the temperature would be too elevated for the turbine blades. 

This limitation is overcome by ramjet engine often used in missiles. At high flight 

speed, deceleration of the air through the inlet provides the required pressure rise, and 

there is no need of a compressor and therefore of a turbine. The main limitation is that 

a ramjet can only work at high speed; therefore it needs to be coupled to a different 

engine for the low speed portion of the flight. Although the flight Mach number is 

supersonic, the air entering the combustion chamber is subsonic. The elevated 

temperature reached in the combustor limits the speed of a ramjet engine to Mach 6. 

Missiles have used ramjet engines to fly up to Mach 5. At higher speed, rockets are 

currently the only option available. 

In a supersonic combustion ramjet (scramjet) the inlet decelerates the air entering 

the combustor to a lower but still supersonic Mach number, reducing the thermal load 

and allowing greater flight speed. Since the air is decelerated less, for equal flight 
2 

Mach number the pressure rise is lower than in a ramjet, increasing the minimum 

operational flight speed to roughly Mach 5. The commonly reported range of 

operational speed for a scramjet engine is from Mach 5 to 15. Dual mode scramjet 

can operate as a ramjet at lower speed and transition to supersonic combustion at 

higher speed, extending the lower limit of the speed range down to Mach 3. 

A hypersonic air-breathing aircraft that can fly to and from a runway must use a 

combined cycle engine, rocket based (RBCC) or turbojet based (TBCC) for the low 

speed portion of the flight envelope, operating as a ramjet between Mach 3 and 6, and 

transitioning to a scramjet for speed above Mach 6. For access to space applications, a 

final rocket stage would be necessary for insertion into orbit. Figure 1-1 shows the 

schematic of a TBCC vehicle during the high speed operation. Oblique shock waves 

departing from the vehicle forebody and from the inlet and the oblique shock train in 

the isolator decelerate the air entering the combustor to a lower supersonic speed and 

increase its pressure. The combustor is a variable area duct where the incoming air 

Figure 1-1: Schematic of a TBCC concept

J. C. McDaniel, H. Chelliah, C. P. Goyne, J. R. Edwards, P. Givi, and A. D. Cutler, "US National 

Center for Hypersonic Combined Cycle Propulsion: an Overview," in 16th AIAA/DLR/DGLR 

International Space Planes and Hypersonic Systems and Technologies Conference 2009
3 

reacts with the injected fuel. The area increase along the combustor is to offset the 

pressure rise and the Mach number reduction due to the heat release. The nozzle does 

not require a throat since the flow is already supersonic. During ramjet operation, a 

normal shock train is developed at the inlet, and the heat released from the 

combustion accelerates the combustion products to sonic speeds (thermal throat). 

At NASA Langley Research Center, where the research for this dissertation was 

conducted, the focus is on access to space applications. For access to space an 

airbreathing vehicle offers several advantages when compared to a rocket based 

vehicle. The airbreather does not need to carry the oxidizer, therefore offering the 

potential of a reduced gross take-off weight, and larger payload. The use of a turbine 

based combined cycle vehicle would allow horizontal take off and landing, providing 

much greater flexibility than a conventional rocket. The ability of the vehicle to self 

ferry to any site would open several launching and landing options. Other advantages 

include an extended launch window, and the possibility to abort at any point during 

the mission, resulting in increases in safety. 

On the other hand a hypersonic air-breathing vehicle is a much more complex 

system than a rocket. Aerodynamically efficient integration of the low speed engine 

to the dual mode scramjet is challenging and so is the transition from one operational 

regime to the other. A scramjet combustor can have a simple geometry, but the fluid 

dynamics involved is very complex. Achieving efficient supersonic combustion is not 

an easy task. Typical residence times of the air in a scramjet combustor are of the 

order of a millisecond. Therefore the injected fuel needs to mix with the ingested air, 

and react within tenths of milliseconds. Proper understanding and modeling of 
4 

supersonic combustion is critical to the design of a scramjet engine capable of 

operating efficiently over a wide range of flight Mach number. 

1.2 Experimental Data for CFD Development and Validation

Flight tests of hypersonic air-breathers are costly, challenging and can provide 

only limited data. Only a few successful flight tests of scramjet engines have been 

accomplished to date. Ground testing cannot perfectly reproduce the test condition. 

Electrically (resistance heated or arc) heated or combustion heated facilities, that can 

operate for relatively long time, can only simulate the lowest flight Mach numbers 

(up to 7). Excess water in combustion heated facilities is known to affect the 

combustion.[5] Shock tubes can simulate the entire range of speed but the test 

duration is limited to milliseconds. In addition vibrational non-equilibrium and excess 

nitric oxide and atomic species can affect the combustion. 

For these reasons design and analysis of scramjet engines relies on computational 

fluid dynamics (CFD) simulations. Both RANS (Reynolds Average Navier-Stokes) 

and LES (Large Eddy Simulation) codes employ models to describe the turbulent 

mixing and the turbulence-chemistry interactions. The models developed for subsonic 

combustion are not adequate in the compressible regime. New models need to be 

developed and validated in order to successfully simulate a scramjet engine, and large 

experimental databases are needed. 

The primary role of ground testing in supersonic combustion is to provide data to 

the CFD community. Ground testing of an actual scramjet engine, not only is 

extremely challenging for the experimentalist, but the data may be difficult to 
5 

interpret by the modelers (i.e., it may be difficult to identify what aspect of the 

modeling or boundary conditions is at fault when there is a discrepancy with the 

data). Experiments for CFD validation typically address only a sub-set of physical 

phenomena, so that specific numerical models can be tested. 

When the goal is to study mixing and combustion in supersonic flows, testing is 

limited to the combustor. An actual scramjet combustor would have a complex 

geometry with several injectors operating simultaneously. A scramjet combustor 

model for CFD development typically has a simple geometry (variable area duct) and 

a single injector. Examples of this approach are the combustor used for the 

SCHOLAR test program [6] or the Dual-Mode Scramjet experiment at UVA. [7] 

When the focus is on supersonic mixing and combustion, many researchers 

choose to study chemically reacting compressible shear layers in a nozzle exit 

pressure-matched open-jet configuration. This class of flows maintains the 

fundamental physics related to the turbulent mixing and turbulence-chemistry 

interaction, but removes the complications due to the walls, shock waves, and 

streamwise pressure gradients. Furthermore such unducted flows simplify the 

application of spectroscopic measurement techniques. A supersonic-combusting 

coaxial free-jet is the flow of interest for this work, and is described in details in 

Chapter 7. 

1.3 Measurement Techniques

Making measurements in a supersonic combusting flow is very challenging 

because of the elevated speed and temperature. Any probe directly inserted in the 
6 

flow would have to be designed to tolerate high temperatures and pressure loads, and 

can strongly perturb the flow. High levels of vibration and noise, limited or no access 

to the facility during a test run, high levels of turbulence and strong temperature 

variations further complicate data acquisition in supersonic combustion experiments. 

The harsh test environment generally limits the applicability of conventional 

measurements techniques to the combustor walls. Static pressure taps and 

thermocouples along the combustor walls are commonly employed in supersonic 

combustion testing. [5, 6, 8] Skin friction gauges have been used to determine the 

drag and a thin film gauge has been used to measure the heat transfer on the wall of a 

supersonic combustor. [9] Ryan [10] used a thrust stand to measure the thrust 

produced by a supersonic combustor. Robinson [11] used a three-component stresswave force balance for measurements of thrust, lift and pitching moment on a large 

scramjet model in a reflected shock tunnel.

Intrusive probes, properly outfitted to stand the harsh test environment, have been 

used in several experiments. Pitot probes or rakes are often used to measure total 

pressure in supersonic mixing experiments. [12-19] A thermocouple probe to measure 

stagnation temperature in supersonic combusting flows was developed at the 

ONERA. [20] Gas sampling probes have been used in supersonic flames to measure 

species concentrations. [21-23] These measurements are intrusive and strongly 

perturb the flow, but allow measuring useful quantities such as total pressure and total 

temperature. 

Several imaging techniques have been used to visualize structures in the flow. 

Sometimes useful information can be obtained simply by direct video imagining. OH 
7 

chemiluminescence is visible; therefore videos and pictures with conventional 

cameras can provide useful information on the location of the combustion region and 

on the flame structure. [24, 25] Whitehurst used a high speed camera at 6 kHz to 

study ignition and flameholding in a supersonic combustor. [26] Infrared (IR) 

cameras operating in the mid-IR have also been used to visualize the flame structure. 

[24, 27] The Schlieren technique, which images the first derivative of the density, has 

been employed to visualize turbulent structures in compressible mixing layers, [14, 

15, 28] and near the injector in scramjet combustors. [29-31] 

Several laser-based imaging techniques have been implemented to study 

supersonic combustion. Laser-based techniques are particularly advantageous for 

measurements in supersonic combustion because they provide more information than 

direct imaging, while still being non-intrusive. OH planar laser induced fluorescence 

is often used to obtain 2D images of the OH concentration in supersonic combustors. 

[8, 31-37] In addition to qualitative images of the reaction zone, the PLIF technique 

can also provide quantitative information. Allen [35] extracted temperature 

distribution from NO PLIF in a shock tube scramjet experiment, in a non-reacting 

region of the flow. Quagliaroli [36, 38] measured the OH concentration from OH 

PLIF images with an uncertainty of ~21%. Gauba [37] used OH-PLIF to obtain 

planar velocity fields with a 200 μm resolution and a 6-8% uncertainty in a scramjet 

combustor. 

Accurate velocity measurements are important for CFD validation. Hot wire 

probes can easily perturb the flow, causing large uncertainties in the measurements, 

and can only be used in mixing studies. [39] Particle-based velocimetry techniques 
8 

such as laser Doppler velocimetry (LDV) [40, 41] and particle imaging velocimetry

(PIV) [42-44] have been applied to supersonic combustion experiments. Threedimensional velocity field have been acquired with stereoscopic PIV in a dual mode 

scramjet combustor. [45] In particle based velocimetry laser radiation is scattered 

from tracer particles seeded in the flow. The particle lag (where the particle does not 

travel as the same speed as the flow) is a potential source of inaccuracies in presence 

of shocks or strong accelerations. [46] Furthermore, there are difficulties in seeding 

all parts of the flow with particles, as well as the windows of the facility becoming 

coated with particles.[45] 

Laser-based molecular velocimetry measures directly the gas speed, rather than 

the speed of particles moving with the flow. In laser-induced fluorescence the 

velocity can be determined from the Doppler shift of the emission. PLIF velocity 

measurements have been performed using emissions from OH, [37, 47, 48] NO [49] 

and iodine. [50] Molecular tagging techniques mark a molecule with a laser (by 

excitation or photo-dissociation) and follow the motion of the tagged molecule to 

determine its velocity. Hydroxyl tagging velocimetry has been used to study cavity 

stabilized supersonic non-reacting and reacting flows. [52] In depth reviews of laserbased velocimetry techniques can be found in Ref. [52, 53]. Interferometric Rayleigh 

scattering has also been used to measure velocity in supersonic combustion open 

flames. [51] 

Several laser-based techniques have been applied to measure species 

concentration in supersonic combustion experiments. Tunable diode laser absorption 

spectroscopy (TDLAS) is a line-of-sight technique that allows simultaneous 
9 

measurements of temperature and species concentrations, including water, [54-56] 

OH and water, [32] and O2. [57] Two-dimensional, spatially (but not temporally) 

resolved measurements are possible using tunable diode laser tomography, which 

combines several TDLAS measurements with tomographic image reconstruction. 

[57, 58] 

UV Raman has been used to measure temperature, CO, O2, C2H4, H2O and H2

simultaneously in a scramjet combustor. Laser-induced fluorescence from 

combustion byproducts and from the windows, and the UV emission from the 

flame, partially obscure the Raman spectra in some region of the flow, 

diminishing the quality of the measurements. [59, 60] 

Coherent anti-Stokes Raman spectroscopy (CARS) does not suffer from the 

same issues of UV-Raman thanks to the coherent nature of the signal. The signalto-noise ratio is higher than in Raman, and it does not require large windows, 

making it particularly attractive for measurements in ducts, where optical access 

is limited. Compared to TDLAS the main advantage is that it is spatially and 

temporally resolved, allowing study of the turbulence fluctuations present in the 

flow. The feasibility of CARS in supersonic reacting flows was first demonstrated by 

Anderson. [61, 62] Waidmann [29] used N2 vibrational CARS to measure 

temperature in a combustor chamber. Gong [25] obtained CARS temperature 

measurements along the centerline of a scramjet combustor and of a supersonic 

diffusion flame. Zhao [63] measured N2 vibrational temperature at two points 

simultaneously in a scramjet combustor. Yang [64]obtained simultaneous 

measurements of O2, and the S(5) and S(6) H2 rotational lines. Magre [20, 65] 
10 

measured temperature in a supersonic combustor from the N2 Q-branch and then the 

H2 Q-branch. Previous CARS applications at NASA Langley are discussed in the 

next section. Details on the technique are found in Chapter 2. 

From this short review of the available diagnostic techniques, it is clear that there 

is not a single instrument that can provide all the measurements needed to the CFD 

modelers. For this reason experiments are often repeated applying different 

measurements techniques. An on-going test on a dual-mode scramjet at the University 

of Virginia [7] includes stereoscopic PIV, TDLAS, OH PLIF and dual-pump CARS 

measurements (performed using the instrument developed for this work). 

Replicating a flow-field and measuring a different parameter at a different time 

does not allow determining statistical correlations between different parameters that 

would be available if the quantities were measured simultaneously. However with a 

CARS instrument that measures simultaneous temperature and species mole fractions 

it is possible to obtain temperature-mole fraction co-variances. Simultaneous 

acquisition of multiple parameters combining different time resolved techniques can 

be very challenging, but it also provides very useful additional information. An 

example is the IRS-CARS instrument developed by Bivolaru and Tedder for 

simultaneous measurements of temperature, species, and 2 components of velocity. 

[66] 

1.4 CARS in Supersonic Combustion Experiments for CFD Validation 

at NASA Langley Research Center
11 

NASA Langley Research Center has a long history of applying CARS in scramjet 

combustors and supersonic flames. The first attempt was from Jarret in 1987. [67] He 

applied dual Stokes CARS for simultaneous measurements of temperature, N2 and O2

to a supersonic H2-air open flame. He also applied LDV for velocity measurements in 

the same flame. The two measurements were not simultaneous. The flowfield was an 

axisymmetric jet of vitiated air, with a center jet of H2, provided by a small burner. 

The nozzle exit diameter was 17 mm for the vitiated air, 1.5 mm for the H2 centerflow. The size of the CARS measurement volume was 4 mm; therefore several 

features of the flow could not be resolved. Measurements were taken at several points 

along diameters at 5 axial locations. Only 100 shots were taken at each point and only 

average results were reported. Flow asymmetries were found and a diamond shock 

system at the exit of the nozzle dominated the flow, making comparisons between the 

experimental results and the numerical simulation challenging. [68] 

Smith [69] successfully measured temperature using N2 vibrational CARS in a 

scramjet combustor model, featuring a rearward facing step, and a single normal 

injector. The combustor was connected to the exit nozzle of the NASA Langley 

Direct Connect Supersonic Combustion Test facility (DCSCTF).This was the first set 

of CARS measurements in DCSCTF. The facility provided hot “vitiated” air at Mach 

2, simulating the air entering a scramjet combustor flying at Mach 5.4. The test could 

run for only 10 seconds at a time, because of heating of the combustor model. The 

CARS instrument was operating at 10 Hz and the amount of data acquired was 

strongly limited by the short run duration. The heat load caused the model to 

deteriorate during the test.
12 

A new scramjet combustor model, named SCHOLAR, was developed in 1999 and 

installed in DCSCTF. The new combustor featured a single H2 injector with a Mach 

2.5 nozzle inclined at 30 degrees with respect to the combustor wall. The model could 

operate for 20 seconds during each run. Springer [12] used N2 vibrational CARS 

thermometry at 30 Hz to characterize the flow at the entrance of the SCHOLAR 

model when simulating flight Mach number equal to 7. The CARS signal-to-noise 

ratio was too low because of the low power and poor beam quality delivered by the 

higher repetition rate laser. Data were collected only at a single location on the 

centerline, 12 cm from the nozzle exit. Cutler performed N2 CARS thermometry over 

5 planes of the SCHOLAR model using a more powerful 10 Hz laser. [70] O’Byrne 

applied dual-pump CARS (DP-CARS) for simultaneous measurements of 

temperature, O2, N2 and H2 concentration in the same model. Validation 

measurements in a flat flame burner showed that H2 mole fractions were 

systematically low; therefore H2 measurements in the combustor were not 

reported.[6] Accurate CFD modeling of the SCHOLAR experimental data proved to 

be very challenging. [71] In particular the numerical simulation had problems 

predicting the distance between the injector and the combustion-induced pressure 

rise. Calibration of the numerical models based on the experimental data was not 

possible because the flow was complex and several numerical models were involved 

in the simulation. 

In 2005 an axisymmetric supersonic combusting coaxial jet flowfield was 

developed. [24] The flowfield consists of a center-jet of vitiated air, and a co-axial jet 

of N2 for mixing studies, or H2 or ethylene for combustion studies. The flow-field 
13 

allowed the study of mixing and combustion in a supersonic flow, removing all the 

complications encountered in SCHOLAR due to the presence of walls, pressure 

gradients and shock waves. The free-jet offers optical access on all sides downstream 

of the nozzle exit, simplifying the use of laser diagnostics. The flow field was 

developed in two sizes: a laboratory-scale supersonic burner, with center jet nozzle 

exit diameter of 10 mm described in details in Chapter 7, and a larger scale nozzle 

connected to DCSCTF [72], with center jet nozzle exit diameter of 63.5 mm. The 

laboratory-scale burner has three interchangeable silicon carbide nozzles, providing 

center jet exit Mach numbers of 1, 1.6 and 2 to study the effect of compressibility, 

and can provide center jet enthalpy that simulates flight speeds between 5 and 7. Only 

one nozzle with exit Mach number 1.6 was tested for the scaled up version. 

CARS measurements in the large scale facility allow better resolution of some of 

the turbulence structures, compared to the laboratory-scale version. On the other hand 

it is much more costly to operate and requires a test engineer and several technicians, 

where the laboratory scale burner can be operated by one technician. Typical duration 

of a run in the DCSCTF was 50 seconds, whereas the small scale burner can operate 

continuously for hours at a time; therefore a much larger data-set could be acquired in 

the same time-frame.

The laboratory-scale jet was used in 2007 to test a modified version of O’Byrne’s 

DP-CARS system, employing a modeless dye laser as Stokes beam to improve the 

instrument temperature precision. Data were collected only at a couple of locations, 

and have no relevance for CFD validation.[66] Measurements in a Hencken burner 

flame using this setup showed poor mole fraction accuracy, attributed to low signal-
14 

to-noise ratio and a broadband dye laser that was too spectrally narrow, as well as to 

inaccuracy in the data processing. No improvements in the temperature precision 

were observed, and the modeless dye laser was replaced with a conventional dye laser 

in subsequent work. 

An instrument combining interferometric Rayleigh scattering for single-point 

measurements of two velocity components and DP-CARS for measurements of 

temperature, N2, O2 and H2 was developed by Bivolaru and Tedder. [66, 73] The 

instrument was mounted on a mobile cart, placed in the basement directly below 

DCSCTF, and tested in the scaled-up version of the free jet. The test proved to be 

very challenging and only limited data were analyzed. CARS temperature results for 

a mixing case (no co-flow) have been reported in Ref. [72, 74], but only 54% of the 

spectra that could be analyzed (data yield) mostly because of beam steering effects 

preventing CARS signal generation. Mole fraction measurements were not reported, 

because later analysis of experiments in a Hencken burner flame performed at same 

time showed poor accuracy in species mole fractions. Lack of linear polarization in 

one of the laser beams was suggested as a possible source of the error in mole fraction 

measurements, but this explanation could not be verified because the instrument had 

already been dismantled when the problem was found. [75] CARS measurements 

were attempted for a combustion case, but the laser failed before the test was 

completed and the data were never analyzed. The data yield was even lower than in 

the mixing case, and a significant amount of background light from the flame was 

overlapped with the CARS signal. 
15 

1.5 Development of a Dual-Pump CARS Instrument for Supersonic 

Combustion Experiments

Preliminary DP-CARS measurements in the laboratory scale burner and the test 

campaign with the scaled-up free-jet showed several issues with the instrument, 

which had to be resolved in order to obtain good quality CARS measurements in 

future supersonic combustion experiments. The research conducted for this 

dissertation had two main objectives. The first was to develop a DP CARS instrument 

capable of accurate temperature and mole fraction measurements in the harsh 

environment of supersonic combustion experiments in ducted or open jet 

configurations. The other goal of this work was to apply the DP-CARS instrument to 

generate a database of temperature and mole fraction measurements in the laboratoryscale supersonic combusting jet, for CFD validation.

The physics behind the CARS techniques is described in detail in Chapter 2. 

Chapter 3 provides a description of the DP-CARS instrument. Improvements to the 

instrument hardware, to the data acquisition software, and the data processing are 

discussed in detail. 

DP-CARS measurements collected by Tedder [72] in the large scale supersonic 

free-jet presented low data yield (54.4% for a mixing case in the large supersonic free 

jet). Low data yield is a critically important problem because missing data can 

potentially bias averaged temperature measurements, as described in Chapter 6. A 

small fraction of the data (7.2 %) was rejected because the signal was too strong and 

it was saturating the camera detectors. A new approach was developed to reduce the 

number of spectra that saturate the camera (Chapter 3) and to obtain useful data from 
16 

saturated spectra (Chapter 5). Most of the data loss (38.2%) was a consequence of 

beam steering due to turbulence and vibrations. Chapter 4 describes a new technique 

developed to mitigate the effects of beam steering.

Chapter 5 describes a study of the high irradiance perturbation effect to determine 

thresholds for the laser irradiances. The study indicates that these perturbation effects 

were probably responsible for the poor accuracy in the H2 mole fraction 

measurements of O’Byrne.[6] 

In providing measurements for CFD validation it is important to characterize the 

instrument in terms of accuracy, precision and spatial resolution. Changes to the 

theoretical modeling of the CARS spectra, calibration of some molecular parameters, 

and the removal of high irradiance perturbation effects, allowed for better accuracy 

than obtained in previous experiments. Precision at low temperature was improved as 

a result of higher spectral resolution, and changes to the fitting algorithm. 

Measurements in a flat flame burner are used as benchmark to determine the accuracy 

and the precision. The instrument characterization study is described in details in 

Chapter 6. 

Chapter 7 provides a detailed description of the laboratory-scale supersonic free 

jet, and CFD simulations of the flow inside the facility. About 800,000 single-shot 

CARS spectra have been acquired and analyzed for a variety of conditions in the 

laboratory-scale supersonic free-jet. Results of the measurements are discussed in 

Chapter 8. The conclusion summarizes the accomplishments of this work, and 

includes recommendations for future development of the instrument. 
17 

CHAPTER 2 -Coherent Anti-Stokes Raman 

Spectroscopy

2.1 Introduction

 Coherent Anti-Stokes Raman Spectroscopy (CARS) is a non-intrusive, 

instantaneous and spatially resolved, laser-based measurement technique that has 

been implemented by several researchers to measure temperature and species 

concentration in scramjet combustors.[60-72] In CARS, three laser beams, 

conventionally named pump, probe and Stokes, are focused and crossed at their focal 

point, where a fourth laser-like beam is generated containing the Raman spectrum of 

the probed species. Laser frequencies are chosen so that the pump-Stokes frequency 

difference corresponds to the Raman shift associated with a molecular rotationalvibrational transition. 

The technique was originally developed in 1965 by Maker [76] and applied in 

liquid benzene, but it was the work of Taran and the ONERA group [77, 78] in the 

mid seventies that demonstrated its potential as diagnostic tool in combustion. Since 

then, CARS has been adopted in a variety of combustors [79] and several variations 

of the original technique have been develop to extend the capability of the technique 

to multiple species (dual pump CARS, [80, 81] triple-pump CARS,[82] dual pump 

dual-broadband,[83, 84] WIDECARS[85]) and to detect minor species (electronicresonant-enhanced CARS [86]). 

This section includes a brief background of the fundamental physics behind 

molecular spectroscopy that is at the core of the CARS technique. Following is a 
18 

derivation of an expression for the CARS signal, largely based on the more detailed 

calculations found in Chapter 6 of Ref.[87]. The dependence of the CARS signal on 

the temperature and species concentration of the probed gas is shown. “Multi-color” 

CARS techniques that expand the capabilities of the original CARS technique to 

simultaneous measurements of multiple species are described.

 

2.2 Molecular Energy States and Population Distributions

The fundamentals of molecular spectroscopy are briefly illustrated in this section, to 

introduce concepts and definitions that will be often used in the rest of this work. The 

internal energy of a molecule is distributed between electronic, rotational and 

vibrational energy. Based on the Born-Oppenheimer approximation the three 

contributions can be decoupled and the total energy can be expressed as: 

EE E E =++ erv (2-1) 

According to quantum mechanics, energy levels are discrete, and can be 

computed as solutions to the Schrödinger equation. CARS probes transitions between 

different ro-vibrational levels. Combustion phenomena generally do not alter the 

electronic state of a molecule, therefore for the application discussed in this 

dissertation Ee is constant. 

Vibrating diatomic molecules (such as N2, O2 and H2 probed by this CARS 

instrument) can be modeled as anharmonic oscillators. The vibrational energy Ev is 

obtained as a solution of the Schrödinger equation and can be expressed as: 

2 34 11 1 1 ....... 22 2 2 E hc v x v y v z v v e ωω ω ω e e e e e e

      = ++ + + + + +            

(2-2) 
19 

where h is the Planck`s constant, c the speed of light, ωe the vibrational frequency 

expressed in wavenumbers (cm-1), ωexe, ωeye, ωeze are additional vibrational constants 

that describe that anharmonicity. Values for ωe, ωexe , ωeye and ωeze for several 

molecules can be found in Ref.[88]. The quantity v is the vibrational quantum number 

which takes positive integer values. 

The rotational energy for diatomic molecule can be obtained as solution of the 

Schrödinger equation for a rigid rotator: 

2 2 ( 1) ( 1) E hc B J J D J J rv v = +− +     (2-3) 

The rotational quantum number J is a positive integer Bv is the rotational constant and 

Dv is the centrifugal distortion constant. Since the molecule vibrates and rotates at the 

same time, its moment of inertia is not constant; therefore Bv and Dv are function of 

the vibrational quantum number v: 

2

1 1 ... 2 2

BB v v v ee α γ e

   =− + + + +       (2-4) 

1 ... 2

DD v v ee β   =+ ++     (2-5) 

The energy separation between electronic states is ~ 10 times the separation between 

the different vibrational states and 100 times the separation between different 

rotational states. 

For a gas at equilibrium the population distribution among the different energy 

states is governed by the Boltzmann distribution function: 

/

/

i kT

i

i

i kT

i

i

g e N N

g e

ε

ε

−

− =

∑ (2-6) 
20 

where Ni is the number density of the molecules at the energy state ei (uniquely 

determined by the vibrational and rotational quantum numbers); N is the total number 

density, k is the Boltzmann constant, T the temperature and gi the degeneracy of the 

state. The denominator is the sum over all possible energy states, and is called the 

partition function. The population distribution is very sensitive to temperature; 

molecular spectroscopy can measure the population distribution, and therefore can 

determine the temperature. More specifically the population distribution over the 

vibrational levels within an electronic state is given by: 

/ / (1 ) e e vhc kT hc kT N Ne e v

− − ω ω = − (2-7) 

The population distribution between the rotational energy states within a 

vibrational level is given by: 

Figure 2-1: Vibrational population for N2 as function of the temperature
21 

( 1) /

( 1) /

0

(2 1)

(2 1)

BJ J hc kT

J

J

BJ J hc kT

J

Ng J e N

J e

− +

∞ − +

=

+ =

∑ +

(2-8) 

Figure 2-1 shows the population distributions for the first three vibrational levels of 

N2 as function of temperature. It is evident that even at high temperature, most 

molecules are at the ground vibrational states. The first vibrational band is populated 

(> 1%) for temperature above 700 K. 

Figure 2-2: a) Rotational population for N2 and b) H2 for three values of 

temperature
22 

Figure 2-2 shows the population distribution of the rotational levels for three 

values of temperature. It is evident that, especially at low temperatures the rotational 

population distribution is much more sensitive to temperature. Also notice that the 

population difference between two consecutive even or odd values of J drops rapidly 

with the temperature. 

Molecular spectroscopy probes Raman transitions between different molecular 

energy states. Based on quantum mechanics only transitions that satisfy the selection 

rules are allowed. In particular the CARS system discussed here probes Q-branch and 

S-branch transition. A Q-branch transition is one for which Δv = 1,2,3... and ΔJ = 0. 

The transitions for Δv = 1 are the strongest. The frequency of the transition can be 

computed as: 

( ) ( ) 1 1 ( ') ( '') ( ', ) ( '', ) ( 1) ... Q v v E v E v E v J E v J JJ r r v e hc hc

υ = − + − = + ++ υ α (2-9) 

where v ' and v '' are the vibrational quantum numbers of the upper and lower states, 

and υv is the frequency of the transition for J=0, generally called the vibrational 

bandhead. Since the vibration-rotation interaction coefficient αe is very small 

(0.0173 cm-1 for N2), all the ro-vibrational transitions in the Q-branch are closely 

spaced. Notice in particular that the spacing is proportional to J(J+1), hence the 

spacing is greater for higher rotational numbers. With the CARS system described 

here, the Q-branch of N2 and O2 are probed. The vibrational bandhead are 2330.7 cm1

 for N2 and 1556 cm-1 for O2. S-branch transitions are purely rotational transitions 

with Δv=0 and ΔJ=2. The transition frequency for a S-branch transition can be easily 
23 

obtained from Eq.(2-3). The CARS system described here probes the S(5), S(6) and 

S(9) transitions of H2 , with frequencies at 1447.2, 1637 and 2130.1 cm-1. 

2.3 Molecular Spectroscopy

A photon, at a frequency that matches an electronic or a ro-vibrational transition 

frequency, can excite a molecule to a higher energy state. In the process the light is 

absorbed and the energy transferred to the molecule. This one photon process 

underlies absorption spectroscopy. Infra-red light is typically required to probe rovibrational transitions using absorption. 

If the frequency of the incident light does not match any transitions, interaction is 

still possible in the form of elastic (Rayleigh) and inelastic (Raman) scattering. The 

incident photon drives the molecule to a virtual state that is not an allowable energy 

level (not a solution of the Schrödinger equation). The molecule cannot exist in this 

state, so it relaxes and either returns to its original state (Rayleigh scattering), or to a 

different, allowed energy state (Raman scattering). In both cases a photon is emitted, 

but in Rayleigh scattering no energy has been absorbed and the photon is at the same 

frequency of the incident light; in Raman scattering, the molecule has absorbed (or 

emitted) energy, therefore the frequency of the emitted photon is (Raman) shifted by 

the change in energy of the molecule (in frequency units). 

Figure 2-3 shows the energy diagram for CARS. It is a four photon, non-linear 

optical process that is more complex than the linear, two-photon Raman process. The 

energy of the molecule is increased by the pump laser beam, at frequency ω1 and 

decreased by the Stokes laser beam at frequency ω3< ω1. The probe beam at 
24 

frequency ω2 scatters the light from the molecule generating a laser-like CARS signal 

blue-shifted at frequency ω4= ω1 - ω3 +ω2. When the pump-Stokes frequency 

difference (ω1-ω3) matches the energy of a vibrational-rotational transition, the 

combined effect of the two lasers is to induce a Raman coherence between the ground 

state and this excited state. Under this condition, the CARS signal is resonantly 

enhanced and the emitted signal contains information on the temperature and mole 

fraction of the species probed. Note that no energy is absorbed by the molecule in the 

process. 

2.4 Derivation of CARS Signal 

The CARS signal derivation presented here is based on more detailed calculations 

found in Chapter 6 of Ref.[87]. Interaction between light and any media is described 

by the Maxwell`s equation, which for gases with no free charge density, nor 

distributions of current simplifies to the wave equation: 

2 2

2

22 2

1 oE P E

ct t

μ

∂ ∂ ∇− =

∂ ∂

   (2-10) 

Figure 2-3: CARS energy level diagram
25 

where E

 is the electric field , c the speed of light, μ0 the permeability of the free 

space. P



, which appears as a source term in the wave equation, is the generalized 

induced polarization. E and P can be expanded in Fourier series, and the induced 

polarization can be expressed as power series of ωi: 

(1) (2)

0 0

,

(3)

0

, ,

( ) ( )( ) ( , , )( )( )

( , , , ) ( ) ( ) ( ) ....

i i i j i j k j k

j k

i jkl j k l

jkl

P E E E

EEE

ω εχ ω ω εχ ω ω ω ω ω

εχ ω ω ω ω ω ω ω

= ± ± + ±±± ± ±

+ ±±±± ± ± ±+

∑

∑ (2-11) 

where ε0 is the permittivity of the free space and χ

(n) the nth order susceptibility. The 

frequency of the induced polarization is determined by conservation of energy 

according to the relation: 

0 ±± ± ± = ωωω ω i jkl (2-12) 

The first order term of the power series is what generates Rayleigh scattering and 

spontaneous Raman scattering, two linear techniques mentioned in the previous 

section. For isotropic media, such as gases, the second order susceptibility is zero 

because of inversion symmetry. The lowest order non-linear interaction that can occur 

in gases is therefore third order. Eq. (2-12) shows that there are several wave mixing 

combinations possible. Based on the energy diagram the third order polarization term, 

responsible for the CARS signal is 

(3) (3)

4 0 412 3 1 2 3 ( ,) ( , , , ) ( ) ( ) ( ) P r i ω εχ ω ω ω ω ω ω ω =− − ijkl EEE j k l

 (2-13) 

The third order susceptibility is a third order tensor, but for a gas only 21 terms are 

not null, and only three are independent. If all three beams have the same polarization

(as in the present work), Eq.(2-13) reduces to: 
26 

(3)

4 0 412 3 1 2 3

0 123

( ,) 3 ( , , , ) ( ,) ( ,) ( ,)

( ,) ( ,) ( ,)

xxxx

CARS

P r E rE rE r

E rE rE r

ω εχ ω ω ω ω ω ω ω

εχ ω ω ω

=− −

=

 

 (2-14) 

Substituting Eq.(2-14) into the wave equation, assuming a refraction index of 1, 

solving for the electric field of the CARS signal, and integrating over the length of the 

probe volume l, the time averaged irradiance of the CARS signal can be expressed as: 

2

2

3 2 2

4 2 123

0

sin

2

2

CARS CARS

kl

I III l

c kl

ω

χ

ε

  ∆

  =   ∆    

(2-15) 

where I1, I2 and I3 are the irradiances of the three laser beams, and Δk is the phase 

mismatch defined as: 

4132 ∆= − + − kk kk k     (2-16) 

where k

 are the wave vectors defined as: 

k r

c

ω

=

  (2-17) 

Eq. (2-15) shows that the CARS signal is proportional to the product of the 

irradiances of the three laser beams. High irradiance effects such as optical 

breakdown, Stark broadening, and stimulated Raman pumping limit the laser 

irradiances and the CARS signal. These phenomena will be discussed in details in 

Chapter 5. 

The CARS signal also depends on the phase mismatch and the interaction length 

l, parameters related to the geometric arrangement of the laser beams. The CARS 

irradiance is maximized if the phase mismatch is zero. 

4 123 ∆k k kkk = ⇔ = + − 0     (2-18) 
27 

Eq.(2-18) is known as the “phase matching” condition and is a statement of 

conservation of momentum. Physically this condition means that the CARS signal 

generated at any location is in phase with the signal generated anywhere else. There 

are several geometries that satisfy the phase matching condition; the most common 

are collinear, USED, planar and folded BOXCARS. The criteria for the selection of 

the phase matching geometry are discussed in Chapter 4. 

Derivation of the CARS susceptibility χ CARS from quantum mechanics is reported 

in detail in books [87] and review papers, [79] and it will not be repeated here. The 

CARS susceptibility is generally expressed as sum of a resonant and a non-resonant 

susceptibility. The resonant portion contains all those contributions for which 

combination of the frequencies coincide with a Raman resonance; all the other terms 

are lumped in the non-resonant contribution. 

2

j j

CARS NR

j j j

K

i χ χ

ω

Γ = +

∆ −Γ ∑ (2-19) 

where the summation is over all the Raman resonance transitions at frequencies ωj.

Δωj is the detuning defined as ∆= −+ ω ωωω j j 1 3 , Γj is the linewidth. Kj is defined as: 

( )2 4

0

4

2

4 j

j

j j

c N

K

π ε σ

ω

∆   ∂ =    Γ ∂Ω   (2-20) 

where N is the number of molecules, Δj is the fractional population difference 

between the 2 energy levels involved in the wave mixing process,  is the Planck`s 

constant divided by 2π, ∂σ

∂Ω

the differential Raman cross section. This term (Kj) is 

where the potential of CARS as a diagnostic tool is. In fact the CARS susceptibility is 
28 

proportional to the number of molecules N and it depends on the temperature through 

the fractional population difference, as shown in Eq.(2-6). 

The modulus of the CARS susceptibility appears squared in Eq. (2-15). For this 

reason CARS spectra are more complex than spontaneous Raman spectra, since 

constructive and destructive interference occurs. Additionally in typical diagnostics 

application the Stokes beam is spectrally broad and several Raman resonances are 

excited at once. Neighboring transitions can interfere further changing the spectral 

shape. Generally CARS spectra cannot be obtained analytically, but numerical 

routines are required to simulate the spectral shape and intensity.

2.5 Lineshape Models

Transitions between energy levels are not infinitely sharp but have a finite width 

(linewidth), generally indicated with the symbol Γ. Knowledge of this quantity is very 

important, since it appears in the expression of the CARS susceptibility (Eq.(2-19)). 

Based on the Heisenberg uncertainty principle, the energy of a molecule cannot be 

precisely known, causing a spread of the emission (or absorption) frequency that is 

the natural linewidth. The resulting line-shape is a Lorentzian. The natural linewidth 

can be expressed as: 

1 2

111

2πτ τ

  Γ= +    

(2-21) 

where τ1 and τ2 are the lifetimes of the 2 states involved in the transition. In a gas 

other broadening mechanisms occur, changing the linewidth of the transition.
29 

In a gas the lifetime of an energy level can be shortened if collisions between 

molecules occur, increasing the linewidth of the transition. This effect is known as 

pressure (or collisional) broadening. The lineshape is still a Lorentzian, but the 

linewidth is proportional to the pressure, and approximately proportional to the 

inverse of the square root of the temperature, depending on the cross section of the 

molecules colliding. 

Radiation emitted by a molecule with a non-null velocity in the direction of 

propagation of the light will be shifted in frequency. This effect is the Doppler shift 

and is the principle behind several velocimetry techniques. In a gas, in addition to a 

macroscopic flow velocity, there is always a random motion of each molecule. The 

motion is function of temperature and the velocity distribution is given by the 

Maxwell-Boltzmann expression. As result of the velocity distribution the lineshape is 

a Gaussian, with a linewidth that is function of the temperature alone. 

At low pressures and high temperatures, Doppler broadening is the dominant 

term, where at low temperatures, pressure broadening is dominant. In most practical 

applications both collision broadening and Doppler broadening are significant, and 

the resulting lineshape is a Voigt function. This is the lineshape model used for 

computing the theoretical N2 and O2 CARS spectra reported in this work. 

Collisional (motional or Dicke) narrowing [89] is a mechanism that alters the 

linewidth of Doppler broadened lines. From the uncertainty principle the velocity 

obtained from the Doppler shift is averaged over a displacement of ~ 2

λ

π , where λ is 

the wavelength of the incident light. If there are many velocity-changing collisions in 

the time necessary to travel 2

λ

π

then the average velocity is reduced, and so is the 
30 

Doppler frequency shift. The effect is a reduction of the Doppler broadening, and a 

lineshape that differs from the Voigt. Two analytical models are available to model 

this process, the hard collision [90, 91] and the Galatry (soft) collision model. [92, 93] 

The first assumes that the velocity after the collision is completely uncorrelated to the 

velocity before the collision. In the Galatry model the change in velocity after each 

individual collision is negligible, and the velocities before and after a collision are 

strongly correlated. The hard collision model is more appropriate when the molecule 

that is interacting with the radiation is considerably less massive than the collider. In 

practice the numerical values of the two models are almost the same. The Galatry 

model requires the knowledge of an additional quantity, the motional narrowing 

parameter β, which is related to the optical diffusion coefficient Do via the relation: 

o

kT

mD β = (2-22) 

where k is the Boltzmann constant, m the molecular mass, and T the temperature. 

Units of β are cm

-1/atm. Physically it represents the effective frequency of velocitychanging collisions. Several studies show that the optical diffusion coefficient Do

differs from the conventional mass diffusion coefficient Dm, although they have the 

same order of magnitude.[90, 94, 95] 

The motional narrowing is significant for transitions with large rotational spacing 

in which the Doppler broadening is dominant, and should not be neglected for H2.[96] 

The Galatry model has been used to compute the H2 rotational lines in the theoretical 

spectra, and a calibration of the optical diffusion coefficient is discussed in Chapter 6.

Eq.(2-9) shows that in Q-branch spectra the spacing between adjacent rovibrational line is proportional to J(J+1). Since the rotation-vibration interaction 
31 

coefficient αe is small, the ro-vibrational lines are overlapped for low values of J. 

For such conditions, computation of the lineshape as an isolated line undergoing 

pressure broadening is no longer adequate. Collisional narrowing, “which causes a 

coalescence or collapse of adjacent transitions toward a frequency center of gravity 

determined by the most populous rotational state” [97] becomes significant. This 

phenomenon is relevant at low temperature, where only the lower rotational states are 

populated. For higher values of J, the line splitting, proportional to J(J+1), increases 

and collisional narrowing is no longer significant. In Chapter 6 the effect of the 

lineshape models on the measurement accuracy is discussed. 

2.6 Multi-Color CARS

In early CARS experiments a narrowband tunable dye laser acted as Stokes beam, 

exciting a specific molecular transition. Spectra were constructed piecewise, by 

scanning the frequency of the laser. This approach offers the best spectral resolution, 

limited only by the linewidth of the laser, but it is not appropriate for turbulent 

combustion, where instantaneous single-shot measurements are desirable. In 

broadband CARS the Stokes beam is a broadband dye laser, so that an entire rovibrational band can be excited simultaneously.[98] Broadband CARS probing of the 

N2 Q-branch is the most common approach to CARS thermometry, because N2 is 

generally present in combustion environments while also having a spectrum from 

which temperature can be measured sensitively. Broadband CARS requires a 

spectrometer to disperse the CARS signal. The spectral resolution of a broadband 

CARS signal is often determined by the spectrometer, rather than by the laser 
32 

linewidth. Therefore broadband CARS spectra are less resolved than scanning CARS 

spectra. In a broadband dye laser several spectral modes are excited and are 

competing, causing shot-to-shot intensity fluctuations, known as mode noise. Loss of 

spectral resolution and mode competition within the broadband laser make the 

broadband vibrational CARS less precise than scanning CARS, but the advantage of 

the instantaneous measurements outweigh the loss of precision when studying 

turbulent flames. 

Figure 2-1 and 2-2 show that the population distribution between vibrational 

levels is much less sensitive to temperature than between rotational levels. In addition 

the frequencies of the different ro-vibrational transitions within the Q-branch are 

closely spaced, especially for the lower J`s. The spectrometer, needed to disperse the 

CARS signal, limits the spectral resolution and the ro-vibrational transitions are often 

overlapped for the lower values of J. In particular at lower temperatures, only the 

lower J’s in the ground vibrational state are populated. This reduces the sensitivity of 

N2 Q-branch broadband CARS at lower temperature, and therefore its accuracy and 

precision. Because of this limitation, for low temperature applications it is often 

preferred to probe the pure rotational transitions (rotational CARS) since they are 

more widely spaced than the rotational-vibrational transitions used in the current 

work. An approach often used for pure rotational CARS is the dual-Stokes CARS in 

which the pump and the Stokes are provided by the same broadband laser. Rotational 

CARS provides better precision and accuracy at low and moderate temperature. At 

higher temperature, the signal-to-noise ratio decreases rapidly, because the population 

differences are smaller as observed in Figure 2-2; for this reason vibrational CARS is 
33 

a better choice for measurements in high temperature flames flames, such as in the 

current work where temperatures up to ~2400 K are expected from H2-air 

combustion. 

Since the rotational spectra of most species are close to each other, rotational 

CARS offers the potential for multiple species detection with the same detection 

system. In reality, the spectra from different species are overlapped and interfere with 

each other. Ultimately the major species dominate the spectra. Several CARS 

techniques other than rotational CARS have been developed to allow simultaneous 

detection of multiple species. One of the most popular is dual-pump CARS,[81] 

which is the technique used in this work. In DP-CARS the pump and probe laser 

beams have different wavelengths, and their role interchanges so that two different 

regions of the Raman shift are probed simultaneously. Figure 2-4 shows the energy 

level diagrams for DP-CARS. Opportune choice of the frequency difference between 

the pump and probe beams allows avoiding spectral overlap, while keeping the 2 

regions close enough so that a single spectrometer and camera can be used. DPFigure 2-4: Dual-pump CARS energy level diagram
34 

CARS has been used for simultaneous measurements of N2-O2,[81] N2-CO2,[99] N2-

CH4, [100] N2-H2. [101] Recently Tedder [85] has demonstrated a variation of DPCARS called WIDECARS in which a very broad Stokes beam is used to 

simultaneously probe the vibrational band of N2, O2, CO, C2H4 and CO2 and two 

rotational H2 lines (S(3) and (S4). 

The version of DP-CARS used in this work was originally proposed by 

O’Byrne,[6] and allows simultaneous measurements of N2, O2 and three pure 

rotational H2 lines S(5), S(6) and S(9) . If two or more species are resonant, CARS 

can measure the ratio of the mole fractions of the resonant species. Measurements of 

absolute mole fractions require knowledge of the CARS non-resonant susceptibility, 

which varies with composition. If all but one of the major species is resonant, and all 

non-resonant third-order susceptibilities are known, the composition can be fully 

determined. A dual-pump CARS instrument probing N2, O2, and H2 allows absolute 

mole fractions to be determined in a H2-air flame since the only other major species 

present is water (radicals, such the hydroxyl radical, OH, which can be present at a 

level of only a few tenth of a percent are neglected). 

All the CARS systems mentioned above use pulses that are nanoseconds long and 

have repetition rates of tens of Hz. These ns pulses are short enough to freeze the 

flow but the repetition rate is too slow to resolve time fluctuations in the flow; 

instead, each spectrum is uncorrelated with prior or subsequent measurements. In 

recent years there has been a growing interest toward the use of femtosecond lasers 

for CARS diagnostics that allow repetition rates of kHz or more. CARS system based 

on pico-second lasers are also being developed. They offer the advantage of 
35 

suppressing the non-resonant background (particularly important in hydrocarbon 

flames) [102] and the possibility of using fiber optics to deliver the lasers. [103] 

These systems are still in development and have not been demonstrated in large scale 

facilities. Ref. [79] provides a much more detailed review of the CARS technique.

For the case of supersonic combustion, a repetition rate on the order of many 100’s of 

kHz would be required to time-resolve flow structures. Even the highest performance 

fs CARS systems in development today are 1-2 orders of magnitude too slow to meet 

this requirement. Still, acquiring non-time-resolved data at a higher rate (eg. 5 kHz 

vs 20 Hz) is an attractive feature for future CARS systems. 
36 

CHAPTER 3 -The Dual-Pump CARS Instrument 

A dual-pump (DP) CARS system has been developed for this work. The 

instrument is based on the DP-CARS system of Ref.[72], but most components have 

been upgraded and several new features added. The instrument is designed to acquire 

data in supersonic combustion experiments for CFD validation. Mobility of the 

instrument was a requirement so that it could be transported to different test facilities. 

The instrument has a modular structure. The three lasers needed for the CARS 

process are located on a mobile laser cart. Mirrors relay the beams from the cart to the 

combining optics, which focus and cross the beams at the measurement volume. The 

receiving optics separate the CARS signal from the other beams, and direct it to a 

spectrometer. The combining and receiving optics are mounted on two aluminum 

plates for easy transportation. 

Databases for CFD validation require a large number of measurements to 

acquire statistical variances and correlations. The data acquisition system has been 

heavily automated, to improve the data acquisition rate, especially in facilities that 

can operate continuously. Addittionally, there was a significant effort in reducing the 

time needed to analyze the CARS data.
37 

3.1 Experimental Set-Up 

3.1.1 The Laser Cart

Figure 3-1 shows a picture of the laser cart with all the lasers running. The 

laser cart consists of a lower and upper level, each housing an optical table. The lower 

level contains the Nd:YAG laser, optics to separate the visible 532 nm beam from the 

1064 nm beam, and the dye circulators for the two dye lasers. The upper level 

contains the two dye lasers and several additional optis. The core of the instrument is 

an injection seeded Nd:YAG (Quanta-Ray Pro-350) laser operated at 20 Hz. It 

replaced the Quanta-Ray Pro-290 used in Ref.[72]. This laser provides one of the 

Figure 3-1: Picture of the laser cart
38 

three laser beams generating the CARS signal, and acts as the energy source (pump) 

for the narrowband and the broadband dye lasers. The output of the Nd:YAG laser, at 

1064 nm, is frequency-doubled to 532 nm. At the output of the doubling crystal the 

visible 532 nm beam is overlapped with unconverted 1064 nm light. Dichroic mirrors, 

that reflect the visible light and transmit the infrared (IR), separate the two 

wavelengths. The IR light transmitted through the first dichroic mirror passes through 

another doubling crystal generating a secondary 532 nm laser beam. The remaining 

IR light is separated from the visible and carefully blocked. Pellin-Broca prisms in the 

path of the primary 532 nm beam separate it from incoherent broadband blue light 

coming from the laser flashlamps. The two 532 nm beams have a pulse width of ~10 

ns and a linewidth < 0.003 cm-1. Mirrors relay the 532 nm laser beams from the lower 

to the upper level of the cart. The primary 532 nm beam, approximately 900 mJ per 

pulse, is divided three ways: 170 mJ to pump the amplifier of the broadband dye 

laser, 415 mJ for the narrowband dye laser, and 280 mJ for the green CARS pump 

beam. The secondary 532 nm beam, approximately 80 mJ per pulse, pumps the 

oscillator of the broadband dye laser. 

Figure 3-2 is a schematic of the laser cart upper level. The drawing is not to 

scale, but provides a qualitative overview of the optical set-up. The narrowband dye 

laser chosen for this instrument is a Quanta Ray PDL 3. It is a more compact laser, 

easier to align and more efficient than the one used previously.[72] An adjustable 

grating in the oscillator cavity allows selecting the output wavelength of the laser 

beam. The estimated linewidth is ~0.5 cm-1, based on fitting of experimental N2

CARS spectra. An etalon can be added to the oscillator cavity to narrow the 
39 

linewidth, but was not used for this work. Typical energy of the output beam is 75 

mJ. Wavelength selection is accomplished by changing the angle of the grating 

making up one end of the oscillation cavity, and the peak wavelength is set to 551 

nm. A solution of Rhodamine 575 in methanol is the lasing medium in the oscillator 

and the amplifier. The dye concentrations for the oscillator (~ 80 mg of dye in 700 ml 

of methanol) and amplifier (~ 33 mg of dye in 700 ml of methanol) are optimized 

separately to maximize the power output of the laser at the desired wavelength. 

The same home-made conventional broadband dye laser used in Ref.[72] is 

employed in this instrument. The laser peak is centered at 604 nm and has a FWHM 

of ~10 nm and output energies of 40 mJ per pulse. The peak frequency and the 

spectral width are determined by the choice of the dye, of the solvent and by the dye 

concentration in the oscillator. Adding dye increase the peak wavelength, adding 

methanol decreases it. The spectral width of the laser can be increased by using a 

Figure 3-2: Schematic of the optical set-up on the upper level of the laser cart
40 

mixture of two dyes. For the oscillator, a mixture of 8.4 mg of Rhodamine 610 and 1 

mg of Rhodamine 640 in 500 ml of methanol was used. This solution provided a peak 

wavelength of 604 nm, a FWHM of ~ 10 nm, and 4.7% conversion efficiency, for an 

input power of 1.1 W. The concentration of dye in the amplifier is set to maximize the 

power output of the laser. A solution of 8.3 mg of Rhodamine 640 in methanol was 

used for the amplifier with a conversion efficiency of ~ 20%. 

Delay lines are included on the path of each laser beam. They are used to match 

the total path-length of all the lasers, so that the beams arrive simultaneously at the 

measurement volume. Telescopes are present on the path of each beam to collimate 

the beam while avoiding local focusing or hot spots in the beam irradiance 

distribution. An adjustable telescope inside the narrowband dye laser expands the 

output of the oscillator cavity to match the amplifier. A lens was placed in the path of 

the Nd:YAG beam pumping the narrowband amplifier to slightly focus it, so that it 

would match better the size of the expanded oscillator output, thereby improving the 

laser efficiency. The telescope of the broadband dye laser was used to expand the 

beam size and set the beam divergence so that it would focus at the same location as 

the narrowband. 

A combination of a half-wave plate and a polarizer is installed on the path of each 

beam. The half-wave plates are mounted on a rotation stage. By rotating the wave 

plate, it is possible to carefully control the beam energy without affecting its pointing 

and its focusing. The half-wave plate installed on the path of the Nd:YAG beam is on 

a motorized rotation mount that can be remotely controlled. 
41 

A planar BOXCARS phase-matching geometry, with the narrowband and the 

broadband dye lasers collinearly overlapped, and a crossing angle between the dye 

laser beams and the Nd:YAG beam of 4.5 degrees, was chosen for this set-up. This 

configuration mitigates the beam steering effects (Chapter 4) while maintaining a 

good spatial resolution. The narrowband and broadband dye lasers are overlapped 

using a dichroic mirror which lets the broadband beam through but reflects the 

narrowband. 

3.1.2 Combining and Collecting Optics

The beams are relayed to the combining optics plate through four 3” diameter 

mirrors. Typical aser energies at the measurement volume are approximately 90, 30 

Figure 3-3: Schematic of the combining and collecting optics
42 

and 20 mJ for the Nd:YAG, the narrowband and the broadband dye laser, 

respectively. Figure 3-3 shows the optical set-up used for the combining and 

receiving optics. The Nd:YAG beam coming from the laser cart is collected by a 

mirror, and sent through a polarizer and a 600 mm focal length spherical lens. The 

lens is mounted on a translation stage so that the location of the focal plane can be 

varied. The lens is rotated to add astigmatism and to generate an elliptical-shaped 

beam at the focal plane. This feature is used in the beam shaping technique to 

mitigate beam steering described in Chapter 4.The overlapped dye laser beams are 

collected by a mirror and sent through a polarizer and an 850 mm focal length 

spherical lens mounted on a translation stage. The polarizers ensure that the beams 

interacting at the measurement volume have the same linear polarization. 

Commonly CARS systems use a single large lens to focus all three beams. The 

use of two separate lenses has several advantages. First of all it allows the crossing 

angle to be more easily set. The crossing angle, together with the focal spot size 

determines the spatial resolution. In order to obtain the same crossing angle, if a 

single 600 mm focal length lens were used, the beam separation would have been 2”, 

therefore requiring a 3” or greater lens. The separation would be bigger for longer 

focal length. Three inches lenses are expensive and larger sizes are generally custom 

made. In addition, when using two lenses, the beams are centered on the lens, 

reducing spherical aberrations, which are worse near the edges of a lens. Another 

advantage is the possibility of using lenses of different focal lengths for the two 

beams, so that the beam sizes at the focal plane would be better matched, maximizing 
43 

the CARS signal. In our specific set-up it also offered the possibility of shaping one 

of the beams to an ellipse, while keeping the other beams circular. 

Several factors need to be considered in choosing the focal length of the two 

lenses. Geometrical constraints, such as the width of the combustor model and of the 

region where the measurements are performed set a minimum focal length (since the 

lenses must not strike the model). High irradiance perturbation effects (Chapter 5) 

and the damage threshold of windows, if present, also limit the minimum focal 

length. Increasing the focal length excessively reduces the spatial resolution and 

decreases the signal. The focal length values selected are a compromise between 

these constraints. 

Two beam viewing systems[104] are used to image a cross section of the three 

beams in the vicinity of the measurement volume. The first beam viewing system is 

placed before the measurement volume and consists of wedged glass plate (front 

surface is uncoated, back surface has an anti-reflection coating) placed in the path of 

the beams at 45 degrees which creates a secondary (low irradiance) beam crossing. A 

microscope objective lens, filters, and a CCD camera are used to detect an image of 

the crossing. This beam viewing system is used to accurately focus and cross the 

beams so that the CARS signal is maximized. The wedged glass plate is removed 

during data acquisition to maintain the crossing location. The second beam viewing 

system is placed after the measurement volume, and also contains a splitter, but 

differs from the first by an achromatic spherical lens that refocuses the three beams to 

form another secondary beam crossing that is imaged by another microscope 

objective and CCD camera. The system is used to monitor the position and the 
44 

focusing of the beams during a test, and to evaluate the effect of beam steering and 

temperature changes of the optics. 

At the measurement volume the three beams interact and generate a coherent 

laser-like beam containing a broad CARS spectrum centered at 490 nm. As shown in 

the figure, the collecting optics separate the CARS signal from the overlapped 532 

nm beam and direct it to the spectrometer. A multi-pass dichroic mirror separates the 

CARS signal from the overlapped 532 nm beam and two additional low pass filters 

remove the residual green light. The signal is then focused by a spherical lens on the 

input slit of a one-meter McPherson spectrometer equipped with a 2400 lines/mm 

grating. The CARS signal is dispersed by the spectrometer and recorded by a back 

illuminated CCD camera (Princeton Instruments PIXIS 100B). The camera detector 

has a 26.8 x 2.0 mm imaging area with 1340 x 100 imaging pixels. Each pixel is 20 x 

20 μm and the dynamic range is 16 bits. The device is thermoelectrically cooled to 

−80°C providing a dark charge of 0.0014 e-/pixel/s. The read noise is 12.61 e- (rms), 

the gain is 1.05 (e-/ADU), and the non-linearity is below 1%. Spectral rates, with a 2 

MHz digitalization are up to 387 Hz, measured with all rows vertically binned. 

3.1.3 Wavelength Selection

The selection of the wavelength of the dye lasers determines what species the 

instrument probes. The wavelengths reported here are selected for simultaneous 

detection of the Q-branch of N2 and O2, and of three H2 rotational lines. The red curve 

in Figure 3-4 shows a theoretical dual-pump CARS spectrum containing all the 

transitions probed by this instrument. This DP-CARS instrument probes two regions 
45 

of the Raman shift; the first region is between 2050 cm

-1 and 2350 cm-1 and contains 

the N2 Q-branch and the H2 S(9); the second is approximately between 1420 cm

-1 and 

1720 cm

-1 and includes the O2 Q-branch, and the S(5) and S(6) rotational transitions 

for H2. One of the advantages of DP-CARS is that the two probed regions appear 

close to each other in the CARS spectra. Conventionally the horizontal axis in plots 

of DP-CARS spectra corresponds to the Raman shift for the CARS process in which 

the 532 nm laser is the pump laser (ω1 in Figure (2-3)). Along this axis the Raman 

shift for the CARS process for which the narrow band dye laser is the pump laser is 

shifted by the frequency difference between the 532 nm and the narrowband dye 

laser. The wavelength of the narrowband dye laser can be tuned to minimize the 

spectral overlap between the species probed by the two Raman processes. 

The CARS signal at any particular Raman shift frequency is proportional to the 

spectral irradiance of the broadband (Stokes) dye laser corresponding to that 

Figure 3-4: Theoretical dual-pump CARS spectrum (red) and 

experimental non-resonant signal spectrum (blue) collected in Argon
46 

frequency. The blue curve in Figure 3-4 is an average CARS spectrum taken in argon. 

Argon has no resonances and signal is generated only by the constant CARS nonresonant susceptibility, so the spectrum of the non-resonant CARS signal is 

determined by the spectrum of the broadband dye laser. In the current work it is 

roughly Gaussian. The CARS susceptibility spectrum is recovered by dividing the 

CARS signal spectrum by the spectrum of the non-resonant gas. The wavelength of 

the broadband dye laser is chosen so the argon peak is between the O2 bandhead and 

the H2 S(6) lines. For typical test conditions in combustion environments, O2 CARS 

signal is lower than N2 because of the lower mole fraction, and the H2 S(6) is weaker 

than S(5); centering the broadband between the O2 and the H2 (S6) increases the 

signal-to-noise ratio for these weaker spectral lines and helps avoiding exceeding the 

detector dynamic range for the stronger lines. 

3.1.4 Laser Alignment 

Working with pulsed dye lasers (class 4) requires safety eyewear to avoid 

permanent eye damage in case of accidental exposure to laser light. Protective 

eyewear that blocks all the wavelengths in the DP-CARS system (ranging from 532 

to 620 nm and 1064 nm) is available, but also blocks most of the visible light. Blue 

led lights have been mounted on the cart to improve the visibility when wearing the 

protective eyewear. Fluorescent cards and cameras are used to visualize the beams. 

Alignment of a DP CARS system can be a complex and time consuming task, 

especially when the beams have to travel several meters to reach the measurement 

volume. A procedure has been developed that simplifies this task and greatly 
47 

improves safety. The initial alignment of all the mirrors used in the optical set-up is 

performed using two low power green laser pointers, simulating the Nd:YAG and the 

narrowband dye laser, and a low power HeNe laser at 632 nm, replacing the 

broadband dye laser. Operation of these lasers does not require the use of protective 

eyewear. Mirrors, mounted on flip mounts, are used to insert the laser pointers beams 

into the path of the pulsed lasers. The low power lasers are used to set-up and adjust 

several mirrors on the laser cart, the relay mirrors, and all the optics on the combining 

and receiving plates. The low-power beams are crossed at the measurement volume 

with the help of the beam viewing system on the combining optics plate. 

A beam from a blue laser pointer passes through the Nd:YAG mirror on the 

combining optic plate, and is overlapped to the beam from the green pointer. The blue 

beam is used to set-up the multi-pass dichroic mirror, and the optics relaying the 

signal to the spectrometer. The mirrors are adjusted so that the blue beam is centered 

on the spectrometer entrance slit, and on the CCD camera. Once the system is 

aligned, irises are added to the path to outline the position of the beams, and the 

mirrors that inserted the pointer beams into the path flipped down. 

The next step is to turn on the high-power lasers, and simply align them to the 

irises. The power of the laser during this alignment procedure is reduced to a working 

minimum, by rotating the half-wave plates. This approach does not change the 

pointing or the focusing of the lasers. The beams will appear on the beam viewing 

system camera, but they will be out of focus if they were focused using the laser 

pointer beams because the divergence of the pointers does not match the divergence 

of the high-power beams. The lenses are mounted on translation stages with motion 
48 

aligned to the beam path and can be adjusted until the beams appear focused on the 

beam viewing system (imaging the beams at the crossing plane). This operation is 

performed to set the focus of the Nd:YAG and the narrowband dye lasers. The 

telescope on the path of the broadband dye laser is then adjusted so that also the 

broadband beam is also focused at the crossing plane. 

At this point all the beams are crossed and focused at the same location and the 

optics are set-up so that the resulting CARS signal would be directed to the 

spectrometer. The mirror for the first beam viewing system is flipped down, the 

power of the laser increased, and a CARS signal is detected on the camera. The signal 

needs to be focused on the CCD camera, and this can be done by adjusting the 

distance between the spherical lens and the entrance slit of the spectrometer. Fine 

adjustments can be performed to maximize the CARS signal using the 2 mirrors on 

picomotor controlled mounts. These allow fine adjustments of the overlap of the dye 

lasers on the Nd:YAG beam, and of the overlap of the two dye laser on each other. 

The same two picomotor-controlled mirrors can be used to remotely adjust the 

position of the two dye lasers with respect to the Nd:YAG beam during a test. For 

example the picomotors can be used to counter the effect of temperature changes of 

the mirrors, as discussed in Chapter 8. 

3.2 The Data Acquisition System

A graphical interface written in Labview controls a pulse generator, a translation 

stage, a rotation stage (for a half-wave plate), and the PIXIS CCD camera. The data 

acquisition software has been optimized for measurements in facilities that can run 
49 

continuously, like the laboratory scale supersonic jet of Chapter 7, or the dual mode 

scramjet combustor discussed in Ref.[105]. The data acquisition has been strongly 

automated, so that the overall data acquisition rate is improved.

For all the data presented in this work a three axis translation stage was used to 

move the burner, so that different locations in the flame could be probed. In large 

scale facilities the combining and collecting optics plate are mounted on the 

translation stage, allowing the movement of the CARS measurement volume within 

the flow of interest. 

The camera has a detector of 1340 x 100 pixels. The Labview interface allows 

binning of the CCD camera. For all the data presented in this work the CCD is binned 

into three rows (1340 x 33 pixels) to reduce the read-out time and to allow data 

acquisition at 20 Hz. Binning also increases the signal-to-noise ratio. The CARS 

signal is only in the central bin (bin 2); the upper and lower bins are used for 

background subtraction as described in more details in the next section.

The dynamic range of the camera is 16 bits, limiting the maximum number of 

counts to 65535. CARS signal intensity is strongly dependent on the temperature (

3.5 T − ∝ ), therefore a large variation of the signal intensity is expected in combustion 

studies. When the CARS signal exceeds this threshold, it can be lowered by reducing 

the energy of the Nd:YAG laser; this is accomplished by rotating a half-wave plate 

followed by a polarizer, placed on the path of the Nd:YAG beam on the laser cart. 

The half-wave plate is mounted on a motorized rotation stage controlled by the same 

Labview code that controls the camera acquisition and the translation stage. During 

acquisition of a typical dataset, the software moves the translation stage to the desired 
50 

location; once it has arrived, it collects typically 20 spectra and counts how many 

have peak intensity above a user-defined threshold (set to 50,000 counts for all the 

data presented in this work). If 10% of the spectra are above the threshold, it rotates 

the wave plate to a preset value, reducing the signal intensity, and samples the flow 

again. The process is iterated until fewer than 2 (10%) of the spectra are above the 

threshold. In previous works, [6, 66, 72] the dynamic range issue was solved by 

adding a neutral density filter in the path of the signal when the signal exceeded the 

saturation threshold. In those works the process was not automated, and the operator 

had to verify the threshold level and insert the appropriate neutral density filter. The 

process described here is completely automated (integrated in the Labview routine 

that controls the camera and the translation stage), greatly increasing the number of 

spectra per hour that can be acquired. The approach guarantees that a large percentage 

(~90%) of the shots at a given location does not saturate the camera. Preventing 

detector saturation in 100% of the shots, by signal reduction, can be 

counterproductive in a very turbulent region of the flow. In a location where the 

temperature range is very large, it is preferable to let the coldest 10% of spectra 

saturate the camera, rather than lowering the signal-to-noise ratio below acceptable 

levels at the highest temperature. It is not possible to analyze spectra with signal that 

is too low, but we can still extract information from spectra having saturation in some 

pixels, as it will be shown in Chapter 6. 
51 

3.3 Data Analysis 

CARS data analysis consists of three steps. First, the pre-processing extracts the 

square root of the CARS signal from the raw data. The second step consists of 

generating a library of theoretical spectra to compare to the experimental spectra. The 

final step is the fitting of the preprocessed experimental spectra to the theoretical 

library to extract temperature and mole fractions. The procedure described in the next 

section is the one followed for the data analysis of the CARS spectra in the 

supersonic combusting free-jet, described in Chapter 8. Some of the steps were not 

necessary in analyzing the data from the laminar Hencken burner flame discussed in 

chapter 6. 

3.3.1 Data Pre-Processing

The raw signal collected by the CCD camera contains not only the CARS signal 

but also contributions from other sources that have to be removed. A major 

contribution is the camera dark noise. This contribution is almost identical in all three 

bins (within 1 count); shot-to-shot variations of dark noise in each binned pixel have a 

standard deviation of 4.5 counts. The mean value typically changes 1-2 counts over a 

few hours (depending on the CCD temperature) as long as the camera has been 

warmed up for few hours before the test. Ambient light, primarily from the room 

illumination, can reach the camera. Barriers, built around the camera and the relay 

mirrors limit this contribution to 1-2 counts above the dark noise level, provided the 

room overhead lights are extinguished. With the current set-up some light from the 

Nd:YAG laser flashlamps reaches the camera. The light is collinear with the Nd:YAG 
52 

beam, and therefore partially overlapped to the CARS signal itself, because in the 

planar boxcars phase matching geometry the signal beam is collinear with the green 

pump beam. The portion of the light at the same wavelength as the CARS signal 

reaches the camera’s central bin (bin 2) as shown in Figure 3-5. Contribution in the 

other two bins (bin 1 and 3) is negligible. The two set of spectra shown in figure were 

collected before (red lines) acquiring CARS data in a laboratory-scale supersonic jet 

(see Chapter 8), and 4 hours later, after the data acquisition was completed (blue 

lines). The figure shows the average signal obtained blocking the dye lasers so that no 

CARS signal could be generated, and subtracting the average camera dark noise in 

each bin. The contribution is not uniform over the CCD, but has a well-defined 

spectral distribution. Use of Pellin-Broca prisms on the cart reduces its peak 

amplitude to ~ 20 counts. This emission passes through and is altered by the halfwave plate and the polarizer used to reduce the signal intensity in the presence of 

detector saturation. To take into account this contribution 250 background spectra are 

taken for each value of the half-wave plate angle used during the test, by blocking the 

narrowband dye laser on the cart. For each test run, we subtract, bin by bin, from the 

raw signal the average of the background obtained with the same angle of the halfwave plate used for that specific run. 
53 

The procedure described above does not remove the contribution from the flame 

emission. This contribution depends on the location of the flame, and therefore could 

not be taken into account by subtracting a reference spectrum. This contribution is 

present in all three bins, but it is higher in the central bin (the one containing also the 

CARS signal) as shown in Figure 3-6. In this work, significant contribution from the 

flame was observed for the combustion cases in the laboratory-scale supersonic freejet, but not the mixing cases, discussed in Chapter 8. The ratio of the flame luminosity 

between bins is approximately constant (within 10%) with the flame location. This 

ratio (scaling factor) is determined once for each test case from spectra taken with all 

lasers blocked and the supersonic burner operating at test conditions. To take into 

account the flame luminosity contribution, the algorithm subtracts from the central 

Figure 3-5: Contribution from the Nd:YAG flashlamps
54 

bin the average of the bin containing the least signal, multiplied by the scaling factor 

that takes into account the different light distribution in the three bins. 

Data acquisition in the supersonic jet typically lasted as long as 4 hours. Small 

changes with time in the background spectra are taken into account by interpolating 

between spectra taken before and after the test. Tests in the Hencken burner (Chapter 

6) were generally completed within an hour, and variations of the background spectra 

with time were neglected. 

CARS spectra have resonant and non-resonant parts. In DP-CARS absolute mole 

fraction measurements are determined by the ratio between the resonant and the nonresonant portion of the spectrum. The non-resonant baseline intensity ranges from 15 

counts to a few hundred; therefore it is comparable to the contributions from the 

Figure 3-6: Contribution from the flame luminescence
55 

flashlamps and the flame luminescence. Correct removal of spurious light from the 

non-resonant baseline is therefore critical for accurate measurements of absolute mole 

fractions. 

The CARS signal, obtained by removing the background from the raw signal, 

needs to be normalized by the non-resonant spectrum. This spectrum is obtained by 

averaging 500 single-shots CARS spectra obtained in a flow of argon. Non-resonant 

spectra are collected at the beginning and at the end of the test day. During the several 

hours required for data acquisition, the measured non-resonant spectrum changes its 

peak wavelength and its shape as shown in Figure 3-7. The change is due to several 

factors, including changes in the temperature of the dye, solvent evaporation, laser 

misalignment and changes in the intensity of the Nd:YAG beams that pump the dye 

cells. The preprocessing algorithm determines the difference in the peak locations of 

Figure 3-7: Average non-resonant spectrum in argon
56 

the two non-resonant average spectra (before and after a test), shifts the non-resonant 

spectrum collected at the end of the test so that the peaks overlap, and computes the 

difference between the two spectra, to determine the change in shape. For each run, 

the time passed from the acquisition of the first non-resonant spectrum is computed 

and divided by the time between the acquisitions of the two non-resonant spectra. An 

interpolated spectrum is then obtained by adding to the first non-resonant spectrum 

the product of this ratio and the difference between the two non-resonant spectra. This 

accounts for the changes in shape. The result of this operation is then shifted by a 

number of pixels equal to the product of the time ratio defined above and the 

difference in the peak location of the two non resonant spectra. This approach 

assumes that the changes in the non-resonant spectrum are linear with time – an 

assumption that was shown to be sufficient for measurements in the Hencken burner. 

Over the four hours of a typical test in the supersonic jet, the change in the nonresonant spectrum peak wavelength is not monotonic; therefore the linear 

approximation can cause errors. Unfortunately this was not anticipated at the time of 

data acquisition, and only two non-resonant spectra are available, one before and one 

after the whole data set is acquired. Figure 3-8 a) shows the fit to the theory of an 

average spectrum obtained with the non-resonant referencing described above. The 

left side of the spectra is lower than the theory, the right side higher. This error is a 

typical consequence of an erroneous referencing (due to an incorrect shift in the 

Gaussian shape of the non-resonant spectrum) and can be corrected by shifting the 

non-resonant spectrum by an additional 35 pixels as shown in Figure 3-8 b). Visual 
57 

inspection of all data is impractical given the large amount of data collected in a 

typical test campaign. 

In Ref. [6] O`Byrne faced a similar problem and determined the position of the 

non-resonant spectrum by fitting the middle one third of the spectra obtained in each 

run for three or more values of the center wavelength of the non-resonant spectrum, 

and determining the optimal values as the one minimizing the fitting residual. This 

approach is time consuming since it requires multiple fits of each dataset; given the

large amount of data a less accurate but faster approach was chosen. Figure 3-8 a) 

shows that an incorrect non-resonant shift causes an erroneous slope in the nonresonant baseline. An algorithm was developed that evaluates the ratio of the average 

experimental spectra in the 2085-2090 cm-1 to the average in the 2240-2245 cm-1

region. This ratio is a function of temperature and composition, but does not change 

much in the range of temperature and concentration expected. For the combustion 

case, values of the ratio are ~1.04 for the nozzle exit composition and temperature, 

0.84 for the pure H2 or N2 co-flow, and 0.95 for air, based on theoretical spectra 

obtained with CARSFT. The ratio is mostly sensitive to changes in the O2 and H2O 

mole fractions. The algorithm first determines if significant amounts of O2 are present 

(peak of the O2 spectrum greater than 10% of the total spectrum peak, before 

normalization by the non-resonant), to choose which value of the average ratio to use 

(0.84 if O2 is negligible, 1.04 otherwise). Then it computes the ratio in the 

experimental average spectra that have been normalized by the interpolated nonresonant spectrum, and by the same spectrum shifted by ±60 pixels. Finally, it fits the 

computed average ratios with a quadratic function to determine the shift necessary so 
58 

that the ratio in the experimental data matches the desired value. The algorithm 

returns the shift in the non-resonant spectra up to 100 pixels, and change in the shift 

computed for two consecutive runs is within 30 pixels. 

The main limitation of this approach is that the theoretical ratio is not known a 

priori and is approximated to one of two set values. For the range of temperature and 

concentrations expected in the test, the ratio can take values in the 0.84-1.1 range; for 

a given spectrum the difference in the non-resonant shift computed by the algorithm 

using the two limit values is 32 pixels, therefore an uncertainty of ±16 pixels is 

caused by not knowing the exact composition and temperature in the preprocessing. 

In terms of measured mole fraction, a 16 pixel shift corresponds to ~2% change in the 

measured absolute mole fraction, 5% in the relative mole fraction, and 1% in the 

temperature. Shot-to-shot referencing schemes as used in Ref. [106] might remove 

this source of uncertainty and greatly improve the instrument accuracy.

 Errors in background subtraction can lead to bigger errors when this algorithm is 

used because they affect the baseline, and therefore the ratio used to determine the 

non-resonant shift. This is especially problematic for spectra taken in colder gases, 

where the laser irradiance has been strongly reduced to avoid detector saturation in 

the spectral peak. For this reason the algorithm uses the shift determined for the 

previous set of spectra for spectra having less than 25 counts on the non-resonant 

baseline. 
59 

Figure 3-8: Experimental spectra and theoretical fit before (a) and after (b) 

shifting the excitation profile
60 

The last step in pre-processing is the conversion from pixel to wavenumbers. In 

previous works, a linear conversion relation was used, but tests with calibrated 

spectral lamps show that the spectrometer is non linear. In this work the following 

quadratic relation is used: 

7 7

2

10 10 e ap bp c d

ω = − + +

(3-1) 

where p is the pixel number and ωe the corresponding wavenumber. An algorithm has 

been developed to determine the mapping coefficients (a,b,c,d). The algorithm 

requires a high temperature experimental spectrum containing N2 and either O2 and 

H2, and a theoretical spectrum generated from CARSFT containing the same species, 

and roughly at the same temperature (i.e. same peaks) is also required. A graphical 

user interface allows selecting any numbers of peaks for each species in the 

theoretical spectra, and the corresponding ones in the experimental spectra. The 

mapping coefficients are obtained as the values that minimize the function:

( ) (( ) ( ))

(1) (2)

1 1

1

2 2 2

(1) (1) (2) (2) (2) (2)

(1) (2)

1 1

1 1 (,,, ) i i j j

n n

e t e e t t

i j

f abcd

n n

ωω ωω ωω

= =

    − + −−− =

 

∑ ∑ (3-2) 

The superscripts (1) and (2) indicate the peaks associated to the first (N2, and H2

S(5)) and to the second (O2, H2 S(6) and S(9)) CARS process, respectively (see 

Figure (2-3)). The sum goes from 1 to the number of peaks selected for each of the 

two CARS processes (n(1) and n(2)). Equation (3-2) is a measure of the difference 

between the theoretical and the experimental location of the selected peaks, for a 

given set of the mapping parameters. The location of the peaks associated to the 

second process is a function of the frequency difference between the Nd:YAG and the 
61 

narrowband dye laser, that is not well known at this stage of the preprocessing . For 

this reason for the peaks associated to the second CARS process, the distance from 

the first peak selected appears in the equation, rather than the actual frequency. The 

parameters used to convert from pixel to wavenumber are the ones that minimize Eq. 

(3-2). The initial guess for the conversion parameters are a=0, b=0.006 (from spectral 

lamp measurements), c=center wavelength of the CARS signal and d=wavelength of 

the narrowband dye laser. 

The parameters for the conversion from pixel to wavenumber are determined once 

for each day of testing. Beam steering and changes in temperature of the optics can 

move the location of the CARS signal on the camera. If the location (pixel number) of 

the ro-vibrational peaks changes from the value used to determine the mapping 

parameters, then the experimental spectra will appear shifted with respect to the 

theoretical. Small differences, below 1 cm-1 are taken care in the fitting algorithm, 

which has as a fit parameter a frequency shift. The fitting algorithm does not perform 

well in presence of larger frequency differences, and corrections in the pre-processing 

algorithm are needed. The pre-processing algorithm shifts the spectra so that the 

location where the N2 band is 20% of its peak values is always at the same pixel 

location. For spectra where only H2 is present the algorithm shifts it so that the S(5) 

peak is at a fixed pixel location. For this experiment, typical movements of the 

spectra on the CCD were limited to few pixels, but larger movements have been 

observed in previous work in the large scale jet.[72] 
62 

3.3.2 The Theoretical Library

The preprocessed spectra are analyzed using the fitting algorithm developed by 

Cutler.[107] The algorithm interpolates from a library of theoretical spectra generated 

with a version of CARSFT [108] modified by Hancock [109] and O’Byrne [110] for 

use with DP-CARS. 

CARSFT requires several experimental parameters to generate the theoretical 

spectra. In addition to the molecular parameters, CARSFT requires the spectral line 

width of the pump laser (Nd:YAG), the instrument function (mainly owing to the 

focusing of the signal on the spectrometer entrance slit, on the camera pixel size, and 

on the spectrometer), the spectral line width of the probe laser (narrow band dye 

laser), and the offset in wavenumbers between the pump and probe beams. These 

parameters are determined by fitting experimental spectra to theoretical spectra, using 

the fitting routine included in CARSFT. The offset between the pump and probe is 

determined using CARSFT, so that the distance between the N2 and O2 spectra is the 

same in the theory and in the experiment. When the non-linearity of the spectrometer 

is properly taken into account, the position of the H2 lines (S(5) and S(6)) are then 

also the same in theory and experiment. The Nd:YAG laser is injection seeded, and 

its width is considered infinitesimal in the spectral convolution. The instrument 

function is assumed to be a Gaussian and its width is determined as a result of a 

fitting over the O2 portion of the spectrum. This region is chosen because the O2

spectrum is not broadened by the finite width of the narrowband dye laser. The line 

width of the narrowband dye laser is determined by fitting this parameter in the N2
63 

region, using the width of the instrument function determined in the previous step. In 

this procedure all parameters are decoupled, and only one parameter at a time is 

determined by fitting. 

Some changes have been made in the CARSFT code. The original code did not 

allow different spectral linewidth models to be selected for different molecules. The 

code has been modified to always use the Galatry linewidth model for the H2 spectra 

and the linewidth model input to the code is applied to both N2 and O2. The impact of 

this change on the mole fraction accuracy is discussed in Chapter 6. 

The differential Raman cross section   ∂σ

    ∂Ω appears in the expression of the 

CARS susceptibility (Eq.(2-20)). The effect of the interaction between the rotational 

and vibrational modes, on the differential Raman cross section is taken into account 

through the Herman-Wallis correction factor. [111] CARSFT originally uses the 

James Klemperer model [112] for the Herman Wallis factor, but recent studies[113, 

114] showed improved CARS accuracy when using the Tipping Bouanich [115] 

model. I added to the CARSFT code the possibility of choosing between these two 

models or to neglect the Herman Wallis factor. [114] 

3.3.3 Spectral Fitting

A new fitting algorithm has been developed by Cutler [107] and has been used for 

all the spectral fitting used in this code. The algorithm fits the experimental spectra to 

a sparse library of theoretical spectra. At each iteration of the code, theoretical spectra 

are interpolated from the library. Temperature, absolute mole fraction of the resonant 
64 

species, and a horizontal wavenumber shift are obtained as a result of a fitting 

algorithm that minimizes an appropriate residual between the experimental CARS 

signal intensity and the theoretical CARS spectra. Details on the criteria to generate 

the libraries and on the fitting algorithm can be found in Ref. [107]. 

The code is at least ten times faster than CARSFT since it uses a library of pregenerated spectra, rather than computing theoretical spectra at each iteration step. In 

addition, CARSFT tends not to converge to a global minimum, being very sensitive 

to the initial condition, when more than three parameters are fit simultaneously. The 

new method also offer advantages with respect to the library based algorithm used by 

O’Byrne, [6] since it uses sparse libraries rather than fully populated ones. The sparse 

libraries are smaller, and the increase in processing speed becomes increasingly 

significant as the number of the chemical species is increased (as for example in 

WIDECARS, [85] where 6 species are probed). 

The algorithm offers the possibility of choosing between a weighted least square 

fitting to the CARS intensity (originally suggested by Snelling) [116], and least 

square fitting to the square root of the CARS intensity used in CARSFT. The first 

reduces the random error, and ultimately improves the instrument precision as shown 

in Chapter 6. 

Another useful feature of the algorithm is the possibility of blocking selected 

regions from the fitting. A blocked region is not included in the computation of the 

residual. In this work the S(6) and S(9) H2 lines are sometimes blocked, as well as 

regions of the spectra that saturate the detector, as it will be shown in Chapter 6. 
65 

CHAPTER 4 -Mitigation of Beam Steering Effects

4.1 Introduction

Laser beams travelling through a turbulent combustion environment are subject to 

small displacements in their path. Turbulence at the interface between combustion 

products and air, or between a supersonic jet and quiescent air, causes rapid spatial 

and temporal variations of density, which translate directly into refractive index 

gradients. Larger eddies with size comparable to the beam diameter randomly deflect 

the laser beam (beam wandering), and are responsible for phase shift fluctuations 

leading to the appearance of speckles in the beam profile. Smaller eddies scatter the 

light and cause a spreading and a defocusing of the beam [87, 117-119]. In CARS, 

three beams are focused and overlapped at the measurement volume, where they 

interact and generate a coherent signal containing the Raman spectrum of the probed 

species. Beam displacements of as little as a few tens of micrometers can prevent the 

beams from fully overlapping, causing a reduction in the CARS signal. The CARS 

signal is proportional to the product of the irradiance of the three laser beams; 

therefore beam defocusing also causes a reduction in the CARS signal. In addition to 

refractive index gradients, vibrations of the optics, either acoustically excited or 

transmitted through the optic’s supporting structure, also affect the beam path. Beam 

steering is the motion of the beam at the focal plane of the measurement volume 

induced by both refractive index gradient induced wandering and by vibration of the 

optics.
66 

Numerous studies have been conducted to evaluate the applicability of CARS in 

turbulent environments. Beam steering is tolerable for measurements in small 

combustors, but becomes an issue in supersonic free jets, or large flames. [87] AttalTrétout [120] observed considerable CARS signal fluctuations and data yield (percent 

of acquired spectra that resulted in a good fit for temperature) below 50% when a 

turbulent hot air flow was interposed between the focusing lens and the measurement 

volume. Beam steering due to large density gradients was responsible for frequent 

loss of CARS signal in measurements performed by Klimenko [121] in a cryogenic 

LOX-H2 rocket combustion chamber. Hemmerling [122] attempted single-shot folded 

BOXCARS temperature measurements in a high pressure combustor, but signal-tonoise ratio was too low because of severe beam steering. Beam steering is a potential 

problem for any laser based technique in which the laser beam coherence is critical 

and two or more laser beams needs to be overlapped. For example Herring [123] 

showed that beam steering is a serious obstacles to LITA measurements in highdensity, compressible, and turbulent flows.

Recently, significant beam steering effects on CARS measurements were 

observed in a large, supersonic combusting, axisymmetric free jet, [66, 72] resulting 

in large variations of the signal to noise ratio, and data yield as low as 40%. [72] Such 

low data yields are undesirable because facility run times must be increased to 

acquire the necessary data and also because averaged temperatures can exhibit bias 

towards lower temperature, since spectra obtained at lower temperatures tend to have 

larger signal intensity and are therefore more often included in the average. [74, 120] 

Beam steering was less important for measurements in ducted combustor. [6, 105] In 
67 

a supersonic combusting free jet, the large density gradients at the turbulent interface 

between the hot reaction products and the atmospheric air are responsible for the 

severe beam steering effects.

The objective of this chapter is to investigate a new approach to reduce the 

sensitivity of CARS to beam steering. This new approach combines elliptical beam 

shaping and planar BOXCARS to achieve this goal, while leaving the length of 

measurement volume unaltered. The new technique is compared to previous 

methodologies used for measurements of large turbulent flows. Advantages and limits 

of this approach are investigated numerically and experimentally.

4.2 Beam Steering Mitigation Technique

In order to obtain a strong CARS signal, three incident beams have to be aligned 

so that the signal generated at some point will be in phase with the signal generated at 

subsequent points. Several strategies have been devised to satisfy the phase matching 

requirements while maintaining adequate spatial resolution. In the presence of beam 

steering some phase matching geometries are more robust than others. In USED 

(Unstable-resonator Spatially Enhanced Detection) CARS [124] the pump beam is 

donut shaped and the Stokes beam is concentric to the pump. Because of the 

concentric geometry and of the common propagation axis of the beams, beam 

steering has less effect on the beams overlap, but this approach greatly lengthens the 

probe volume and adds uncertainty to the location of the measurement volume. For 

example, Eckbreth [125] reported measurements in a jet engine exhaust using this 

approach, but the spatial resolution is 0.1 mm in diameter and 50 mm long, thirty 
68 

times longer than reported in Ref.[6, 70, 72]. Hemmerling [122] adopted the USED 

CARS phase-matching to obtain single shot temperature measurements in a high 

pressure combustor, with a spatial resolution of 11 mm. In most turbulent applications 

a higher spatial resolution is desirable, strongly limiting the applicability of USED 

CARS. 

Folded BOXCARS [126] was used to collect the data in the large free jet 

described in Ref. [66, 72, 74]. This is a three-dimensional arrangement that allows 

good spatial resolution and signal strength. This phase matching strategy is prone to 

be affected by beam steering, since each beam travels along a different path, 

encountering different turbulence structures, and thus is refracted differently. 

Figure 4-1: Planar BOXCARS

Direction of 

“out-of-plane” 

motion

Direction of 

“in-plane” 

motion

Nd:YAG

laser

Overlapped

dye lasers

CARS signal 

overlapped to Nd:YAG

y

x

z

Focal 

Plane (x-y)
69 

Planar BOXCARS (Figure 4-1) has all the beams travelling in the same plane. 

The reference system introduced in Figure 4-1 has its origin at the crossing point of 

the three beams before the effect of beam steering; the z axis is in the direction of the 

CARS signal beam, the x axis is in the plane of the beams and orthogonal to z, and the 

y axis is orthogonal to x and z. The planar BOXCARS phase matching condition 

requires that two of the three beams are almost superimposed as shown in Figure 4-1. 

In this instrument, the broadband Stokes dye laser (in red) and the narrowband pump 

dye laser (in yellow) are overlapped, and the CARS signal beam (in blue) is 

superimposed on the Nd:YAG pump beam (in green). Dichroic mirrors are used to 

combine the two dye laser beams and to separate the signal from the Nd:YAG beam. 

The beams are crossed at their respective waists (which are forced to be coincident), 

at the “focal plane”. Signal is generated at the beam intersection, a region that 

resembles a very elongated ellipsoid with maximum cross section diameter 

determined by the smallest beam. The length of the probe volume is determined by 

the angle between the beams and by the beam diameters at the focal plane. [127] The 

main disadvantage with respect to “folded” BOXCARS is the weaker CARS signal 

[128] (40% lower for given probe volume length) and the need of dichroic mirrors to 

combine and separate beams. The advantage is that the superposition of two beams 

ensures that those beams remain overlapped at the focus, even in the presence of 

beam steering, whereas in folded BOXCARS all three beams can move 

independently. 

Loss of signal will occur if the two superimposed beams do not overlap with the 

third beam. Any motion of the beams with respect to each other can be expressed as a 
70 

sum of two components, one “in-plane” (i.e. along the x axis), and the other “out-ofplane” (i.e. along the y axis). Figure 4-2 shows the effect of “in-plane” motion on the 

beam`s crossing. The “in-plane” motion does not prevent overlap, but moves the 

crossing location away from the common focal-plane (the x-y plane in figure), to a 

different z location. As a result the location of the probe volume is shifted and the 

beam irradiances at the crossing are lower causing a small reduction of the signal 

level. 

Figure 4-3 shows the effect of “out-of-plane” motion on the beam crossing. The 

figure show the 3 beams sectioned by the x-y plane that is the common focal plane. In 

absence of beam steering (Figure 4-3a) the beams overlap and generate the strongest 

Figure 4-2: Effect of “in-plane” beam motion: a) beams sectioned by the x-z plane; the 

dashed red line around the overlapped dye lasers indicates the beam displaced by the 

beam steering; b) beams sectioned by the focal plane (x-y) without beam steering, and 

c) with “in-plane” beam steering 
71 

CARS signal. Just one beam diameter of displacement in the “out-of-plane” direction 

(i.e. along the y axis) is sufficient to prevent overlapping (Figure 4-3b) and CARS 

signal generation. An elliptically-shaped Nd:YAG beam, with the major axis in the 

direction orthogonal to the plane of the beams as shown in Figure 4-3c, would allow 

beams to overlap for larger displacement “out-of-plane” than a round beam. Thus an 

elliptical beam in the planar BOXCARS geometry will generate a signal less sensitive 

to beam steering, but weaker because of the decreased irradiance, since the same 

energy is now spread across a larger area. 

Often in CARS setups high irradiance perturbation effects such as optical 

breakdown, stimulated Raman pumping, and Stark broadening limit the laser 

irradiance at the measurement volume and excess laser energy is not used (see 

Chapter 5 for details). This extra energy allows beam shaping, i.e., increasing the 

major axis diameter of the Nd:YAG beam (leaving the minor and other beam 

diameters unchanged), while keeping the irradiance at the focus constant to prevent 

Figure 4-3: a) No beam steering, optimal beam overlap and maximum CARS signal; b) 

effect of “out-of-plane” beam motion when using a round Nd:YAG beam and c) an 

elliptical Nd:YAG beam 
72 

any signal loss. From geometric considerations, [127] the length of the interaction 

region is determined by the minor axis beam diameters, and does not depend on the 

major axis diameter. The diameter of the interaction region is given by the diameter 

of the smallest beam. Although the length of the measurement volume is not affected 

by this approach, uncertainty is added to the location of the measurement volume.

4.3 Numerical Results

This section includes a numerical evaluation and comparison of the CARS signal 

strength and probe volume length for planar BOXCARS with and without beam 

shaping. 

The total CARS signal PCARS can be expressed as: [129] 

( ) ( )

4 2 1/2 3

1 2

2 CARS PCARS p p S I I I dz dxdy

c

πω

χ

  =     ∫∫ ∫ (4-1) 

where ωCARS is the signal frequency, Ip1, Ip2 and IS the two pump and the Stokes beam 

irradiances, χ

(3) the third order susceptibility. The coordinate system used for this 

calculation is the same of Figure 4-1. Some simplifying assumptions have been made: 

each beam’s irradiance distribution is approximated to a bivariate normal with null 

covariance; 

( ) ( )2 2

2 2

1 ( , , ) exp 2 2

y x

x y x y

P x y Ixyz μ μ

πσ σ σ σ

    − −     = −+  

     

(4-2) 

P is the total beam power, σx and σy are 1⁄2 of the exp(-2) beam diameter along the x

and y directions, μx and μy the coordinates of the beam centroid. The beam centroid 

locations are a function of z; 
73 

tan x μ α = ⋅ z (4-3) 

where α is the angle between the direction of the beam and the z axis; = 0 μ y for all 

three beams because the beams are coplanar. The variation of the beam diameters 

with z are approximated by the Gaussian beam relation: [130] 

1/2

2

0 2 1

R

z

z

σ σ

 

= +    

(4-4) 

where σ0 is 1⁄2 of the exp(-2) beam width at the focal plane and zR is the Rayleigh 

range. The parameters P, σx, σy, and α, are different for each beam. The length of the 

measurement volume is defined as the distance along z over which the signal goes 

from 5% to 95%. The integral is computed numerically on a grid of 50 × 50 × 100 

cells. (Doubling the number of grids points in each direction produces differences 

below 0.5% in the signal and measurement volume length.) 

Figure 4-4 shows two sets of plots of the CARS signal as a function of the axis ratio 

of the Nd:YAG beam. The continuous lines are for a full width at half maximum 

(FWHM) diameter of 50 microns for all the beams (except that the major diameter of 

the elliptical Nd:YAG beam is larger). The dashed lines are representative of the 

setup used for the experimental portion of this work: the FWHM are 40, and 100 and 

120 μm for the Nd:YAG, the narrowband and the broadband dye laser beams, 

respectively. For both cases, the angle α is 4.5, 4.3 and -0.18 degrees, for the 

broadband, the narrowband and the Nd:YAG beam respectively, conforming to phase 

matching requirements. The results are normalized by the CARS signal obtained for a 

round Nd:YAG beam, so that they are independent of the beam power. The CARS 

signal has been computed using two different assumptions: a fixed Nd:YAG laser 
74 

energy (and therefore its irradiance decreasing linearly with the axis ratio), or fixed 

irradiance (assuming unlimited Nd:YAG laser energy can be used). These are 

indicated by the red and blue curves in Figure 4-4. If the laser energy is kept constant 

the CARS signal drops when increasing the axis ratio, but less than linearly because 

of the Gaussian shape of the beams. If the laser irradiance is kept constant, then the 

signal increases by 19% for the 10:1 ratio. The results shown in Figure 4-4 are almost 

independent of the beam crossing angle and are only weakly dependent on the beam 

diameter if the diameter is equal for all the beams. The curves differ in the case of 

unequal beam diameters (dashed lines). As a consequence of the larger beam 

diameter for the two dye lasers, the signal strength decreases more slowly with 

increasing the axis ratio for the cases of constant energy. When keeping the peak 

irradiance constant the difference is even larger, with a signal for a 5:1 axis ratio that 

is 76% higher than the signal obtained for a round beam. The red dots in the figure 

are experimental results, and agree with the expected theory to within 2%. The length 

Figure 4-4: Normalized CARS signal as function of the axis ratio of the Nd:YAG beam.

Results are normalized dividing by the values obtained for round beam. Red dots are 

experimental results
75 

of the probe volume is independent of the axis ratio. Figure 4-4 shows that using the 

elliptical beam, in the case of available Nd:YAG laser energy, will cause an increase 

in signal compared to the conventional arrangement. This arrangement defends 

against beam steering and vibration while maintaining the same probe volume size as 

a conventional planar BOXCARS configuration. 

The numerical results allowed characterizing the effect of the beam shaping on 

CARS signal for perfect beam overlap, providing a baseline for the behavior in the 

presence of beam steering that is investigated both experimentally and numerically in 

the next sections. 

4.4 Experimental Results

4.4.1 Experimental Set-Up 

The beam steering mitigation technique has been tested using the dual-pump 

CARS system described in Chapter 3. For the test described here, the beams are 

focused by two 25 mm diameter, 600 mm focal length spherical lenses, one for the 

superimposed dye laser beams, and the other for the Nd:YAG beam. The half-wave 

plate and polarizer on the path of the Nd:YAG beam (see Figure (3-2)) are here used 

to tune the power of the Nd:YAG beam. This feature is used to avoid optical 

breakdown when a round beam is used and to maintain constant beam peak irradiance 

when the axis diameter ratio is modified. With a round beam the Nd:YAG beam 

energy is limited by laser induced breakdown to 68 mJ, therefore up to a 4:1 ratio is 

possible with this system while keeping the peak irradiance constant. The energies of 

the broadband and narrowband laser beams at the measurement volume are 
76 

approximately 20 mJ and 50 mJ, respectively. The beam viewing system placed after 

the measurement volume (see Figure (3-3)) is used to image the beams at the focal 

plane, measure their size and their relative distance.

Elliptical beam shaping is easily achieved by rotating the focusing lens of the 

Nd:YAG beam. When the direction of the beam is not parallel to the lens axis, 

astigmatism occurs; therefore the “in-plane” (horizontal) and “out-of-plane” (vertical) 

foci occur at different locations along the path. Figure 4-5 shows pictures of a crosssection of the Nd:YAG beam taken at the “in-plane” focus for several rotation angles 

of the lens and Figure 4-6 shows the “in-plane” and “out-of-plane” FWHM diameter 

Figure 4-5: Images of the Nd:YAG pump beam at the “in-plane” focus, for different lens 

rotation angle. The numbers are the axis ratios
77 

of the beam as function of the lens angle. Rotating the lens the “in-plane” beam 

diameter (minor axis of the ellipse) at the focus stays constant and the “out-of-plane”

beam diameter at the “in-plane” focus (major axis) increases exponentially. Small 

angles are sufficient to obtain a large axis ratio. 

In this set-up the spherical lens used to focus the Nd:YAG beam is mounted on a 

rotation stage with axis of rotation orthogonal to the plane of the beams. The lens is 

mounted in a translation stage to shift the “in-plane” focus of the Nd:YAG beam 

along the beam axis to the focus of the dye lasers, where all three beams are crossed. 

With this setup, the axis ratio of the beam can be varied continuously and no 

additional lenses are required. Additional cylindrical lenses instead of a rotated 

spherical lens could have alternately been used to achieve a similar effect, but 

additional optics increase the complexity of the system and introduce beam energy 

losses.

Figure 4-6: FWHM diameter of the Nd:YAG pump beam at the “in-plane” focus, as 

function of the lens rotation angle
78 

4.4.2 Beam Displacement Experiment 

Two experiments have been performed to characterize the efficacy of this 

approach. In the first experiment the two superimposed beams are intentionally 

misaligned using adjustments on the last mirror before the focusing lens. The 

displacement is monitored through the beam viewing system. The dimensionless 

coefficient (BD) quantifies the displacement of the beam. It is defined as: 

( ) , , x y

x y

l l

BD BD BD

r r

  = =    

(4-5) 

where r is the narrowband dye laser FWHM measured at its focal plane, l is the 

average distance between the centroids of the dye lasers and Nd:YAG beams at the 

focal plane, and the subscript x or y indicates displacement “in-plane” or “out-ofplane” , respectively. In the experiments presented in this work, the narrowband dye 

laser has an “in-plane” FWHM smaller than the broadband dye laser, but larger than 

the Nd:YAG. Since the two dye lasers are overlapped, the CARS signal strength is 

determined by the overlap between the Nd:YAG laser and the narrowband dye laser 

(i.e. the smallest of the two overlapped dye lasers). The choice of normalizing the 

beam displacement by the FWHM of the narrowband dye laser was arbitrary, and 

alternatively the FWHM of the Nd:YAG laser could have been used. 
79 

The goal is to design a system to provide a useful CARS signal even in flows with 

large BD. The BD is determined experimentally using the beam viewing system (see 

Chapter 3). Three axis ratios of the Nd:YAG beam at the “in-plane” focus have been 

considered for this experiment: 1:1, 2.6:1 and 10:1. Figure 4-7 shows images of all 

three beams obtained with the beam viewing system for these three axis ratios; note 

that the Nd:YAG and the overlapped dye lasers have been intentionally separated to 

make them distinguishable The “in-plane” FWHM are 40, and 100 and 120 microns, 

for the Nd:YAG, the narrowband, and the broadband laser, respectively. 

Figure 4-7: Three images of the beams at the focal plane, with circular and elliptical 

configurations of the Nd:YAG
80 

With the round Nd:YAG beam in a fixed location, the superimposed dye lasers 

were moved back and forth “in-plane” and then back and forth “out-of-plane” (see 

Figure 4-2 and Figure 4-3). Ambient air spectra were collected at each position. The 

area under each collected spectrum was integrated to obtain the signal. The 

normalized signal is the signal averaged over 1000 shots, divided by the peak average 

signal which occurs at BD = 0. The normalized signal plotted as a function of beam 

displacement, for the case of all round beams, is shown in Figure 4-8. Movement “inplane” shifts the crossing point, so the beams are no longer crossing at the focal 

plane. The curve has a flat top because the beams stay focused for a distance and then 

the curve slowly drops as the beam diameters at the intersection increase and 

irradiances decrease. Movement “out-of-plane” causes a rapid drop in the signal level 

because the beams no longer overlap. Where a displacement of 4 BD “in-plane” 

Figure 4-8: Sensitivity of the CARS signal to displacement of the overlapped dye lasers 

relative to the Nd:YAG beam; signal normalized by the peak signal, displacement 

expressed in narrowband dye laser diameters. Solid lines are a Gaussian fit
81 

decreases the signal level by less than 10%, a displacement of 1 BD “out-of-plane” is 

sufficient to drop the energy to one third. The data follow a Gaussian curve with a 

FWHM of 1.3 BD. 

The effects of “out-of-plane” displacement with elliptical Nd:YAG beams of three 

different axis ratios but the same power are shown in Figure 4-9. For beams crossing 

at the focal plane (BDy = 0), the signal with the elliptical beam is 60% (2.6:1 ratio) 

and 17% (10:1 ratio) of the signal achieved with a round beam, because of the 

decreased irradiance at the focal plane. The values are in agreement with numerical 

calculations (61% and 18% as shown in Figure 4-4). The FWHM of the Gaussian fit 

to the data is 1.3 BD for the round beam, increases to 2.2 BD when using a 2.6 axis 

ratio, and to 3.8 BD for the 10:1 ratio. This is evidence of the effectiveness of this 

Figure 4-9: Sensitivity to “out-of-plane” beam displacement for round and elliptical 

Nd:YAG beam; signal normalized by dividing by the peak signal for round Nd:YAG 

beam. Solid lines are a Gaussian fit
82 

strategy to defend against beam displacement. The plot suggests that in the presence 

of severe beam steering, an elliptical beam can produce a stronger signal than a round 

beam. For |BDy | > 0.7, the 2.6 axis ratio beam produces a stronger signal than a 

round, where a 10:1 axis ratio becomes more efficient for |BDy | > 2. 

Figure 4-10 shows the same data points of Figure 4-9, normalized by the peak 

signal for that axis ratio. This applies to a situation where the power of the Nd:YAG 

beam is changed to keep the peak irradiance constant as the axis ratio is changed. 

With the current configuration the irradiance is limited by breakdown, and only 25% 

of the available Nd:YAG energy could be used when the beam is round. 

Figure 4-11 shows the CARS signal obtained with simultaneous “in-plane” and 

“out-of-plane” displacement, when using an elliptical Nd:YAG beam with a 5:1 axis 

Figure 4-10: Sensitivity to “out-of-plane” displacement for round and elliptical Nd:YAG 

beam; signal normalized by the peak signal. Solid lines are a Gaussian fit
83 

ratio. Each curve was obtained by varying the “out-of-plane” displacement BDy for a 

fixed amount of “in-plane” displacement BDx. The signal is normalized by the signal 

when the beams are crossed at the focal plane (BDx = BDy = 0). Figure 4-11 shows 

that, for BDx < 0, the signal is weaker but less sensitive to “out-of-plane” 

displacements. Unexpectedly, for BDx > 0 the signal is stronger but more sensitive to 

“out-of-plane” motion. Notably, this behavior is also predicted by the theory.

Figure 4-12 helps explain this behaviour. “In-plane” displacement shifts the 

crossing point away from the focal plane (the location of the narrowband, broadband 

and Nd:YAG laser “in-plane” foci). Figure 4-12 shows pictures of the Nd:YAG beam 

at the crossing plane, for the same values of “in-plane” displacement as plotted in 

Figure 4-11. Negative values of BDx shift the crossing point toward the focusing lens, 

Figure 4-11: Sensitivity to combined “out-of-plane” and “in-plane” displacement for an 

elliptical Nd:YAG beam. Solid lines are a Gaussian fit
84 

therefore there is a small increase in the Nd:YAG beam major axis and an increase in 

the Nd:YAG minor axis and in the dye lasers diameters. Larger beam waists produce 

a weaker CARS signal that is less sensitive to “out-of-plane” beam displacement as 

shown in Figure 4-11. Positive “in-plane” displacement moves the crossing point 

toward the “out-of-plane” focus, therefore the major axis decreases and the minor 

axis increases. For BDx > 0 the CARS signal is stronger, because of the increased 

irradiance of the Nd:YAG beam, but is more sensitive to “out-of-plane” displacement 

because of the reduced size of the Nd:YAG beam in the “out-of-plane” directions. 

These effects do not compromise the usefulness of beam shaping. 

The results presented above depend quantitatively on the diameters of the beams 

though the trends remain the same as diameters are changed. Figure 4-13 shows 

results obtained for the round beam and the 8:1 elliptical beam when the beam waist 

FWHM are 50, 60 and 120 microns for the Nd:YAG (“in-plane”), the narrowband 

and the broadband lasers, respectively. (Recall that in Figure 4-10, the beam 

diameters were 40, and 100 and 120 microns, respectively.) The FWHM of the 

Figure 4-12: Nd:YAG beam at the location of the beam crossing where the crossing 

point is moved by “in-plane” displacement
85 

Gaussian fit to the data in Figure 4-13 is1.42 BD for the round beam and it is 8.1 BD

for the elliptical beam. The increase in the width of the fit for the elliptical beam is 

associated with the smaller radius of the narrowband dye laser beam, r, used in the 

normalization to compute BD. Using small diameter Nd:YAG and narrowband dye 

laser beams without beam shaping make the conventional geometry very susceptible 

to beam steering, while using the elliptical beam makes the setup much more robust. 

The dotted lines in Figure 4-13 are results obtained numerically using the 

algorithm introduced in the previous section, and assuming 

μ y y = BD r (4-6) 

Figure 4-13: Sensitivity to “out-of-plane” displacement for round and elliptical Nd:YAG 

beam. The signal is normalized dividing by the peak signal. Continuous curves are 

Gaussian fits; dotted curves are obtained by numerical simulation
86 

for the dye lasers centroids. The numerical results predict a FWHM of 1.37 BD for 

the round beam (in agreement with the Gaussian fit to the experiment), and 7.1 BD

for the elliptical beam (12% narrower). The validated numerical algorithm can be 

used to estimate the normalized CARS signal for any combination of “out-of-plane” 

beam displacement, beam diameters and Nd:YAG beam axis ratio.

The beam displacement experiment provides quantitative results which 

prove that the technique makes the CARS signal more insensitive to misalignment. 

The results can be used as guidelines to select an optimum axis ratio for the Nd:YAG 

beam in the presence of beam steering. 

4.4.3 Turbulence Effects Experiment

Beam refraction caused by turbulence in variable density flows is a more complex 

problem than displacement due to vibrations. Two effects generally coexist: beam 

wandering and beam spreading. In these flows, density, and therefore index of 

refraction is not uniform either in space or time. Turbulent structures smaller than the 

beam refract some parts of the beam differently than others, increasing the beam 

diameter at the focus and making the beam irradiance profile more chaotic. Larger 

turbulent structures are responsible for the random wandering of the beam. Severe 

refraction effects are generally observed in large supersonic free jets [72] or the 

exhaust of jet engines [131], and high-pressure combustors [121, 122] because of 

long beam paths, large density gradients and high levels of turbulence. Replicating 

such flows in the laboratory was not feasible so only their effects on the beams are 

simulated. Variations in the index of refraction can be obtained through changes 
87 

either in pressure, temperature or gas composition. Helium has a very low refractive 

index in comparison to air; the difference in index of refraction between helium and 

air is roughly the same as the difference between air at 2300 K and room temperature 

air. 

Turbulent effects were obtained through the device shown in Figure 4-14. A flow 

of 107 SLPM of helium enters a 25 mm internal diameter, “T” shaped pipe fitting, 

then bifurcates, generating two jets of helium. The two dye laser beams pass through 

the fitting. The Nd:YAG beam passes below the fitting and therefore it is only 

slightly affected by the flow. The device is placed 5 meters before the focusing lens. 

For this experiment the beam FWHM’s at the measurement volume were 50, 60 and 

120 μm for the Nd:YAG, narrowband and broadband lasers, respectively.

Figure 4-15 a) shows the narrowband dye laser centroid position normalized by its

FWHM at the focal plane for 100 shots with and without the jet. The standard 

deviation of BDy is 0.09 without the jet, 1.24 with the jet. Figure 4-15 b) shows single 

Figure 4-14: Schematic of the helium jet used to generate beam steering
88 

shots images of the yellow beam at the focal plane. The image in the upper left corner 

was obtained without the jet, the others with the jet. The steering of the beam is 

clearly visible in this set of pictures, as well as the spreading effect due to turbulence. 

The beam is generally larger and the irradiance distribution is chaotic. The Nd:YAG

beam does not pass through the pipe fitting and is only slightly affected by the helium 

jet; with no jet the standard deviation of BDy is 0.2, and with the helium jet is 0.35 for 

the Nd:YAG beam. Displacements of the Nd:YAG beam cannot be neglected. 
89 

Figure 4-15: a) Centroid position of the narrowband dye laser with and without the 

turbulent helium jet; b) Images of the narrowband dye laser at the focal plane. The 

image on the left, upper corner is obtained without the helium jet
90 

Five hundred ambient air spectra were collected with and without the helium jet 

for three axis ratios and the signal level evaluated as in the previous experiment. 

Figure 4-16 shows histograms of the signal level for the round and two elliptical 

beams without the helium jet. The irradiance of the Nd:YAG beam was tuned so that 

approximately the same signal level was obtained with the elliptical and the round 

beam. Signal levels are normalized by their average value. The use of the elliptical 

beam makes the CARS signal more stable even with the Helium jet turned off: The 

standard deviation of the signal level distribution is 11% of the average signal for the 

elliptical beam of axis ratio 8:1, is 15% for a 4.5:1 axis ratio and 24% for the round 

Figure 4-16: Histograms of the CARS signal for various axis ratios without the helium 

jet
91 

beam, and for a round beam the histogram is no longer symmetric. The increase in the 

standard deviation is caused by beam steering. In fact the beams are aligned for 

optimum overlap, thus any beam steering can only lower the signal generating an 

asymmetry in the distribution. 

CARS signal intensity is proportional to the product of the power of the three 

laser beams. Relative power fluctuations measurements for each laser were obtained 

by sending a small portion of the beam to a detector. Five hundred pulses for each 

beam were collected and analyzed. Measurements for each beam were not 

simultaneous. Since the Nd:YAG beam energy is a fixed fraction of the beams that 

pump the two dye lasers, some correlation in the power of the three beams is 

expected. To estimate the effect of the laser energy fluctuations on the CARS signal 

Figure 4-17: Comparison between the histograms of the CARS signal and the products 

of the laser intensities
92 

the product of the three laser powers is evaluated in the two limit cases of full and no 

correlation. Physically full correlation implies that the fluctuation in the dye lasers are 

due exclusively to fluctuations in the pumping beam, no correlations assumes that 

factors other than the pump energy are predominant. The standard deviation of the 

product of the three laser powers is 11% of the average for no correlation and 18% for 

perfect correlation. Figure 4-17 compares the histogram of CARS signal obtained 

with an 8:1 axis ratio beam to the histograms of the product of laser intensities in the 

two limit cases. The CARS signal histogram lies within the two limit cases suggesting 

that for the 8:1 ratio the fluctuations are due mostly to power fluctuations, and not to 

beam steering. On the other hand, the round-beam results from Figure 4-16 show a 

much larger standard deviation (24% of the average) and cannot be attributed to

pulse-to-pulse variations in laser intensity. 

Figure 4-18 shows the results obtained with the helium jet flowing. CARS signal 

level is normalized dividing by the average signal level when the jet is off. The 

average signal increases with the increase in axis ratio, going from 8.2% for the round 

beam, to 20% for the 5:1 ratio, and 27% for the 8:1 ratio. The signal level distribution 

is broader for the elliptical beams; the standard deviations are 0.064, 0.126 and 0.129 

for the round, 4.5:1 and 8:1 cases, respectively. More importantly, the signal standard 

deviations as a fraction of the mean decrease with elliptical beams, indicating a more 

steady and repeatable signal level. The change in the shape of the distributions as the 

ellipticity increases resembles the change in shape of a Poisson distribution as the 

number of samples is increased: for large ellipticity the distribution becomes more 
93 

Gaussian and the number of CARS spectra having very low counts becoming 

vanishingly small.

One of the major problems caused by beam steering is low data yield. [66, 120, 

122] When the signal-to-noise ratio is too low, data have to be rejected. Assuming as 

0.1 the threshold below which the data for this experiment are rejected, the data yield 

would be 30 % for the round beam, 76% for the 4.5:1, and 94% for the 8:1 ratio. The 

threshold chosen is completely arbitrary, but shows the effectiveness of the beam 

shaping technique in increasing the data yield. 

Figure 4-18: Histograms of the CARS signal for various axis ratios with the helium jet
94 

4.5 Modeling the Effects of Beam Spreading

In the presence of the helium jet, laser power fluctuations, beam steering, and 

beam spreading affect the CARS signal level producing the histograms of Figure 

4-18. Based on the experimental data collected, the effects on the CARS signal of the 

power fluctuations and of the beam wandering can be modeled, so that the effect of 

the beam spreading can be isolated. In an ideal case, where none of these 

perturbations are present, relative signal level would be constant and equal to 1. In the 

presence of power fluctuations, based on the results shown in Figure 4-16 and Figure 

4-17, the CARS signal level has a Gaussian distribution with average 1 and standard 

deviation 0.11. According to the results of the beam displacement experiment (Figure 

4-13), the relative signal level SCARS, in the presence of the beam steering, can be 

expressed as a Gaussian function in BDy with standard deviation σe, (equal to 

FWHM/2.35), of 0.6 for the round beam, 3.44 for the 8:1 axis ratio elliptical beam. 

When both beam steering and power fluctuations are present, the relative signal level 

can be expressed as: 

2

3 2 exp 2

y

CARS P

e

BD

S F

σ

  =⋅ −     

(4-7) 

FP3 takes into account the effect of the random power fluctuation and BDy, the beam 

displacement in the “out-of-plane” direction. FP3 and BDy are normal random 

variables: FP3 ∼ N(1, 0.11), and BDy ∼ N(0, 1.24). Means and standard deviations of 

the Gaussian distributions are obtained from experimental results discussed in the 

previous section. The function N(μ, σ) indicates a generic random variable with 

Gaussian distribution of mean μ and standard deviation σ. Beam displacement in the x
95 

direction (“in-plane”) is neglected. A numerical experiment has been performed 

giving as input to Eq. (4-7) five hundred values of P3 and BDy extracted randomly 

from their respective distributions. The results are representative of what would have 

been obtained experimentally if the beam spreading effect was negligible. 

Figure 4-19 shows histograms of the numerical results. For the round beam the 

average normalized signal is 0.43, its standard deviation 0.38, and 32% of the values 

are below 0.1. For the elliptical beam the average is 0.93, standard deviation 0.14, and 

the signal is always above 0.1. However the average values are lower in the 

Figure 4-19: Histograms of the CARS signal computed with the helium jet, neglecting 

beam spreading
96 

experimental results (Figure 4-18) because the spreading makes the beam diameter 

larger at the focal plane. The reduction of the irradiances of the beams causes a 

clustering of the data in the lower bins. However the increased size of the beams 

makes the signal less sensitive to the beam steering. When using a round beam, these 

two effects combined produce a lower standard deviation relative to the mean in the 

experimental data than in the computed values. 

Beam spreading can be added to the numerical model to simulate the effect of the 

turbulent helium jet on CARS signal. For each beam a spreading coefficient is 

defined as the ratio of the beam diameters with and without the turbulent jet flowing 

( )

( ) ( )

, ,

turbulent turbulent

x y

x y

x y

D DD σ σ

σ σ

  = =  

 

(4-8) 

Average and standard deviation of the spreading coefficient were evaluated from 

focal plane images of fifty single shots of the yellow beam taken with the turbulent jet 

flowing (similar to what shown in Figure 4-15 b). From these measurements the D of 

the narrowband lasers have a normal distribution: Dx ~ N(1.53, 0.27) and Dy ~ N(2.86, 

1.03). The same distribution is used for the broadband. In the presence of beam 

spreading, beam steering and power fluctuations the CARS signal level can be 

estimated as 

CARS P CARS 3 S FP = ⋅ (4-9) 

PCARS is evaluated from Eq.(4-1) using the algorithm previously described in this 

paper. The irradiance of the narrowband and broadband beam is given by Eq. (4-2) 

but the parameters μ and σ are modified by beam wandering and spreading 

respectively: 
97 

( , ) (tan( ) , ) μμ α x y = −⋅ ⋅ BD r BD r x y (4-10) 

( )( ) ( , )( , ) turbulent turbulent σ σ σσ x y =⋅ ⋅ D D xxyy (4-11) 

FP3, BDx, BDy, Dx, and Dy are normal random variables with mean and standard 

deviations evaluated experimentally. 

A numerical experiment has been performed, evaluating the CARS signal level 

for five hundred values of the random variables above. Figure 4-20 compares the 

numerical results to the experimental results. The numerical simulation predicts an 

average signal of 0.1 for the round beam, and 0.28 for the elliptical beam, only 

slightly higher than the measured 0.08 and 0.26. The standard deviations obtained 

Figure 4-20: Histograms of the CARS signal with the helium jet from experiments and 

numerical simulations including beam spreading
98 

numerically are 0.11 and 0.16, compared to 0.06 and 0.13 experimentally. The 

discrepancy between the numerical and experimental results is consequence of the 

simplifying assumptions in the modeling, but the agreement is surprisingly good 

given the complexity of the problem. The validated numerical model can be used to 

predict the CARS signal level distribution, for any given beam steering conditions 

and beam diameters, and therefore determine the optimal axis ratio for given 

experimental conditions. 
99 

CHAPTER 5 -High Irradiance Perturbation Effects 

5.1 Introduction

The CARS signal amplitude is proportional to the product of the beam irradiances 

and to the square of the probe volume length. However it is highly desirable to reduce 

the length of the measurement volume so that smaller turbulence structures can be 

resolved. The measurement volume size can be reduced by using shorter focal length 

lenses to focus the beams to a smaller diameter and shorter crossing length, for 

example. Sensitivity of CARS spectra to Stark broadening and saturation is strictly 

intertwined with the spatial resolution. Generally, CARS spatial resolution for 

combustion measurements at atmospheric pressure is 1-2 mm long, typically 

insufficient to resolve the smallest turbulence structures. Focusing the beams more 

tightly, reduces the probe volume length, while maintaining a good signal-to-noise 

ratio. Unfortunately focusing more tightly may cause optical breakdown, saturation or 

Stark broadening because of the increased irradiance.[79, 120, 132, 133] 

At low irradiances CARS is a non-intrusive technique and the collected spectral 

shapes are independent of the laser irradiance. At sufficiently large irradiances, the 

large electric field generated by the focused pulsed lasers induces a dipole moment in 

homonuclear molecules and causes a shift and a broadening of the transition line 

(Stark broadening). The magnitude of this effect is directly proportional to the electric 

field, and therefore to the sum of the irradiances of the three beams. Further 

increasing the electric field amplitude, the gas may “break down”, generating a spark 

and becoming ionized. 
100 

Large values of the product of the pump and Stokes irradiance can also cause 

stimulated Raman pumping (SRP), which is the process of changing the population 

distribution of the rotational and vibrational states being probed by the CARS 

process. This is a saturation mechanism and causes a reduction of the CARS signal in 

the ground vibrational band and an increase in higher vibrational bands. The effects 

of high irradiance perturbations on CARS measurements has been previously 

investigated, [132-135] but no systematic study of high irradiance perturbation effects 

in dual-pump CARS measurements of temperature and multiple species concentration 

was found in the literature. 

The goal of the study described in this chapter is to provide guidelines to discern 

the presence of such perturbations in experimental spectra, estimate their effects on 

measurement accuracy, and validate criteria to determine the threshold below which 

these effects are negligible. A background section provides a short review of previous 

theoretical and experimental works on saturation and Stark broadening. Simple 

theoretical models, previously proposed by other authors, are applied to the specific 

conditions of our dual-pump CARS system. It provides a framework to correctly 

interpret the changes in spectral shapes observed in the experimental CARS spectra, 

discussed later in the chapter. It also provides simple criteria to determine 

perturbation thresholds. Then, a results and discussion section describes experimental 

results obtained for several levels of irradiances in ambient air, fuel-lean and fuel-rich 

flames. This is the first systematic, experimental study investigating, the effect of 

high irradiance spectral perturbations on dual-pump (DP) CARS measurements of 

temperature and absolute concentration. The role of temperature in changing CARS 
101 

signal sensitivity to high irradiance effects is experimentally observed. Saturation and 

Stark broadening thresholds are determined and compared to the theoretical criteria.

5.2 Background 

Several research groups investigated the effects of Stark broadening and 

saturation on CARS spectral shape, both theoretically and experimentally. This 

section presents a brief review of the findings published in these works. The section is 

divided in two sub-sections, one dealing with Stark broadening, the other with 

saturation. In each subsection, first we describe the physics of the process, based on 

simple models introduced by other authors. Changes applied to the models specific to 

our dual-pump CARS instrument are discussed. Criteria to determine irradiance 

thresholds for a dual-pump CARS system are proposed. We also review some of the 

experimental work from previous authors, with emphasis on providing guidelines to 

identify the high irradiance effects in experimental spectra. The few available works 

dealing with the effects of Stark broadening and saturation on temperature and 

concentration measurements are reviewed. 

Optical breakdown has not been investigated experimentally for this work. Clean 

air breakdown threshold are ~ 350 GW/cm2

, [136] and values up to 1000 GW/cm2are 

anticipated in clean flames. [137] These values are higher than the Stark broadening 

and stimulated Raman pumping thresholds, therefore optical break down is not the 

liming factor in setting the laser irradiances. Threshold values in practical 

applications are much lower because of the presence of dust or large particles in the 

gas. Occasional breakdowns, occurring when the lasers hit these large particles, are 
102 

allowed for, and are removed in pre-processing. In the presence of breakdown the 

CARS signal is completely destroyed; therefore the occasional breakdowns can be 

easily identified and removed during the data pre-processing. Less than 5% of the 

spectra collected in room temperature air present optical breakdown. This percentage 

is much lower in flames, and the overall percentage of breakdown spectra is less than 

0.3 % of the total for the data set discussed in Chapter 8. 

5.2.1 Stark Broadening

To generate the CARS signal, three pulsed laser beams are crossed at the common

focal spot, generating a strong electric field. For molecules having no permanent 

dipole (such as N2, O2 and H2), the electric field induces a small dipole moment,

proportional to the electric field itself. [88] The electric field interacts with the 

induced dipole, changing the energy level of each state by an amount proportional to 

the irradiance (quadratic Stark effect). The dipole moment is a function of the 

rotational and the orientational (magnetic) quantum number; it also depends on the 

vibrational quantum number through the polarizability tensor. The change in the 

energy levels, induced by the Stark effect, causes a shift of the Raman transitions to 

lower frequencies. Because of the dependency of the dipole moment on the magnetic 

quantum number, the orientational degeneracy is lifted and line splitting occurs in the 

presence of a strong electric field. For S-branch transitions, the frequency Stark shift 

of each energy sublevel can be expressed as: [138], [139] 

( ) ( )

2 2

, ,

, ',

3 '( ' 1) 3 ( 1)

3 2 ' 1 (2 ' 3) 1 2 )

1

2 (3

v j m v Total

vjm v

m j j m jj

hc j

I

j jj ν γ

    − + −+ ∆ =     − − + −+    

(5-1) 
103 

where ITotal is the total irradiance defined as the sum of the average irradiances of all 

the beams present; γ is the anisotropic part of the polarizability tensor; v, j, and m are 

the vibrational, rotational and magnetic (orientational) quantum numbers of the lower 

state of the transition; v’, j’, m’ are the quantum numbers of the upper state of the 

transition. S-branch transitions are characterized by Δv = 0 and Δj = 2. Equation (5-1) 

is valid when the polarizations of all lasers are parallel, for which only transitions 

with Δm=0 are allowed. The magnetic quantum number m can assume values 

between –j and j, and appears squared in the equation above. The electric field splits a 

given transition into j+1 sub-lines which are double degenerate, except for the one 

with m=0. The fractional strength, F, of a sub-level is defined as the ratio of its 

intensity to the sum of the intensity of all sub-lines in a given transition. For S-branch 

transitions, it can be computed as: 

( )

( ) ( ) ( ) ( )

2 2 22

,

2,

2 ( 1) 15

2 1 2 2 1 2 3 (2 5)

j m

j m

j ml m

F

jj j j j +

  + − +−      = ++ + + +

(5-2) 

In broadband CARS the spectral resolution is not sufficient to resolve the 

splitting, thus the lifting of the orientational degeneracy causes a broadening of the 

line. For Q-branch transitions, expressions for the Stark shift and the fractional 

strength can be found in Ref. [138]. 

The Stark effect strongly perturbs the spectral shape of the Raman transitions, 

causing a shift and a broadening of the lines. Stark perturbations have been observed 

in Raman spectra of all the molecules of interest for this work (O2, N2, and H2). Rahn 

[140] observed a shift of 0.12 cm-1 in the H2 S(3) line when applying 200 mJ of 

infrared (IR) light focused to a 80 μm focal spot. Splitting of the S(2) and S(6) pure 
104 

rotational lines of N2 were observed by Farrow. [139] Dyer [141] measured Stark 

shift and splitting for the Q(0) and Q(1) H2 lines. Owyoung [142] reported Stark shift 

and splitting for the pure rotational transitions of O2. In the Q-branch rotationalvibrational manifold the transitions are not isolated lines. Each line interacts with its 

neighboring lines through constructive interference, affecting the amplitude and the 

line shape of the transitions and reducing the peak-to-valley ratios. [140] 

In all the works listed above, an intense IR laser beam superimposed on the 

Raman spectra generating beams provided the strong electric field that generated the 

Stark effect. The focal waist and the pulse length of the IR beam were twice or more 

the size of the other beams, so that the electric field producing the Stark shift was 

spatially and temporally uniform. In more typical CARS applications, where this 

extra laser beam is absent, the total irradiance is not constant in the region where the 

CARS signal is generated, either in space, or time, leading to asymmetrical 

broadening of the rotational-vibrational lines. Moosmuller [138] investigated Stark 

broadening of N2 Q-branch CSRS spectra in a collinear phase matching 

configuration. [87] In a collinear geometry, a significant portion of the signal is 

generated in low irradiance regions where the Stark effect is negligible. Therefore the 

overall Stark broadening is smaller than in the more typical crossed beam geometry 

where the signal generation is confined to a relatively high irradiance region. Herring 

[143] observed that in a crossed beam geometry, with crossing angles above one 

degree, the Stark broadening is doubled as compared to a collinear geometry. 

Detailed models that integrate the Stark broadening into the computation of the 

CARS susceptibility have been proposed [132, 143, 144] but are computationally 
105 

intensive and require a good knowledge of the distribution of the irradiance over the 

entire measurement volume. Fluctuations in the laser power, vibrations, and beam 

steering effects in real world environments prevent a good knowledge of the 

irradiance distribution over the entire CARS probe volume, limiting such models to 

very controlled environments. 

CARS concentration and temperature measurements are typically obtained by 

fitting an experimental spectrum to a theoretical one. Since Stark effects are generally 

not included in the theoretical model, large electric fields can compromise the 

accuracy of the measurements. CARS fitting codes can generally fit experimental 

spectra containing Stark broadening to theoretical models that do not include these 

effects, [132, 135] but the fitted temperature and concentration may be inaccurate.

Vibrational temperature measurements obtained this way are not very sensitive to 

Stark broadening since the mechanism acts on all the vibrational levels in a similar 

way, although errors of 20-30 K in temperature have been observed at subatmospheric pressure. [132] Rotational temperature obtained from isolated lines, such 

as the H2 S transitions considered in this study, are affected because of the j

dependence of the Stark shift. 

Measurements of the ratio of mole fractions of O2 to N2 are not sensitive to Stark 

broadening because the broadening effects on the Q-branch of these species are 

similar. The effect of Stark broadening on the isolated H2 lines is different than on the 

N2 Q-branch manifold, making the measurements of the ratio of H2 to N2 sensitive to 

the total irradiance, as will be shown later in this chapter. Absolute mole fraction 

accuracy is compromised by Stark effects because the broadening reduces the 
106 

amplitude of the resonant lines, but leaves the non-resonant baseline unperturbed. 

[135] Since Stark broadening compromises the measurement accuracy, it is critical to 

maintain the total irradiance sufficiently low that its effects are negligible. A crude 

criterion to determine if Stark broadening is significant is to compare the average 

Stark shift to the Raman transition linewidth (full-width at half maximum, FWHM), 

ΓR. For

∆ <Γ ν Stark R (5-3) 

Stark broadening can be neglected. A similar approach was proposed by Péalat. [144-

146] This criterion uses the average Stark shift, computed using a simple algebraic 

formula given in Eq. (5-4), as a rough index of the Stark broadening. 

, ,,

', ' ',

j

jm v jm

Stark j m v j m

m j

ν ν F =−∆= ∆ ∑ (5-4) 

Figure 1a shows the variation of the Voigt linewidth (FWHM) of the N2 Q(5) 

transition with temperature, computed using CARSFT [108] with negligible 

instrument linewidth. Figure 1b shows the average Stark shift (Eq. 5-4) for the N2

Q(5) line against the total irradiance. 
107 

The values of the fractional strength and Stark shift for each sublevel of the N2 Q(5) 

transition are taken from Ref. [138]. It turns out that the average Stark shift is only a 

weak function of the rotational quantum number, so the Q(5) line is representative of 

the whole first vibrational band. Through a simple graphical procedure, the plots in 

Figure 5-1 allow for the determination of the Stark broadening total irradiance 

threshold for a given temperature. The graphical procedure is as follows: locate on the 

horizontal axis in Figure 5-1 a) the given temperature and draw a vertical line to find 

the intersection with the linewidth curve; the ordinate of the intersection is the 

computed linewidth. From the intersection draw a horizontal line that intersects the 

estimated Stark shift line in the plot of Figure 5-1 b). The abscissa of the intersection 

is the total irradiance threshold below which Stark broadening is avoided, according 

Figure 5-1: a) Voigt (continuous) and collision broadened (dashed) N2 Q(5) linewidth 

(FWHM) as function of temperature; b) Estimated Stark shift as function of the total 

irradiance
108 

to the criterion of Eq. (5-3). It may be concluded from Figure 5-1 that increasing 

temperature reduces the N2 linewidth, and therefore Stark broadening is a more 

serious limitation for high-temperature environments. Experimental results, discussed 

later in this chapter, show that the simple criterion can correctly predict the presence 

of Stark broadening in N2 spectra. N2 and O2 have similar molecular parameters; 

therefore it would be expected that the Stark broadening perturbs those molecules in a 

similar way. 

Figure 5-2 a) shows the variation of the collision-broadened and the Galatry 

linewidth (FWHM) of the H2 S(5), S(6) and S(9) transitions at atmospheric pressure 

with temperature. Figure 5-2 b) shows the estimated Stark Shift for the three lines 

with total irradiance. The estimated Stark shift is computed using Eq. (5-1) and Eq. 

Figure 5-2:a) Collision-broadened and Galatry linewidth (FWHM) for three H2 rotational 

lines as function of temperature; b) Estimated Stark shift as function of the total 

irradiance
109 

(5-2) using a polarizability anisotropy γ [147] of 7.1×10-25 cm3

. The same graphical 

procedure described for Figure 5-1 can be used to determine the Stark broadening 

threshold for the H2 lines. For total irradiances between less than 450 GW/cm2 the 

criterion predicts no Stark broadening, if the Galatry model is used to compute the 

Raman linewidth ΓR. This is in contrast with the experimental observations as shown 

later in this chapter. 

The criterion to estimate the Stark broadening, presented in this section, is 

obtained from crude approximations of the physical mechanism involved. Stark 

broadening is a consequence of the lifting of the orientational degeneracy and of 

spatial and temporal non-uniformity of the electric field. Obviously this cannot be 

accurately modeled through the Stark shift alone. 

5.2.2 Stimulated Raman Pumping

When the product of pump and Stokes beams irradiance is sufficiently high, the 

number of transitions from the ground state to an excited state, by a process known as 

stimulated Raman pumping (SRP), becomes significant. [87] This process is a two 

photon process which occurs simultaneously with the CARS process and reduces the 

population difference between the ground and the excited state. The rate of change of 

population difference (slump rate) for monochromatic beams can be approximated 

by: [77, 148] 

( )

2

1

2 2 2

1 4 2

4

R

pS N

S R

N c I I

N t

π σ

τ

ω ω

−

∆

∂∆     ∂ Γ =     = ∆ ∂      ∂Ω ∆ +Γ

(5-5) 
110 

ΔN is the unperturbed population difference,   ∂σ

    ∂Ω the Raman cross section, IpIS the 

product of the pump and Stokes beam irradiances, and ΓR is the Raman linewidth; Δω

is a detuning factor given by ω-(ωp-ωs), where ω, ωp and ωs are the transition, the 

pump and the Stokes circular frequencies, respectively. The probe beam does not 

contribute to SRP. The CARS signal is proportional to the product of the three 

irradiances of the pump, probe and Stokes beams and to the square of the population 

difference. Stimulated Raman pumping is often referred to as saturation, because, 

when present, the CARS signal increases less than linearly with the irradiance. As the 

pump-Stokes irradiance product becomes large, the increase in signal caused by the 

higher irradiance and the decrease caused by SRP balance out and the CARS signal 

becomes a function of only the probe beam irradiance. The change in population is 

most intense at the resonance frequency (Δω=0) and rapidly decreases off resonance, 

causing the appearance of a dip at the centerline of saturated high resolution 

narrowband CARS spectra. This feature has been observed experimentally in both N2 

[149, 150] and H2 [151, 152] lines, and several detailed models have been developed 

to accurately predict it. [144, 153-155] Stimulated Raman pumping perturbs 

broadband CARS spectra in a very different way than narrowband CARS. In 

broadband CARS the dip is no longer observed because of the low spectral resolution, 

but the spectra are modified due to the change in population distribution. Broadband 

CARS of a Q-branch manifold allows simultaneous probing of the SRP induced 

population changes. For room temperature air spectra, only the ground vibrational 

state is thermally populated and CARS probes v=0→1 transitions; SRP pumps 

molecules to higher vibrational states, and vibrational transitions between higher 
111 

states appear in the CARS spectra. For example, SRP-induced population of three 

vibrational bands of N2 at room temperature was observed experimentally by 

Gierulsky. [134] 

Changes in the spectral shape of N2 and O2 Q-branch due to SRP result in errors 

in fitted parameters, such as temperature, concentration and pressure. At high 

temperature, higher vibrational states are populated, according to a Boltzmann 

distribution, causing the appearance of “hot bands”. SRP-induced population changes 

also cause the appearance of “hot bands”. A CARS fitting code will fit the “hot 

bands” to higher temperatures. A fitted vibrational temperature of 2550 K was 

reported by Gierulsky [134] for highly saturated room-temperature spectra. Groundstate rotational temperature is unaltered because SRP is similar for all the rotationalvibrational transitions. [134], [149] Similar effects on N2 vibrational temperature 

measurement were reported by Woodmansee [132] and by Kroll.[133] 

Stimulated Raman pumping, by altering the observed CARS transition 

amplitudes, causes errors in fitted mole fractions. Broadband dye lasers used in 

CARS are spectrally non-uniform, therefore SRP will be more intense for transitions 

pumped near the peak of the Stokes laser spectrum (which occurs for the O2 Q-branch 

in this set-up) and weaker for transitions pumped by the tails of the Stokes laser (N2

Q-branch and H2 S(5) in this set-up). Different species also have different Raman 

cross sections and linewidths, therefore effects on population may differ. In DPCARS, when the two pump beams have different irradiances, SRP will be different in 

molecules pumped by one or the other pump beam. Non-uniform SRP across the 

spectral range of Raman shift probed causes variations in the ratio of N2 and O2 mole 
112 

fraction, since the Stokes beam irradiance can differ by a factor or two or more for 

one molecule than the other. 

In broadband CARS, Eq. (5-5) is still valid as a crude estimate of the rate of 

change of population difference, but only a small portion of the Stokes irradiance 

contributes to the SRP process. Integrating Eq. (5-5) over the Raman linewidth ΓR, the 

rate of change in population difference can be expressed as: 

2

1

2

1 4 S

p N

S S

N c I I

N t

π σ β π τ

ω ω

−

∆

∂∆     ∂ =   =   ∆ ∂      ∂Ω ∆ (5-6) 

The group S

S

β I

∆ω

approximates the spectral irradiance of the Stokes beam at the 

transition frequency ωs. ∆ωs is the FWHM of the broadband dye laser. This approach, 

by Woodmansee [132], is modified by the coefficient β which is the ratio between the 

Stokes spectral irradiance at ωS and the peak Stokes spectral irradiance, which takes 

into account the spectral dependence of the Stokes beam. To prevent the loss of 

measurement accuracy caused by SRP, it is necessary to limit the product of the 

pump and Stokes beam irradiances. A simple criterion to determine the threshold can 

be derived from the simple theoretical model discussed above. Equation (5-6) is 

integrated to obtain the population difference as function of time: 

( )

( ) (0) N

t

Nt N e τ ∆

−

∆ =∆ (5-7) 

If the SRP characteristic time τΔN is much longer than the laser pulse length τ, then 

the change in the population difference is negligible. 

N τ τ ∆ >> (5-8) 
113 

Woodmansee estimated a threshold of 3600 GW2

/cm4 to prevent significant SRP in 

broadband N2 CARS for a 1900 GHz width of the Stokes laser and 10 ns pulses. The 

criterion was validated for ambient air temperature measurements, but no data were 

presented for concentration measurements. 

Wilson-Gordon [153] showed that Eq. (5-5) is mathematically accurate only for 

conditions where SRP is negligible, and is only a rough estimate otherwise. Pressure 

and molecular motion effects are neglected in the SRP model considered. By 

increasing pressure, collisional transfer out of the laser-pumped upper rotational 

levels becomes significant and reduces SRP effects. [155] Molecular motion may 

move the saturated molecules out of the measurement volume replacing them with 

unsaturated ones. This becomes significant when the transit time through the 

measurement volume is comparable to the pulse length, which is true for light 

molecules at high temperatures. [144] 

Because of these simplifications intrinsic to the Stark broadening and SRP 

threshold criteria, they need to be validated for dual-pump CARS for specific 

methods and test conditions. Experimental data are especially needed to validate the 

above criteria for concentration measurements since little information is available in 

the literature. The work described in this chapter attempts to fill this gap through a 

systematic, experimental study of the effect of varying irradiances on temperature, 

mole fractions, and the ratios of mole fractions of different species. This present 

validation is limited to dual-pump CARS measurements of temperature, N2, O2 and 

H2 mole fractions in quiescent air and H2-air flames at ambient pressure. 
114 

5.3 Experimental Set-up 

Details of the DP-CARS instrument used for the experimental portion of this 

work are in Chapter 3. Planar BOXCARS, having the narrowband and the broadband 

dye lasers overlapped, is the phase-matching geometry chosen for this instrument. 

Two distinct lenses focus the beams at the measurement volume. A 500 mm focal 

length lens focuses the Nd:YAG beam; the lens is tilted so that, it shapes the focal 

spot at the beam crossing to a roughly 4:1 axis ratio ellipse with the major axis 

orthogonal to the plane formed by the three laser beams (Chapter 4). Three 

interchangeable lenses of focal lengths 300, 500, and 850 mm are available to focus 

the two, overlapped dye lasers; this allows control of the energy density at the 

measurement volume. The beam viewing system (see Chapter 3) is used to image a 

cross section of the three beams in the vicinity of the measurement volume, and to 

measure the dimensions of the beams at their focus, needed to compute the 

irradiances. 

The maximum energy per pulse at the measurement volume for the Nd:YAG, the 

narrowband laser, and the broadband laser, are respectively: 90, 30, and 20 mJ. The 

beam irradiances at the measurement volume can be controlled by reducing beam 

energies and by selection of lens focal length. A larger spot size at the focus decreases 

the irradiance, but also increases the size of the measurement volume, allowing an 

increased signal at lower irradiances. Using a combination of these two mechanisms 

the total irradiances is varied in the 80-800 GW/cm2

 range and the pump-Stokes 

products in the 102

-105 GW2/cm4 range, while keeping sufficient signal-to-noise ratio 
115 

at flame temperatures. The irradiance reported in this work is the average irradiance 

computed as: 

2

E I

π τ r = (5-9) 

where E is the laser energy per pulse, r is the e-2 radius at the focus and τ the pulse 

length. The pulse length (FWHM) of the Nd:YAG, narrowband and broadband dye 

laser are 10, 6.5, and 5 ns respectively. They have been measured using a fast (<1 ns 

time response) photodiode connected to a 1 GHz oscilloscope. The focal spot 

dimensions are determined from images collected on the beam viewing system 

camera.

The other variables considered in this test are the temperature and composition of 

the flow probed. In addition to ambient air, a Hencken burner, producing a laminar, 

roughly homogeneous, nearly adiabatic H2-air flame, provides the test medium for 

this work (Chapter 6). Two equivalence ratios are considered: φ=0.3 to study effects 

on N2 and O2 and φ=2 to study effects on H2. For the fuel-lean case the adiabatic 

chemical equilibrium temperature is 1180 K. It would have been desirable to go to 

higher temperature where the perturbation effects may have been stronger, but the 

signal-to-noise ratio of the O2 signal would have been too low at irradiance levels low 

enough for this study. Results from three separate tests, differing in the focal length of 

the dye laser focusing lens, are presented. During each test, data were collected 

varying the energy of one beam while keeping the energy of the other two beams at 

their maximum value. The order of the acquisition was fully randomized. All spectra 

presented here are averaged over 250 single shots to reduce effects of the broadband 

dye laser noise. Measurements in the Hencken burner were always taken in the same 
116 

location, 40 mm from the base and on the center line, to avoid errors from nonuniformities in the flow. Air flow rates are 58.6 SLPM and 28 SLPM for the fuel-lean 

and fuel-rich cases, respectively. H2 flow rates are 7.4 and 23.5 SLPM, respectively. 

Accuracy of the flowmeters is 0.3 SLPM. 

5.4 Results and Discussion

The non-resonant background susceptibility is not perturbed by high irradiance 

effects. Spectra are normalized to the signal baseline level (in the non-resonant 

portions of the spectrum) to remove the direct dependence of the signal on the three 

laser irradiances, leaving only the Stark and SRP effects. By fitting the experimental 

spectra to a theoretical library, temperature and absolute concentration measurements 

are obtained. Sensitivity of the measurements to the high irradiance effects is 

discussed. Finally, experimental SRP and Stark broadening thresholds are obtained 

and compared to those predicted by the simple theoretical models presented in the 

previous section. 

Figure 5-3 a) shows spectra collected in ambient air for narrowband dye laser (pump2) irradiances of 100 and 400 GW/cm2 while Nd:YAG (pump-1) and Stokes laser 

irradiances are 153 and 240 GW/cm2 respectively. The Stokes irradiance is multiplied 

by the coefficient β introduced in Eq. (5-6) to take into account the spectral nonuniformity of the broadband laser. SRP for N2 is proportional to the irradiance of 

pump-1 (the Nd:YAG laser), and independent of pump-2 (the narrowband dye laser). 

Vice-versa SRP for O2 is proportional to the irradiance of pump-2 and independent of 

pump-1. Stark broadening is proportional to the total irradiance (that includes both 
117 

pumps). The first vibrational bands of both N2 and O2 are excited, revealing the 

presence of SRP (hot bands for neither molecule should be populated at room 

temperature). The O2 hot band is more pronounced than the N2. Reducing the 

narrowband dye laser irradiance (pump 2) will decrease SRP in O2, and leave it 

unaltered for N2. Stimulated Raman pumping from the ground to the first vibrational 

levels causes the appearance of the first vibrational band and an amplitude reduction 

in the ground band. When the irradiance of the pump-2 laser is reduced by a factor of 

four the O2 hot band is still present, but its normalized peak is reduced by 10% and 

the ground band peak is increased by 15%, consistent with a reduction in SRP. When 

the pump-2 irradiance is reduced by a factor of 4 the total irradiance goes from 793 

GW/cm2 down to 493 GW/cm2. The 5% amplitude increase in the N2 peak can be 

attributed to a reduction in the Stark broadening. Since the Stark broadening is similar 

for both N2 and O2 Q-branches, we can infer that it is present also in O2. When the 

pump-2 and Stokes irradiances are fixed and pump-1 is halved (not shown in the 

figure), we observe a 2.5% increase in the N2 ground peak, a 1.5% reduction in the 

first vibrational band and a 0.8% increase in the O2 peak. The small variation 

obtained when halving the product of pump-1 and Stokes, suggests that the irradiance 

product is close to the SRP threshold. 
118 

Figure 5-3: a) CARS spectra in ambient air and b) in a Hencken burner flame at Φ =0.3, 

narrowband dye laser irradiance varied
119 

The experimental spectra in air are consistent with predictions from the threshold 

criteria of Eq. (5-3) and Eq. (5-8). In the range of irradiances considered in Figure 

5-3, the SRP characteristic time for O2 varies between 1.5 and 6 ns (as compared to 

the laser pulse lengths of ~10 ns). When halving pump-1 irradiance, the N2 SRP 

characteristic time goes from 13 to 26 ns. The criterion of Eq. (5-8) is not satisfied for 

both molecules in agreement with the experimental observation of the “hot bands”. 

The shorter SRP characteristic time for O2 than N2 is consistent with the more 

pronounced first vibrational band observed experimentally in the O2 spectra. Based 

on Eq. (5-4) the Stark shift for a total irradiance of 800 GW/cm2 for the N2 Q(5) line 

is 0.13 cm-1, 40% larger than the 0.08 cm-1 Raman linewidth. According to Eq. (5-3), 

a small spectral perturbation due to Stark broadening is expected, and this is 

consistent with the 5% reduction observed in the N2 peak. 

Figure 5-3 b) shows spectra collected in a Hencken burner flame for equivalence 

ratio of 0.3, using the same irradiance levels as the spectra in Figure 5-3 a). Increasing 

the pump-2 irradiance by a factor of 4 decreases peak amplitudes for the O2 ground 

and hot bands by 21% and 4.5%, respectively. It also decreases peak amplitudes for 

the N2 ground and “hot” bands by 18% and 9%, respectively. Note that at high 

temperature both the ground and the first vibrational bands decrease when increasing 

the irradiance. Based on Eq. (5-6), the change in population difference with SRP is 

proportional to the original population, thus for the first vibrational band the 

amplitude increase caused by stimulated v=0→1 transitions is larger than the 

reduction due to stimulated transitions from v=1 to higher vibrational levels. Also, 

there is no evidence of a second vibrational band in the collected O2 spectra. Stark 
120 

broadening is thus probably responsible for the reduction in the first vibrational band 

of O2. Evidence of a stronger Stark broadening in N2 than was observed in air is 

provided by the reduction of the N2 ground peak that is more than three times what 

was observed in ambient air. Stark broadening acts in a similar way for both O2 and 

N2 molecules, and therefore the amplitude reduction in O2 spectra is also expected to 

be stronger in the flame than in room temperature air. In particular the reduction of 

the first vibrational band caused by the Stark effect is larger than the increase caused 

by SRP. The experimental results are consistent with the theoretical model discussed 

in the previous section. From Figure 5-1, the N2 collision-broadened linewidth at 

1180 K is ~0.04 cm-1, three times smaller than the estimated Stark shift of 0.013 cm-1

expected at 800 GW/cm2

. The theory correctly predicts that the Stark broadening at 

higher temperature is much more significant. 
121 

Figure 5-4 summarizes the results of the tests in the fuel-lean flame for the whole 

range of irradiances considered. The ratio of the peak signal to the baseline signal 

(i.e., without SRP or Stark effects, computed at chemical equilibrium conditions), 

normalized to the theoretical ratio of peak to baseline (from CARSFT calculations), is 

plotted for the strongest line in the ground (filled symbols) and first vibrational bands 

Figure 5-4: Normalized peak to baseline ratio for N2 and O2 measured in a Φ=0.3 

Hencken burner flame (a) as function of the pump-Stokes irradiance product and (b) 

total irradiance. Top horizontal scale provides the calculated SRP characteristic time 

(a) and Stark shift (b). Closed symbols are for the ground vibrational band, open 

symbols for the first vibrational band
122 

(open symbols) of O2 and N2 against the pump-Stokes irradiance product (a) and the 

total irradiance (b). The top axes are the characteristic SRP time (a) and the expected 

Stark shift (b) as computed for the N2 Q(5) line from Eq. (5-6) and Eq.(5-4). The 

continuous lines are best fit second order polynomials. Figure 5-4 a) shows that the 

O2 signal strongly depends on the pump-Stokes irradiance product, suggesting that 

SRP is the dominant effect on O2. The spread around the fitted line visible for βIpIS > 

2 × 104 GW2

/cm4, suggests that at these high irradiances, Stark broadening is also 

significant. For irradiances below 2 x 103 GW2/cm4 the effects of SRP on the O2

spectral shape are negligible. The experimentally determined threshold of 2 x 103

GW2/cm4 correspond to a SRP characteristic time τΔN ~ 75 ns; this is one order of 

magnitude longer than the pulse length, therefore the experimental results are 

consistent with the criterion of Eq. (5-8).The N2 data do not show such a significant 

trend with the pump-Stokes irradiance product, suggesting that Stark broadening is 

the dominant effect. Figure 5-4 b) is a plot of the same set of data as function of the 

total irradiance. The O2 data varies with the total irradiance for ITotal>350 GW/cm2

, 

but the curve fit is poor because SRP effects are also significant, as shown in Figure 

5-4 a). Data correlate poorly with the total irradiance in the 250-350 GW/cm2

 range, 

since SRP is the dominant effect in this region. Below 250 GW/cm2 the peak to 

baseline ratio has converged to the theoretical value, and stays constant. The N2 data 

collapse on the fit line, therefore Stark broadening is the dominant effect. For values 

below 250 GW/cm2 convergence is achieved. The Raman linewidth of the N2

transition is ~0.04 cm-1, the computed Stark shift is 0.037 cm-1, and therefore the 

experimental results are consistent with the criterion of Eq. (5-3). 
123 

High irradiance perturbations affect both concentration and temperature 

measurements obtained by fitting the spectra (Chapter 3). The fitting code is usually 

able to provide a good fit (to incorrect temperature and concentrations) in the 

presence of Stark or SRP perturbation effects. Results are shown in Figure 5-5 for 

temperature (a) and O2 concentration (b) plotted as a function of pump-Stokes 

irradiance product (appropriate to SRP effects). Temperature is not affected 

significantly by perturbation effects other than at high irradiance (IpβIs>2x104

Figure 5-5: Fit (a) temperature and (b) O2 mole fraction as function of the pump-Stokes 

irradiance product
124 

GW2

/cm4), corresponding to a characteristic SRP time shorter than 8 ns. Perturbation 

effects do not significantly change the rotational temperature, but do change the 

vibrational temperature; the fitting method does not distinguish between these 

temperatures, but fits to a single temperature. The large temperature measurement 

spread at the highest irradiance is caused by a poor fitting of the spectra which occurs 

because the rotational and vibrational temperatures are not equal. Oxygen

concentration is strongly perturbed, with errors up to 50% at the highest irradiances. 

Stimulated Raman pumping also affects the O2/N2 mole fraction ratio with errors up 

to 30%. These results differ from Péalat`s, [135] where Stark broadening was 

dominant and relative concentrations were not affected. Keeping the total irradiance 

and the pump-Stokes product below the thresholds described in the previous 

paragraph, temperature and concentration measurements with errors smaller than 3% 

are obtained. Note that Woodmansee [7] suggested as threshold a characteristic SRP 

time equal to the pulse length, but these researchers were interested in obtaining 

accurate temperature only. This is consistent with our results of Figure 5-5 a), where a 

SRP characteristic time lower than 8 ns was necessary to observe variations in the 

temperature. Accurate concentration measurements are much more likely to be 

limited by SRP than are temperature measurements.
125 

Figure 5-6 shows perturbation effects on the rotational H2 lines. Data were 

acquired only with the 500 and 850 mm focal length lenses, with the product of the 

pump and Stokes irradiances up to 104 GW2/cm4 and total irradiances up to 450 

GW/cm2. In the N2 and O2 spectra the SRP-induced population change was revealed 

by the appearance of “hot bands”, but for the H2 rotational lines both Stark and SRP 

produces only an amplitude reduction. Figure 5-6 shows that when the total irradiance 

is increased the amplitude of all the lines decreases. Stimulated Raman pumping is 

proportional to the product of the pump and Stokes irradiances. If the Stokes 

irradiance is changed by a factor of 2 with minor changes to the total irradiance (Test 

D vs Test E), the lines are not significantly affected, and therefore SRP is negligible 

and Stark broadening dominant. 

The ratio of the line peak to the baseline for the rotational H2 lines, normalized by 

the theoretical value of this ratio, for a larger number of tests similar to those in 

Figure 5-6: CARS spectra collected in a Φ=2 Hencken burner flame with different 

irradiances for the S(5), S(6) and S(9) lines; A) ITotal=187, Ip1IS=3250, Ip2IS=800; B)

ITotal=174, Ip1IS=1560, Ip2IS=384; C) ITotal=324, Ip1IS=4050, Ip2IS=3969; D) ITotal=429, 

Ip1IS=1950, Ip2IS=3458; E) ITotal=443, Ip1IS=4050, Ip2IS=7182. Products are in GW2/cm4, ITotal

in GW/cm2
126 

Figure 5-6, is plotted in Figure 5-7. In Figure 5-7 a) it is plotted as a function of the 

product of the pump and Stokes irradiances, and in Figure 5-7 b) as a function of the 

total irradiance. The peak to baseline ratio correlates well with the total irradiance, 

decreasing monotonically with it, but correlates poorly with the pump Stokes 

irradiance product. This again suggests that the Stark effect is dominant. In this 

experiment total irradiance may not have been lowered enough to reach the 

unperturbed condition. Figure 5-7 shows that at 170 GW/cm2, that is the lowest 

irradiance tested, the peak amplitudes differ from the theoretical values by less than 

Figure 5-7: Normalized peak to baseline ratio for H2 rotational lines measured in a Φ=2 

Hencken burner flame as function of the pump-Stokes irradiance product (a) and total 

irradiance (b)
127 

5%. Figure 5-7 b) shows that the amplitude reduction is not the same for the three 

rotational H2 lines. Temperature sensitivity in H2 rotational spectra is given by the 

ratio between the amplitudes of the different lines, therefore the Stark broadening 

compromises temperature obtained by fitting these H2 lines. The fitted concentration 

of H2 is strongly affected by Stark broadening for total irradiances above 170 

GW/cm2. This is probably one of the reason why in previous measurements [6, 66, 

72] the H2 mole fraction was systematically low (see Chapter 6). The Figure 5-2 b) 

shows that the expected Stark shift is much smaller than the Galatry linewidth (Figure 

5-2 a) for the whole range of irradiance considered (150-450 GW/cm2

) so the simple 

model does not predict the observed Stark broadening. Note that, if the collisional 

broadened linewidth is used as ΓR, the criterion of Eq. (5-3) correctly predicts the 

presence of Stark broadening in the range of total irradiances tested. 
128 

CHAPTER 6 -Characterization of the Dual-Pump 

CARS Instrument

6.1 Introduction

In providing measurements for CFD validation it is important to include estimates 

of the measurement uncertainties, so that the difference between the experiment and 

the simulation can be correctly quantified. In this chapter, measurements in a 

Hencken burner flame, to determine the accuracy and the precision of the dual-pump 

(DP) CARS instrument, are described. Changes to the modeling, and calibrations of 

some molecular parameters to remove systematic errors are described. Finally the 

spatial resolution of the instrument is measured and the effects of the spatial 

averaging on the measurements are discussed. 

6.2 The Hencken Burner Flame

The Hencken burner (Research Technologies RD1X1) produces a steady, nearly 

adiabatic, non-premixed flat flame, often used for calibration and validation of nonintrusive optical diagnostics techniques. [156] Similar measurements, obtained at 

NASA Langley with earlier versions of the DP-CARS instrument are reported in Ref. 

[6, 66, 72]. Figure 6-1 shows a top view of the burner used for this test. 
129 

The figure shows the 1.5 in2 hastalloy honeycomb which supports the stainless steel 

fuel tubes, which are in one cell out of every four. Oxidizer flows around the fuel 

tubes and through the honeycomb so that mixing occurs only above the surface. The 

center hole is available for seeding particles for measurements with other laser 

diagnostic technique. The center hole was plugged for the tests described here. The 1 

in2 burner surface is surrounded by a co-flow of inert gas. The co-flow improves the 

flame stability and prevents entraining of ambient air. A N2 co-flow of 28 SLPM was 

used for all the measurements here reported. Four Tylan (model FC-280) mass flow 

controller were available to regulate the flow rate of H2, air and O2 to the burner. 

Each flow controller can provide flow rates up to 30 SLPM with an accuracy of 0.3 

SLPM (1% of full scale). One flow-controller is used to regulate the H2, one is 

dedicated to the O2 flow rate, and the remaining two provide control over the air flow. 

The flow-meters are set to produce mixtures of air and H2 with equivalence ratios in 

Figure 6-1: Hencken burner, top view
130 

the 0 to 3.5 range. Air flow-rates are varied between 17 and 60 SLPM, and only one 

flow controller is needed when the flow rate is below 30 SLPM, that is for Φ>2. H2

flow rates are in the 2.5 to 25 SLPM range. Total flow rates are in the 40 to75 SLPM 

range. The flow rates are doubled with respect to what was used in Ref. [6] and [72]; 

the higher flow-rates ensure that the flame is slightly lifted from the burner surface so 

that heat losses are reduced and the flame is near-adiabatic; in addition it allows for 

operation of the H2 flow controller closer to full scale, reducing the effects of 

inaccuracies of the flow-meter. In addition to air-H2 mixtures, mixtures enriched with

O2 have also been considered, with flow rates chosen so that the products of 

combustion have 21% O2 by mole fraction. Such test cases provide additional 

validation points in conditions more similar to the vitiated air mixture often used to 

simulate hot-air in supersonic combustion experiments. The enriched mixtures are 

limited to equivalence ratio of 0.26, corresponding to a temperature of 1400 K. The 

additional oxygen moves the flame closer to the burner surface, and for higher 

equivalence ratios the larger heat transfer can damage the honeycomb structure of the 

burner. 

6.3 Non-Uniformities in the Hencken Burner Flame

Previous measurements I performed, but not reported here, showed some spatial nonuniformity in the flame produced by the Hencken burner available at NASA Langley. 

For the current work, a more detailed survey of the flame produced from the burner 

has been performed. Two equivalence ratios (Φ) have been considered, one fuel lean 

(Φ=0.3), and the other fuel rich (Φ=2). For each equivalence ratio, data have been 
131 

collected in a vertical plane, orthogonal to both the burner surface and the direction of 

the Nd:YAG laser, and in a horizontal plane, parallel to and 40 mm above the burner 

surface. The test matrix for the vertical plane has 7 locations along the vertical 

centerline (axis) of the burner and 11 in the horizontal direction. The first axial 

location is 5 mm from the burner surface, the last 80 mm. The test matrix for the 

horizontal plane covered a 20x20 mm square region, with 11 data points in each 

direction, for a total of 121 distinct points. The dots in Figure 6-2Figure 6-3 represent 

the CARS measurements locations. Each point is visited twice, and 250 single-shot 

spectra have been acquired each time. The two replications allow verification of 

steady operation. The 250 repetitions are used to determine average and standard 

deviation at each location. The order of the test matrix for each plane and equivalence 

ratio was randomized. Figure 6-2 a) shows contour plots of average temperature in 

the vertical plane for the fuel lean case. The average is computed over the 250 

repetitions and the two replications. Data collected 5 mm from the burner surface 

shows a very hot region (~1400 K) 1 mm from the center of the burner, coupled with 

a much colder region (~1000 K) on its right. This is evidence of an inhomogeneous 

distribution of the local equivalence ratio caused by the obstruction of some fuel 

tubes. Moving downstream, mixing makes the temperature more uniform, but 80 mm 

from the surface there is still evidence of the initial non-uniformity. Figure 6-3 shows 

the average temperature in the horizontal plane 40 mm from the burner. The 

temperature distribution is even more inhomogeneous than shown in the vertical 

plane. The hot region is coupled with a much colder one (less than 900 K) that is not 

visible in the vertical plane image. 
132 

Figure 6-2 b and Figure 6-3 b are obtained for an equivalence ratio of 2. Again 

there is a strong non-uniformity 5 mm from the burner surface, with variations in the 

equivalence ratio that are consistent with what was observed in the fuel lean case. 

Notice that for equivalence ratios closer to 2, reducing the equivalence ratio increases 

the temperature. For given change in the equivalence ratio, the resulting temperature 

variation is larger for fuel lean mixtures than fuel rich. This explains the smaller 

temperature range observed for Φ=2 than for Φ=0.3. Mole fraction measurements of 

H2 are consistent with the temperature measurements, and the range observed is 

comparable to the range of O2 observed for the fuel lean case. Although there are very 

large variations 5 mm from the surface, the flame becomes much more uniform 

Figure 6-2: Temperature contour plot in the vertical plane (y=0) for a) Φ=0.3 and b) Φ=2 
133 

further downstream. The survey of the horizontal plane shows significantly less 

variations than the fuel lean case. 

Based on these plots it appears that it would be best to take validation 

measurements as far downstream as possible. However, moving the probe volume 

downstream weakens the hypothesis of adiabatic flame, because of the cooling effects 

of radiation. In addition, N2 from the co-flow increasingly penetrates the flame further 

downstream, reducing the temperature, affecting the mole fractions, and causing an 

increase in the standard deviation. The study does not show a region that is both 

uniform and for which the assumption of adiabatic, laminar flame is satisfied. 

Lacking a better test-medium, the validation study was performed in the Hencken 

burner flame, but these non-uniformities are taken into account when interpreting the 

results. The data presented in the next section were collected 50 mm above the burner 

surface at the center of the burner. 

Figure 6-3: Temperature contour plot in the horizontal plane (z=40 mm) for a) Φ=0.3 and 

b) Φ=2
134 

6.4 Instrument Accuracy

The instrument accuracy is determined by comparing CARS measurements in the 

Hencken burner to theoretical calculations for several values of the equivalence ratio. 

The calculations, which assume chemical equilibrium, have been performed using the 

Chemical Equilibrium Analysis code (CEA) from NASA Glenn Research Center. 

[108] Figure 6-4 and Figure 6-5compare temperature and mole fraction measured in 

the Hencken burner flame with this instrument (red symbols), to theoretical values 

computed using CEA (continuous black lines) and to measurements in the same 

burner performed by O’Byrne (green triangles) [6] and Tedder (blue squares) [72] 

with previous versions of the instrument. The fitted temperature and mole fractions 

shown here are obtained using the same models and spectral parameters employed in 

the fitting of the data of Ref. [6, 72]. In particular the James-Kemplerer model is used 

Figure 6-4: Measured (symbols) and computed (continuous black line) temperature as 

function of the equivalence ratio Φ
135 

for the Herman-Wallis correction factor, the Voigt model used to model the lineshape 

for all species, and the values of the third order non-resonant susceptibility are based 

on measurements by Lundeen. [157] 

Measured temperature profiles are within 3% of the computed values. The overall 

measured temperature profiles appear slightly shifted toward the right, suggesting an 

error in the mass-flow rates, rather than in the DP-CARS instrument. No significant 

differences are noticeable between the three datasets.

The fitted mole fractions in Figure 6-5 show a poorer agreement with the theory 

(errors up to 10%) than the temperature, for all three datasets. For fuel lean flames all 

datasets show similar behavior, with N2 and O2 being systematically higher, and the 

O2/N2 ratio being smaller than the theory at lower equivalence ratios (and lower 

temperature). The results are significantly different for fuel rich mixtures. In 

Figure 6-5: Measured (symbols) and computed (continuous black line) mole fraction as 

function of the equivalence ratio Φ
136 

particular in the older datasets the ratio of H2/N2 is lower than the computed, where in 

the dataset collected for this work is higher. In Chapter 5 it was shown that Stark 

broadening reduces the H2 line amplitude, causing lower measurements of the H2/N2

ratio. The results shown in Figure 6-5suggest the presence of Stark broadening in the 

data shown in Ref. [6, 72]. 

Systematic errors could be caused by inaccuracies in the theoretical modeling. In 

the following sections we examine some of the modeling choices of Ref. [6, 66]. In 

particular we will discuss the choice of the model for the Herman-Wallis correction 

factor, the lineshape model selected for each molecule, and the values of the thirdorder non resonant susceptibilities. A calibration of some molecular parameters for 

which there is large uncertainty in the measurements is proposed. 

6.5 Herman Wallis Correction Factor 

Based on chemical equilibrium calculation, the max temperature achievable in an 

air-H2 flame is 2396 K. In this work the peak mean temperature measured is 2423 K, 

and Tedder [72] measured a max temperature of 2426 K. The higher measured 

temperature cannot be attributed to errors in the equivalence ratio, but it is a 

systematic error of the instrument. 

In recent years there was a renewed attention on the modeling of the Herman 

Wallis factor, [111] and its effects on CARS temperature measurements. [113, 158-

160] The Herman-Wallis (HW) factor models the effect of centrifugal force on the rovibrational line intensities. The CARSFT code use the James-Kemplerer (JK) model 
137 

[112] for the HW factor, but a more accurate model was proposed in 2001 by Tipping 

and Buoanich (TB-model). [115] 

The discrepancy between the two Herman Wallis factors for N2 and O2, increases 

as function of the J number as shown in Figure 6-6. For this reason larger effects on 

measurements will occur at higher temperature. 

 For this work I modified the CARSFT code to include the option of using the TB 

model for the HW correction. Details can be found in Ref. [114]. Figure 6-7 a) shows 

the percentage difference between the measured temperature and mole fractions 

obtained using the two models, for the Hencken burner data. The difference is 

computed with respect to the TB model, and the horizontal axis shows the 

temperature as measured with the TB model. The top panel shows that the 

Figure 6-6: Herman-Wallis (HW) factor for N2 and O2 as function of the rotational 

quantum number J, according to the JK and TB models
138 

temperature measured with the less accurate JK model is systematically higher 

(~0.6%, for T≥600K) than the temperature measured with the TB model. This result 

is consistent with what reported in previous works. [160] The closed symbols are for 

air-H2 cases, where the open are for the enriched O2 cases. There is a larger 

discrepancy between the two models for the enriched O2 case as consequence of the 

larger difference in the HW factors for O2 than for N2. For this specific dataset the 

max temperature measured using the JK model was 2425 K, where using the TB 

model is 2409 K, closer to the theoretical limit. Note that the fit included the whole 

spectrum, where N2 is dominant (because of the higher concentration). If the fit was 

limited only to the O2 portion of the spectrum the difference would have been greater. 

Figure 6-7 b shows the same plots for mole fractions. Mole fractions obtained 

with the JK model are systematically higher than the ones obtained with the TB 

Figure 6-7: Difference in % between a) temperature and b) mole fractions obtained 

using the JK and the TB models for the HW factor
139 

model. In particular the discrepancy increases with equivalence ratio, as expected 

since at higher temperature higher J lines appear and they`re more sensitive to the 

choice of the model. In comparison O2 is more sensitive than N2, as expected from 

Figure 6-6. The discrepancy is function only of temperature and independent of 

concentration; in fact the open symbols, representative of the O2 enriched cases 

overlap to the closed symbols representing the air-H2 flame. Notice that N2 and O2

were systematically higher, hence the use of the more accurate HW factor also 

improves (slightly) the mole fraction accuracy. This is the first study showing the 

effect of different HW factors on simultaneous mole fraction measurements of O2 and 

N2. 

6.5.1 Temperature Accuracy

Figure 6-8 shows the CARS measured temperature (red circles) obtained using 

the TB model for the HW factor, as function of the equivalence ratio. Theoretical 

calculations (CEA) have been conducted for nominal flow-rates (continuous line) and 

for two limiting cases that bound the inaccuracies due to mass flow meters. One limit 

case is obtained by subtracting 0.3 SLPM from the flow-rate of H2 and adding 0.3 

SLPM to the flow-rate provided by each of the air flow-meters. It is denoted as 

“leaner” limit case (blue dashed line) since it produces a leaner mixture than the 

nominal case. Vice-versa, the “richer” limit case (red dashed line) is obtained by 

subtracting 0.3 SLPM from each oxidizer flow rate, and adding 0.3 to the H2 flow 

rate. 
140 

Fitted temperatures are within 60 K of the expected nominal temperature over the 

entire range, and within 20 K for Φ>2. Measured temperatures are systematically low 

for fuel lean mixtures, and high for rich mixtures with Φ<2. This is evidence of a 

systematic difference between the local equivalence ratio and the global (average) 

which we attribute to non-uniformity described previously. Hancock [156] pointed 

out that the overall shape of the CARS fitted temperature provides a more accurate 

estimate of the equivalence ratio than one computed based on the mass flow-rates. 

For the remainder of this section, we use the composition corresponding to the 

measured temperature for a H2-air flame in chemical equilibrium (except for the 

highest temperature, where a Φ=1.07 corresponding to T=2396 K is used instead). By 

Figure 6-8: Measured (red circles) and computed (lines) temperature as function of the 

equivalence ratio Φ
141 

doing so, we remove the uncertainty of the equivalence ratio, but we make a potential 

error by assuming the temperature measurement to be exact.

6.5.2 Lineshape Models

Correct choice of the lineshape models is essential to obtain accurate CARS 

measurements, since it affects both absolute mole fractions and the mole fractions of 

one species relative to another. The relative mole fractions measurements are 

independent of the third-order non-resonant susceptibilities, but systematic errors can

be caused by inadequate line shape models. Different lineshape models have been 

described in Chapter 2-6. Here their effect on the relative mole fraction measurements 

is discussed. 

Figure 6-9: O2/N2 ratio as function of the equivalence ratio Φ
142 

Figure 6-9 shows the ratio of O2/N2 measured for fuel lean mixtures using the 

Voigt model for both N2 and O2. The error in the mole fraction ratio is below 4% for 

Φ≥0.2, corresponding to temperatures greater than 900 K. At lower temperatures the 

error is significantly larger, 8% at 600 K and 13% at 300 K. The results suggest that 

the line shape model might be inadequate at lower temperatures.

In Q-branch spectra for low values of the rotational quantum number J the rovibrational lines undergo collisional narrowing causing a coalescence of these lines. 

[97] The Voigt model includes the pressure and the Doppler broadening, but not the 

collisional narrowing. Figure 6-10 shows the fit of the average of 500 spectra 

collected in room air, to a theoretical spectrum computed using the Voigt model for 

Figure 6-10: Fit of an average of 500 single shot spectra collected in ambient air to a 

theoretical spectrum computed using the Voigt model
143 

the line shape of O2 and N2. The fit is good, except in proximity of the N2 and O2

band-head, hence confirming that the issue is limited to the lowest J numbers. There 

is the possibility of improving the accuracy at low temperatures by implementing line 

shape models that include the collisional narrowing effect such as the modified 

exponential gap model. [161] At the current time the model is not fully implemented 

in CARSFT, therefore we used the Voigt model for the line shape of O2 and N2. 

When using the Voigt line shape model for all species, as in Ref. [6, 66, 72] the 

measured ratio of H2/N2 is systematically high (in the absence of Stark and SRP 

effects). For H2 at atmospheric pressure, motional (Dicke) narrowing is significant 

and the Galatry model, rather than the Voigt, is recommended. [96] As observed in 

Chapter 2-6 the Galatry model requires the knowledge of an additional quantity, the 

motional narrowing parameter β, which is related to the optical diffusion coefficient 

Do (see Eq.2-22). Do, although of the same order of magnitude, differs from the 

Figure 6-11: H2/N2 ratio as function of the equivalence ratio
144 

conventional mass diffusion coefficient Dm. [90, 94, 95] Unfortunately the optical 

diffusion coefficient has been measured for only a few molecules and temperatures. 

Recently Kulatilaka [162] measured optical diffusion coefficient for the H2Q-branch 

at room temperature, but not for the S branch. 

The optical diffusion coefficient determines the ratio of the measured H2 and N2. 

The ratio does not depend on the non-resonant third order susceptibility. Given the 

uncertainty on this parameter, I calibrated it to minimize systematic errors in the 

measurements. Figure 6-11 shows the ratio H2/N2 obtained using the Voigt model, 

and narrowing parameters computed for D0=Dm and D0=0.67Dm. Increasing the 

narrowing parameter reduces the ratio and provides better agreement with the theory. 

The measurements obtained for the two optical diffusion coefficients have been used 

to extrapolate the optical diffusion coefficient Dcal that would return the theoretical 

H2/N2 ratio for each Φ. The values so determined are fitted to an exponential function 

of the temperature ( 0.0011 0.0059 T D e cal = ) and input to CARSFT while generating the 

theoretical library. The red circles in Figure 6-11show the results obtained using this 

calibrated optical diffusion coefficient.

The calibration ensures that the instrument returns an accurate H2 to N2 ratio for 

the temperature and mole fraction combinations tested with the Hencken burner, but 

problems may arise when conditions vary significantly from those produced by the 

Hencken burner. The calibration is a function only of temperature and if the 

composition in the supersonic burner, for given temperature, differs significantly 

from what is observed in the Hencken burner, the calibration may be in error, 

affecting the accuracy of the composition measurement. Also the calibration assumes 
145 

that the N2 line shape model is correct. This was based on the observation of good 

accuracy in terms of the N2/O2 ratio for fuel lean mixtures at high temperature. Note 

that errors in the ratio of the H2/N2 for the data presented in Ref. [6, 72] cannot be 

explained by the choice of line-shape model (or optical diffusion coefficient). Stark 

broadening [163] of the H2 lines, was likely responsible of the erroneous 

measurements of the H2/N2 ratio reported in those previous works. 

6.5.3 Non-Resonant Susceptibility

DP-CARS is capable of obtaining absolute mole fractions of all major species in 

an air-H2 flame, provided a knowledge of the third order non-resonant susceptibility 

of all the major species, both resonant and non-resonant. Accuracy of the mole 

fraction measurement is obviously limited by the degree to which the non-resonant 

background is known. Unfortunately these parameters are not well known, and 

Figure 6-12: Measured N2 mole fraction in Hencken burner, using Lundeen and Hahn 

values for the non-resonant susceptibilities
146 

although several measurements have been reported, [157, 164-169] they are not 

consistent, and have large uncertainties (10%). Figure 6-12 and Figure 6-13 show the 

changes in the measured N2 and O2 mole fractions when using the non-resonant 

susceptibilities values measured by Lundeen [157] and Hahn. [168] The values from 

Lundeen are the ones used in previous experiments at NASA Langley. [6, 66] 

For this work a calibration of the third order non-resonant susceptibilities of all 

major species was performed to optimize the accuracy of the absolute mole fraction 

measurements. The calibration assumes all other aspects of the modeling are correct 

(such as the line shape modeling), except for the non-resonant susceptibilities. The 

calibration was done in two steps: first the third order non-resonant susceptibilities for 

N2, O2 and H2O were calibrated based on the fuel lean data (excluding test conditions 

for which the error on the O2/N2 ratio is above 10%, that is Φ=0 and Φ=0.1); then the 

H2 third order non-resonant susceptibility was determined from the fuel rich data. 

Figure 6-13: Measured O2 mole fraction in Hencken burner, using Lundeen and Hahn 

values for the non-resonant susceptibilities
147 

Following are details of the calibration procedure. Let`s denote xi the mole fractions 

computed using the Hahn set of non resonant susceptibilities (3)

NRi

χ , NR the total nonresonant contribution fitted and Ns the number of major species. 

(3)

1 i

Ns

NR i

i

NR x χ

=

=∑ (6-1) 

When fitting for species, the code returns the correct ratio of mole fraction to nonresonant baseline i x

NR , but not the correct mole fraction (due to errors in nonresonant susceptibilities) Let`s denote yi the correct mole fractions (expected from the 

theory based on effective Φ), and ci calibration factors for each non resonant 

susceptibility. The following relations are then satisfied for the resonant species: 

ii i

i

xy y CNR

NR CNR x NR

= →= (6-2) 

with 

(3)

1 i

Ns

i i NR

i

CNR c y χ

=

=∑ (6-3) 

Since we can write as many equations as the test cases we acquired, then the 

calibration factors can be determined as solution of an optimization problem. The 

“residual” function we want to minimize is given by:

2 1

1 1

( )

n N j j

i

j j

j i i

CNR y G c

NR x

−

= =

  =  −    ∑∑ (6-4) 

The apex j, indicates the jth test case considered, and n is the total number of test cases 

available for the calibration. For the fuel lean case 10 test cases have been considered, 

with equivalence ratios between 0.2 and 0.6. Data collected at room temperature air, 
148 

Φ=0.1 and for Φ=0.8 have been excluded from the calibration, because showing 

inaccuracies in the O2/N2 ratios above 5%. The O2 enriched test cases were not used 

for the calibration, because there is no unique relation between the temperature and 

the composition, thus no way to correct for flame non-uniformities or errors in the 

flow-meters. The procedure is then repeated for H2 using the fuel-rich test case, and 

all the previously calibrated values of the non-resonant susceptibilities.

Calibrated values of the third order non-resonant susceptibilities are 7.85, 7.79, 

19.74 and 10.02 (in units of 10-18 cm3/(erg amagat)) for N2, O2, H2O and H2, 

respectively. Except for H2, the calibrated values are within the uncertainty range 

(10%) provided with the measurements from Hahn. [168] The value determined for 

H2 is 70% larger than what was measured by Hahn, [168] and 16% larger than the 

highest measurement we found in literature. [169] This suggests that there might be 

additional modeling issues for the fuel-rich mixtures that are being corrected by this 

selection of the third order non-resonant susceptibility of H2. Without this correction, 

errors up to 3% were observed for N2 and H2. 

These calibrations are not direct measurements of the optical diffusion coefficient 

or the third-order non-resonant susceptibilities, but values that are optimized for this 

instrument and may compensate for possible other deficiencies in the modeling, and 

so they can only be applied with confidence in the neighborhood of the conditions for 

which they have been determined. 

Figure 6-14 shows the measured mole fractions of O2, N2 and H2 as a function of 

the equivalence ratio. Continuous lines are the computed values based on an 

equivalence ratio corresponding to the measured temperature. The calibration 
149 

provides an overall reduction of the systematic error. The largest errors are at low 

temperature (below 800 K) and could be caused by not including the collisional 

narrowing in the lineshape model. The measured O2 mole fraction is 1.2% lower than 

expected at 300 K and 0.7% lower at 600 K; N2 mole fractions are 3.5% and 2% 

higher at room temperature and at 600 K, respectively. Errors are reported as a 

percentage of the total composition, not of the measured value. At higher

temperatures, the accuracy significantly improves, with errors in the O2 concentration 

that are below 0.5% (systematically low) and errors in N2 below 1.5% (systematically 

high). H2 mole fractions are within 1% of the total composition. The accuracy is 

significantly improved with respect to what is reported in Ref. [6] (errors in N2, O2

and H2 below 2.6, 2.4 and 5% of total composition) and in Ref. [66] (errors in N2, O2

and H2 below 8, 3.1 and 7% of total composition). Removal of some of the 

Figure 6-14: Measured (symbols) and computed (continuous line) mole fraction as 

function of the equivalence ratio Φ
150 

experimental errors that may have affected previous measurements such as high 

irradiance effects, and improvements in the modeling (more accurate Herman-Wallis 

factors, better line shape model selection, and calibration of the non resonant 

susceptibilities) are responsible for the improved accuracy. 

6.6 Instrument Precision

In the study of turbulent flows, a high precision is desirable since it determines 

the lowest amplitude of fluctuations that can be detected. Instrument precision also 

affects the amount of data that needs to be obtained to meet measurement uncertainty 

criteria. The instrument precision needs to be carefully characterized, so that 

fluctuations in the flow can be distinguished by those caused by the instrument.

Standard deviation, computed from several single-shot measurements in an oven or a 

calibration flame, is often used as a metric for the instrument precision. [64, 106, 116, 

133, 156, 170-174] Commonly reported single-shot temperature standard deviations 

for N2 ro-vibrational CARS are 25-30 K at 300 K. [116, 133, 170, 172] The relative 

standard deviation, defined as the ratio of the standard deviation to the mean

measured temperature, is ~8-10% at ambient temperature. CARS temperature 

precision improves at higher temperatures, with standard deviation of 60 K (3%) at 

flame temperatures > 2000 K. Spectral features in vibrational CARS spectra strongly 

depend on temperature; in particular, as temperature increases, N2 and O2 rovibrational structures becomes more marked, and higher order vibrational bands 

appear above 1000 K, improving the precision at higher temperatures. Still further 

increasing the temperature, this effect is offset by a reduction of the signal-to-noise 
151 

ratio. Improved spectral resolution increases the number of structures in low 

temperature spectra and is therefore helpful in improving the precision at lower 

temperatures.

Vibrational CARS systems with improved precision (10-15 K) at ambient 

temperature have been developed. [106, 173, 175] Such systems are characterized by 

high spectral resolution, and the use of a single mode pump laser and modeless 

Stokes laser. A modeless dye laser has smaller mode amplitude fluctuations than a 

conventional one, therefore reducing the main source of noise in ro-vibrational 

CARS. Kuehner [173] reports a standard deviation of 10-15 K in the 90-295 K range. 

Further improvements were obtained by van Veen [106] thanks to a simultaneous 

referencing that takes into account the shot-to-shot fluctuations in the modeless dye 

Figure 6-15: Temperature standard deviation as a function of the measured average 

temperature
152 

laser. Use of a modeless dye laser was considered for this instrument, and attempted 

in the first preliminary measurements taken in the laboratory-scale free jet, [66] but 

results were unsatisfactory.

Figure 6-15 shows the relative standard deviation computed from 500 single shots 

measurements in the Hencken burner, and compares it to the results presented in 

Ref.[6, 72]. Data from Ref. [6, 66] were analyzed using the algorithm described in 

Ref. [6], which minimizes the mean square error of the square root of the signal 

intensity, the residual function R3, based on the notation of Ref. [107]. This is the 

same residual minimized by the fitting routine in CARSFT. [108] The black 

diamonds are relative standard deviations obtained from the Hencken burner data 

discussed here, using the fitting algorithm developed by Cutler, [107] and using R3. 

Figure 6-15 shows a 2% reduction of the relative standard deviation in the 300-1200 

K range caused by the improved spectral resolution achieved with this instrument. At 

higher temperature, higher order vibrational bands appear and ro-vibrational 

structures become more marked with the more resolved instrument, but no 

improvement in precision is observed. 

Snelling [116] observed that CARS temperature precision is improved by fitting 

to the intensity weighted on a pixel by pixel basis by an estimate of the uncertainty in 

the intensity. This approach is implemented in the fitting algorithm developed by 

Cutler [107] where this so-called reduced χ2 statistic (R2) residual can be selected in 

place of R3. Red circles are relative standard deviations obtained minimizing the 

reduced χ2 statistic. As already observed in Ref. [107] a significant precision 

improvement is achieved through the whole temperature range. In particular at 300 K 
153 

a temperature standard deviation of only 10 K (3.3%) is obtained. Such a low 

precision error is comparable to the one reported by van Veen using a modeless dye 

laser, and simultaneous referencing. [106] The relative standard deviation decreases 

further by increasing the temperature up to 1200 K, reaching a minimum of 2%. 

Precision in the 300 -1200 K range is comparable to what has been reported for pure 

rotational CARS. Further increasing the temperature, the effect of the reduced signalto-noise ratio becomes dominant and the relative standard deviation increases, 

peaking at 3% at stoichiometric temperature (~2400 K). Note also that at the highest 

temperature the choice of the residual has small effect. 

For the equivalence ratios above stoichiometric (empty circles), O2 is no longer 

present, and two or more H2 rotational lines appear. These are isolated lines, and are 

very sensitive to dye laser mode fluctuations. In particular if two or more H2

rotational lines are present their relative ratio is a function of temperature. The ratio 

of the two isolated lines strongly depends on the mode noise in the broad-band dye 

laser and a deleterious effect on temperature precision is expected. To avoid such 

effects the S(9) line is omitted from the fitting and the S(5) and S(6) lines are 

“lumped” together; i.e., in both the theory and the data the two H2 lines are replaced 

with a region of constant amplitude equal to the mean value over the 2 lines. This 

lumping removes any influence on the fitted temperature from the H2 spectra and 

decreases the temperature standard deviation, but the H2 mole fraction standard 

deviation is slightly increased (for example the temperature and H2 mole fraction 

standard deviation at Φ=3.5 are 81 K and 0.03 when the two H2 lines are kept 

separate, 60 K and 0.04 when lumped together). 
154 

The red open triangles are relative standard deviations obtained for the enriched 

O2 case. In this case increasing the temperature past 1200 K further decreases the 

relative standard deviation with the lowest relative standard deviation (1.8%) 

observed at 1350 K. The reason for the improved precision is the higher concentration 

of O2 (~21 %) in the enriched case, and therefore the larger signal-to-noise ratio of 

the O2 spectrum. In the supersonic burner, for the mixing case the center jet is of 

vitiated air and therefore it has a mole fraction of O2 close to 20% as in these data. As 

shown in the insets of Figure 6-10, O2 spectra have better spectral resolution than the 

N2 because the probe beam, which is the injection seeded Nd:YAG laser, has 

negligible line width. In addition, the Stokes laser center wavelength is chosen to 

excite the O2 Q-branch, therefore the mode noise on O2 spectra is lower than on N2. 

For these reasons measurements in O2 rich mixtures are more precise than in O2 free 

environments. 

The temperature standard deviations reported above also include temporal 

fluctuations of the flow in the Hencken burner. If the flow had no fluctuations, then 

the average of the measured fitted single-shot temperatures should coincide with the 

temperature extracted from the fit of the average of the spectra. This is verified for 

measurements in ambient air, but not in the flame, where the temperatures from the 

average spectra are systematically lower than the average of the single shots 

temperatures. The largest discrepancy is 15 K and it is observed at stoichiometric 

conditions. In averaging the spectra, the colder (higher signal) spectra weight more, 

biasing the temperature to lower values.
155 

Figure 6-16 shows the standard deviation of the measured mole fractions. 

The O2 standard deviation stays below 0.6% of the total mole fraction up to Φ=0.5, 

then increases up to 1.7% because of low signal-to-noise ratio. For Φ>1 no O2 is 

detected, and the single-shot measurements are scattered around a null average value. 

The N2 mole fraction standard deviation increases from 1.5% at room temperature to 

3.4% at stoichiometric, and then decreases to 2.5% at the highest equivalence ratio. 

The N2 standard deviation as a fraction of the average increases monotonically with 

the equivalence ratio from 1.7% to 7% over this range. The H2 standard deviation 

increases monotonically with the equivalence ratio, where the standard deviation as 

fraction of the mean is constant and equal to 10%. The greater precision error in the 

H2 measurements is largely due to mode noise in the broadband dye laser spectrum, 

which affects H2 more than N2 or O2 since only two H2 lines are probed, rather than 

the manifolds of lines for N2 and O2. Mole fraction precision for this instrument is 

Figure 6-16: Mole fraction standard deviation as a function of the equivalence ratio Φ
156 

similar to what is reported in Ref. [6, 66] except for H2, which shows a larger 

standard deviation as a fraction of the mean (~10% for this work, 8% in Ref. [6]). 

This is a consequence of moving the S(5) line toward the tail of the non-resonant 

spectrum, where the fluctuation (as fraction of the mean) are larger, and of “lumping 

together” the S(5) and S(6) lines. 

6.7 Instrument Dynamic Range 

Study of the axisymmetric supersonic combusting jet requires an instrument 

capable of operating in the 300 K-2400 K temperature range. Peak CARS signal 

dependence on temperature is approximated by the relation: [176] 

3.5

CARS I T − ∝ (6-5) 

The proportionality constant depends on several parameters, including laser 

irradiances, crossing angle, focusing at the entrance slit, properties of the 

spectrometer and the camera, and many other factors. 

The Pixis 100B camera used for this test has a 16 bit dynamic range, therefore a 

limit of 65535 counts in each pixel of the three bins. The signal is only in the center 

bin; the upper and lower bins contain only the background. For the Hencken burner 

dataset here discussed, the N2 peak signal at the highest temperature (~2400 K) is 

~700 counts above the camera noise level. 

Figure 6-17 plots the peak CARS signal photon counts as a function of 

temperature; the red circles are observed experimental values, the black curve is 

obtained from Eq. (6-5). The figure shows that for temperature below 700 K the 

pixels in the proximity of the N2 peak would be saturated. Notice that the scale is 
157 

logarithmic and for room temperature spectra the number is above one million counts. 

As described in Chapter 3, we use a half-wave plate and a polarizer to reduce the 

Nd:YAG energy to prevent detector saturation when the detected signal is too large. 

The approach guarantees that a large percentage (~90%) of the shots at a given 

location does not saturate the camera. Avoiding detector saturation for all spectra in a 

location would have reduced the signal-to-noise ratio excessively for the higher 

temperature spectra in a turbulent region. 

In previous data sets collected at NASA Langley, spectra with any detector

saturation were simply thrown away; since colder spectra have larger signal, this 

approach biases the average measurements toward higher temperature, and artificially 

reduces the measured range and standard deviation. To avoid the bias, we process the 

spectra that saturate the detector, but the fitting algorithm is instructed to omit (block) 

Figure 6-17: Measured (symbols) and predicted (continuous line) CARS signal 

intensity in camera counts as a function of the temperature
158 

the “saturated” pixels when computing the residual function. A numerical test has 

been performed to evaluate the instrument accuracy when portions of the spectra are 

not available for fitting. In the numerical the detector saturation threshold expressed 

as a percentage of the peak value of the CARS signal for each test case and indicated 

as α is varied. In the numerical test, every pixel for which the CARS signal is above 

the threshold, is considered saturated, and is blocked in the residual computation. 

Figure 6-18 shows a non-saturated spectra (blue line), compared to a numerically 

saturated spectra with α=5% (red line). For visual purposes only, the code fits a cubic 

spline in the saturated region. The filled region indicates the area blocked from the 

fitting. Although most of the N2 spectrum is lost, only few O2 peaks are blocked. 

Figure 6-19 a shows the percentage difference in the temperature measurements 

obtained for the unsaturated spectra and for spectra obtained setting the threshold to 

α. Note that decreasing the value of α, the portion of spectra blocked from the fitting 

becomes larger, is equivalent to a higher degree of saturation. In a real experiment the 

threshold value is set (65535 counts), but the CARS peak intensity varies as a 

function of temperature, composition and beams’ alignment. The right axis of Figure 

6-16 can be used to estimate values of α for given temperatures in the Hencken burner 

flame. Above 1200 K, the N2 peak is unlikely to be saturated, even when accounting 

for laser power fluctuations. At 500 K we expect the threshold to be ~ 30% of the 

peak signal, and only 6% at room temperature. Based on these considerations, α is 

varied in the 2%-75% range for this test. For temperature above 1000 K the error in 

temperature is below 3% for any value of α considered. The error is within 1% when 

we consider more likely values of α expected in our experiment, such as 2-10% for 
159 

room temperature, 10-50% at 500 K, and 50-100% above 800 K. Thus, accurate 

temperatures can be determined from detector saturated spectra taken in fuel-lean 

mixtures. 

Figure 6-19 b and c show errors on the O2 and N2 mole fractions as function of 

temperature for several values of α. In spectra collected with our DP-CARS 

instrument, in a fuel lean air-H2 flame the N2 signal is always stronger than O2 and 

therefore more prone to detector saturation. In the presence of detector saturation of 

the N2 spectra, the measured N2 mole fraction is higher and the measured O2 mole 

fraction lower. The error rapidly increases with decreasing α and with temperature, up 

to 6% for the most extreme cases. When considering more likely values of α at each 

temperature, the error in both mole fractions is within 1%. The test showed that for 

Figure 6-18: CARS spectra for Φ=0.2, acquired (blue line), and numerically saturated 

(red line)
160 

fuel-lean mixtures, spectra with detector saturation can still produce accurate results, 

and no significant bias is introduced. 

For fuel rich mixtures at high temperatures, the H2 S(5) line can potentially 

saturate the detector. Since the H2 lines are not involved in the temperature 

measurement, there is no significant effect on temperature measurements. In the 

previous section we have shown that the S(5) and S(6) lines are lumped together in 

the fitting algorithm. In the presence of an S(5) line saturating the detector, any 

information on the line intensity is lost. For these spectra the fitting algorithm

Figure 6-19: Error in temperature (a), N2 (b), O2 (c) for fuel lean cases as function of the 

temperature and of the ratio between the detector saturation threshold and the CARS 

signal intensity (α); d) error in N2 and H2 for fuel rich cases as function of the 

equivalence ratio when S(5) saturates the detector
161 

automatically excludes the line from the fitting and obtain the mole fraction from the 

S(6) line alone. Figure 6-19 d shows that the resulting error is below 1% in N2 mole 

fraction, and within ~2% in the H2. 

6.8 Spatial Resolution

In turbulent combusting flows, steep gradients are present and the spatial 

resolution affects the measurements. In principle, by changing the crossing angle, or 

reducing the beam focal spot, it is possible to adapt the CARS spatial resolution to 

resolve any flame thickness or turbulence micro-scale. In practice this is not possible 

because of the quadratic dependence of the signal intensity on the length of the 

measurement volume (Eq. 2-15) and of high perturbation effect occurring at high 

irradiance levels (Chapter 5). For this reason, in practical combustion application, the 

probe volume length is between 1 and 2 mm. 

Spatial averaging has several consequences. The flame front appears thicker and 

displaced from its true positions. The fluctuations in turbulent flames are reduced, 

because spatial averaging within the probe volume. In CARS measurements there are 

additional issues related to the strong temperature dependence of the signal. This 

causes a bias toward lower temperature, since colder gas molecules produce a 

stronger signal. When comparing the experimental CARS measurements to the CFD 

results, the spatial averaging effects need to be taken into account. To this purpose is 

necessary to experimentally measure the length of the CARS measurement volume
162 

The CARS measurement volume resembles an elongated cylinder, tapered at each 

end. The diameter of this cylinder is given by the minimum diameter of the laser 

beams at their crossing location and it is roughly 100 μm, much less than the length. 

Therefore averaging effects are negligible in direction orthogonal to the CARS signal 

propagation. The probe volume length for this experimental set-up has been 

determined by scanning a 200 μm microscope slide cover along the CARS 

measurement volume. The energies of all the beams were reduced so that the total 

peak irradiance was below the damage threshold of the cover material. CARS signal 

scales with the square of the density, therefore the signal in solids is orders of 

magnitude higher than in gases, and very low energies and integration volumes are 

sufficient. The CARS signal in glass is non-resonant. The microscope slide cover was 

scanned along the CARS measurement volume, ± 3mm from the location where the 

signal was maximum. 500 non-resonant spectra have been acquired at intervals of 

Figure 6-20: CARS spatial resolution
163 

100 μm, and then background subtracted, averaged, and integrated. Figure 6-20

shows in blue the CARS signal (normalized to the peak), as function of the position 

of the microscope cover. The dotted blue curve is a Gaussian fit of the data, with a 

FWHM of 1.1 mm. Acquiring data in a gas, the CARS signal recorded is the 

integrated signal over the whole measurement volume. The CARS measurement 

volume is often defined as the distance over which the CARS signal goes from 5% to 

95% of its total values. The red curve is obtained as piecewise integration of the 

CARS signal along the measurement volume. Based on the experimental data the L90 

probe volume length is 1.7 mm. 
164 

CHAPTER 7 -Laboratory-Scale Supersonic 

Combusting Jet

The DP-CARS system described in the previous chapters was designed to collect 

relevant data in supersonic combusting flow for computational fluid dynamics (CFD) 

validation and development. Experimental facilities have been designed to provide 

flow-fields relevant to CFD modelers and that can also be studied with the DP-CARS 

technique. [14, 27, 177] 

An axisymmetric supersonic-combusting, coaxial jet was chosen for this 

experiment. The facility provides a center jet of “vitiated” air, reproducing the 

sensible enthalpy of air entering the engine of a hypersonic vehicle flying at Mach 

numbers (Mf) between 5 and 7. The vitiated air is the product of combustion of O2-

enriched air with H2 that has the same O2 mass fraction of air, but high temperature 

and water. Nozzles with exit Mach number (Me) 1, 1.6, and 2 are available to provide 

flows with different effects of compressibility. Hydrogen or ethylene co-flow is 

available in order to generate a supersonic combusting free jet. As an alternative, N2

can be used as co-flow for non-reacting (mixing) studies. 

This flow-field addresses the issue of mixing and combustion in a supersonic 

flow, but without all the complications of an actual scramjet combustor, such as 

walls, mean-flow three-dimensionality, flow curvature and strong shocks. The 

symmetry reduces the number of points necessary to characterize the flow, and 

simplifies the numerical simulation. A free jet offers excellent optical access which is 

a highly desirable feature for laser diagnostics. The possibility of changing the Mach 

number at the nozzle exit, the enthalpy, and the fuel, allows for a large number of 
165 

possible test cases, as described in details in Ref.[14]. In this work the study is 

includes the effects of the compressibility (by varying Me), of the enthalpy (by 

varying Mf), and of the heat release (mixing versus combustion studies). The co-flow 

is either H2 or N2, and, when a H2 co-flow is used, the co-flow flame is always 

attached as shown in Figure 7-1. Visible and infra-red images of test-cases with 

ethylene co-flow and marginally attached or detached co-flow flames are shown in 

Ref.[14], but no CARS measurements were obtained at those conditions. 

Two different sizes of experimental hardware were developed; the laboratoryscale burner has a 1 cm center-jet nozzle exit diameter, and flow rates compatible 

Figure 7-1: Visible image of the laboratory-scale 

supersonic combusting free jet
166 

with a combustion diagnostic laboratory; a second large-scale burner was scaled up 

by a factor of 6.35 from the smaller device and tested in NASA Langley’s Direct 

Connect Supersonic Combustion Test Facility (DCSCTF). 

Previous works describe the large-scale supersonic burner, and both numerical 

[178] and experimental [72, 74] data have been published. The experimental data 

were obtained with a previous version of the DP-CARS instrument, and are limited to 

temperature measurements in a non-reacting case. This chapter and the next focus on 

the laboratory-scale burner. This chapter describes the experimental hardware, 

illustrates results of some numerical simulations of the flow-field, and discusses some 

experimental results (pressure measurements and IR images). The next chapter will 

illustrate the DP-CARS measurements.

7.1 Description of the Facility 

Figure 7-2 shows the burner and the nozzle sectioned along the symmetry plane 

and without bolts, tubes, spark plugs and other fittings. The hardware consists of an 

injection system, a premixing chamber, a water-cooled burner, and a ceramic nozzle 

surrounded by a co-flow nozzle. The H2 injection system consists of a stainless steel 

tube with an external diameter of 1/8th of an inch (3.175 mm) and a 0.084 inch (2.133 

mm) internal diameter. The tube terminates with the external wall inclined at 30 

degrees. The O2 enriched air flows in the annular passage created by the water-cooled 

injector (internal diameter 4.76 mm) and the H2 tube. The relative position of the H2

tube and the combustion chamber determines the length of the mixing chamber. This 

length is fixed to 40 mm in order to ensure adequate mixing before the gases enter the 
167 

combustion chamber, based on previous experiments and preliminary CFD 

calculations. In previous tests, a fully premixed flow entering the combustion 

chamber was attempted, but the flame propagated back to the injection system during 

combustion ignition, resulting in an unsafe operating regime. The injector is water 

cooled, although in the normal operation regime, the heat fluxes on its surface are 

small. The premixing chamber terminates with a sudden expansion where the 

reactants reach the combustion chamber. A spark plug placed at the entrance of the 

combustion chamber ignites the partially premixed gases. The combustion chamber 

consists of an exterior “jacket” and an interior “shell” between which water flows for 

cooling. The “shell” has an internal diameter of 25.4 mm and is 152 mm long. One of 

three interchangeable silicon carbide ceramic nozzles (one sonic, and two supersonic 

with Me=1.6 and 2 respectively) is mounted at the exit of the combustion chamber. 

The nozzles have a 10 mm exit diameter. The nozzle contours were designed using 

Figure 7-2: Schematic drawing of the laboratory-scale burner. Flow is left to right
168 

the method of the characteristics, assuming a ratio of specific heat capacities equal to 

1.3. 

An “annulus” surrounds the nozzle, holding it in place, and with the exterior wall 

of the nozzle it creates an annular, convergent “co-flow” nozzle. The co-flow gas is 

injected into a pre-chamber, which distributes the flow in the circumferential 

direction, and enters the co-flow nozzle through a narrow passage (0.5 mm wide). 

The internal diameter of the co-flow nozzle exit is 8 mm, the external 9 mm. The coflow and center jets are concentric and separated by the 3 mm wide, annular base 

region of the nozzle, orthogonal to the center jet. The co-flow jet is inclined by 15 

degrees towards the burner axis of symmetry. The “annulus” external walls are 

inclined at 60 degrees to improve the optical access.

The injector, the burner (shell and jacket) and the annulus are made of AISI 310 

stainless steel. The three nozzles are made of Hexoloy grade SA silicon carbide. This 

ceramic material was selected because of its elevated maximum operation 

temperature in air (2170 K), its high thermal conductivity (60 to 120 W/mK, which 

varies as a function of temperature) and its low thermal expansion coefficient (5.32 x 

10-6 mm/(mm K)). A high maximum operation temperature was essential in order to 

avoid an active cooling system for the nozzle. Ceramic materials can work at very 

high temperatures and can be shaped into complex forms, but are generally weak in 

tension and lack ductility; hence they are very sensitive to failure due to thermal 

tensile stresses. A large thermal conductivity, allowing a more uniform temperature 

across the component, combined with low thermal expansion, strongly reduces 

thermal stresses. 
169 

Thermal insulating gaskets inserted between the nozzle and the steel components 

are a simple and efficient way to minimize thermal gradients in the structure. Thanks 

to a low thermal conductivity, they assure a more uniform thermal profile in the 

ceramic nozzle, minimizing thermal stresses although producing an overall higher 

temperature. Cotronics ceramic paper 3000F, offering a thermal conductivity of 0.19 

W/(m K) and a thickness of 1/16th of an inch, was selected for this set of experiments. 

Grafoil gaskets are placed on both sides of the ceramic paper layer, to provide better 

sealing and to absorb thermal deformations. 

7.2 Numerical Analysis

Numerical simulations were critical in the design of this facility. Results from a 

preliminary parametric study conducted by Gaffney [177] were used to determine the 

injection angle of the co-flow, and the size of the rearward surface between the coflow and the center jet. Detailed numerical simulations of the internal flow-field were 

performed by me in order to determine whether the combustion would stabilize in the 

combustion chamber, whether the flow at the exit of the nozzle was uniform and free 

of shock waves, and to verify that material temperature and thermal stresses did not 

exceed the limit of the materials. [14, 27] The numerical analysis drove some critical 

changes to the design of the ceramic nozzle, and its integration in the burner.

Detailed numerical simulations also provide profiles of the flow properties at the 

nozzle exit and temperature distribution of the nozzle and annulus exit surfaces. 

These data constitute boundary conditions for numerical simulation of the external jet 
170 

and a benchmark for validation of non-intrusive laser diagnostics (such as dual-pump 

CARS), and other instrumentation. 

Accurate simulation of the internal flow-field requires knowledge of the wall 

temperature profile. In particular, the enthalpy of the gas mixture at the exit of the jet 

is affected by the heat loss through the burner and the nozzle. Heat transfer from the 

nozzle to the co-flow determines the temperature of the fuel.

Two types of calculations were performed: calculations of the internal flow of the 

burner using the CFD code VULCAN, [179] and finite element (FEM) thermal and 

stress analysis using Cosmoworks, a commercial code. The two calculations were 

coupled. A tentative wall temperature profile was assigned to the burner and nozzle 

internal walls as boundary conditions for the CFD calculation. As a result, heat fluxes 

distribution and bulk temperature profiles were obtained. These data were given as 

boundary conditions for the finite element thermal analysis that returned an updated 

wall temperature profile. The process was then iterated until convergence on the wall

temperature was achieved. 

Numerical simulations were performed for the three nozzles (Me=1, 1.6 and 2) 

and values of Mf=5, 5.5, 6, 6.5 and 7. H2 is used as co-flow in all the simulation. Only 

selected results are presented in this work. Additional results and details can be found 

in Ref.[27]. 

7.2.1 Thermal Analysis

The temperature distribution in the burner assembly was computed using 

Cosmoworks, a commercial finite element analysis code. Several heat transfer 
171 

mechanisms compete in determining the temperature distribution in the structure.

There is convection from the hot gas to the combustion chamber and nozzle, from the 

combustion chamber walls to the cooling water, and from the nozzle exterior walls to 

the H2 co-flow. There is conduction between the different components of the 

assembly, and there is radiation between the nozzle and the annulus wall, and to the 

ambient. The complexity of this thermal analysis goes far beyond the capabilities of 

the computational fluid dynamic code chosen. The finite element analysis software 

takes into account all the heat transfer mechanisms, except for radiation from the gas.

A temperature dependent model was generated for the Hexoloy grade SA silicon

carbide based on the specifications provided by the manufacturer. Finite elements 

analysis of the Cotronics ceramic paper used as gasket would have required an 

excessively fine mesh; hence, only its insulating effect is modeled by introducing a 

“thermal resistance”. In analogy with electrical resistance, the thermal resistance per 

unit of area is defined as d / k where d is the thickness of the gasket and k is the 

thermal conductivity. Radiation from the solid surface to the ambient and to other 

surrounding surfaces is computed. The emissivity of stainless steel is assumed 

constant and equal to 0.7, where a constant value of 0.92 is used for the ceramic. 

Temperature of the surrounding environment is assumed constant and equal to 300 K. 

The radiative contribution from the hot gas is neglected. Water-cooled surfaces are 

assumed at a constant temperature of 390 K, which is the approximate boiling 

temperature at the pressure of the water in the cooling passages. The heat convection 

is not modeled directly by the software, but a heat transfer coefficient and an 

adiabatic wall temperature, obtained from the CFD computations are required as 
172 

Figure 7-3: Convective heat transfer coefficient on the combustion chamber and 

nozzle internal wall for several values of exit and flight Mach number

0

1000

2000

3000

4000

-0.175 -0.125 -0.075 -0.025 0.025

axial distance (meter)

convection heat transfer 

coefficient 

(Watt/meter Kelvin)

Me=1.6 Mf=5.0

Me=1.6 Mf=6.0

Me=1.6 Mf=7

Me=1.0 Mf=6.0

Me=1.0 Mf=7.0

Me=2.0 Mf=6.0

Me=2.0 Mf=7.0

input. Heat fluxes from the gas to the burner and nozzle surfaces are obtained as

output of the VULCAN code. Convection heat-transfer coefficient is computed as

aw w

q h

T T = − (7-1) 

where q is the heat flux per unit area, Taw the adiabatic wall temperature, and Tw is the 

wall temperature. The adiabatic wall temperature is approximated to the total 

temperature of the gas outside the thermal boundary layer. It is a function of the axial 

distance and is an output of the CFD code. For the wall temperature, the profile 

obtained as output of the thermal analysis in the previous iteration is used. For the 

first iteration, a tentative constant temperature is assumed for the burner and a larger, 

constant temperature for the nozzle. The convection heat transfer coefficient is chosen 

over the heat flux as input for the FEM code because it decouples the fluid dynamics 
173 

of the flow from the wall temperature. Figure 7-3 shows the CFD computed 

convective heat transfer coefficient applied as a boundary condition to the FEM 

analysis on the internal walls for several cases of interest. The coefficient depends 

strongly on the exit Mach number (since the pressure, which strongly effects heat 

transfer, depends on exit Mach number) and only slightly on the enthalpy of the gas. 

Heat transfer coefficient profiles are also evaluated for the surfaces cooled from the 

co-flow. 

The axisymmetric nature of the problem allowed limiting the analysis to a quarter 

of the structure. Only the combustion chamber, the nozzle and the co-flow-chamber 

are modeled. The analysis is further simplified by eliminating bolts, spark plugs and 

other small features that have a negligible effect on the temperature distribution. A 

non-structured grid of 87175 nodes defining 56426 tetrahedical elements is used for 

all of the calculations. The average element size is 3.0 mm but smaller elements are 

used to describe areas of greater interest or larger temperature gradients such as the 

nozzle, the contact surfaces between the ceramic and the metal, and the region where 

the co-flow impinges on the exterior wall of the nozzle. A grid made of 193092 nodes 

is used to test for grid convergence. The temperature distribution obtained with this 

grid differs less than 1% from the one obtained with the original grid. 
174 

Figure 7-4 shows a typical temperature distribution obtained from the numerical 

analysis. The temperature in the combustion chamber is almost uniform in the axial 

direction, but presents large thermal gradient in the radial direction. The sudden 

change in temperature between the nozzle and the burner is due to the insulating 

material. Thanks to the large thermal conductivity of the silicon carbide, the nozzle 

temperature profile in the radial direction appears to be uniform, although the interior

is subject to a large heat flux from the accelerating gas, and the exterior is cooled by

the H2 co-flow. A larger thermal temperature difference can be seen in the axial 

direction, partially mitigated by the insulating gaskets. The “annulus” is heated by 

radiation from the nozzle and conduction from the combustion burner flange. 

Updated wall temperature profiles are obtained as output of the thermal analysis 

and are given as input to the CFD code. The FEM calculations are repeated and the 

process is iterated until the peak difference between wall temperatures at the same 

location, as evaluated in two successive iterations, is below 1%. Typically 3 iterations 

were sufficient to satisfy this criterion.

Figure 7-4: Temperature distribution for Me=1.6 and Mf=6. Flow is left to right
175 

Thermal analysis results show that all elements are at a temperature below their 

allowed threshold. For the nozzle thermal stresses were a concern because of the low 

tensile strength of the SiC. The thermal profile was used as input for a thermal stress 

analysis. In the original design, no insulation was interposed between the nozzle and 

the steel surfaces. Under these conditions the analysis predicted large thermal stress 

that would have caused nozzle failure. Ceramic paper gaskets, acting as a thermal 

barrier, and soft Grafoil gaskets absorbing some of the thermal expansion, were added 

to the design to reduce the thermal stresses well below the material threshold. 

Transient thermal stress analysis has been performed as well, showing that peak stress 

was reached after 15 seconds, and their amplitude was mitigated in presence of a coflow. For this reason the non-reacting tests have also been conducted with a co-flow, 

in this case with a N2 co-flow. In addition to provide critical information for the 

facility design, the thermal analysis also provides the temperature of the nozzle exit 

surface, which is a boundary condition for simulations of the external flow-field. 

7.2.2 CFD Analysis

All of the computational fluid dynamics results shown in this work were obtained 

by me using NASA Langley`s VULCAN, a CFD code that solves the Favre-averaged 

Navier-Stokes equations using a finite volume method on a structured grid. [179] 

The flow is assumed axisymmetric, and only a plane containing the axis is 

modeled. The structured grid, generated with a separate commercial code (Gridgen), 

has a total of 47225 points subdivided into air injection (61 × 29), H2 injection (49 × 

17), mixing chamber (113 × 45), combustion chamber (313 × 85) and nozzle (145 × 
176 

85). Grid points are clustered at the entrance of the combustion chamber, in the throat 

and expanding region of the nozzle. In the entire domain, the grid spacing near wall is 

such that the dimensionless wall distance (y

+

) is < 50 well within the domain of 

validity of wall matching functions (y

+

<100). [180] The grid is further subdivided 

into 15 blocks to take advantage of the VULCAN block level parallelization. A grid 

convergence study was performed and can be found in Ref.[27]. 

A 2-interval, 7-coefficient curve fit created by McBride from NASA Lewis is 

used to model the mixture of thermally perfect gases. There are seven species (O2, N2, 

H2, H2O, OH, O, and H) and the Langley 7-species 7-reaction model, included with 

the VULCAN distribution, was chosen to model the chemistry. Molecular viscosity is 

computed using the Sutherland’s law, whereas Wassiljewa’s law evaluates molecular 

conductivity. Inviscid fluxes are modeled using the Edwards low dissipation flux split

scheme with second order, kappa=1/3rd MUSCL interpolation and a “smooth” limiter. 

The flow is assumed fully turbulent and the Wilcox k-ω turbulence model is used. 

The turbulent Prandtl number is set to 0.89, and the turbulent Schmidt number is set 

to 0.5. 

Time integration is performed using a diagonalized approximate factorization 

scheme. Each domain is solved elliptically. A 3-level coarse-to-fine grid sequencing 

is implemented to accelerate convergence. The local Courant- Friedrichs-Lewy (CFL)

number is set to 4 for most of the calculations, and the time step is determined 

independently at each cell, based on its dimension and local flow properties.
177 

A quasi 1D analysis provides the inflow conditions for all the entries in the test 

matrix in terms of mass flow rate of H2, O2 and air. The CFD software requires mass 

fractions, total temperature (set to 300 K), velocity, static density, the turbulence 

intensity and the turbulent to molecular viscosity ratio. The product of the inflow 

velocity and static density is used to compute the mass flux and the mass flux is held 

constant. A supersonic outflow boundary with second order extrapolation of all 

variables is used for the simulation of the convergent-divergent nozzles. A subsonic 

outflow boundary condition with atmospheric backpressure is used for the sonic case. 

Figure 7-5: Total temperature (top) and OH mass fraction (bottom) distribution for 

Me=1.6 and Mf=7
178 

For all the walls, a temperature profile is assigned from the FEM calculation and the 

no slip condition imposed. 

Figure 7-5 shows the total temperature and the OH profile in the burner obtained 

from the CFD simulation for Me=1.6 and Mf=6. Flame-holding occurs at the tip of the 

H2 injection tube, and not at the entrance of the combustion chamber as originally 

expected. This was also verified experimentally. A thermocouple was inserted right 

after the exit of the H2 tube, paying special attention to minimizing the perturbation to 

the flow. The measured temperature immediately increased above the limit of the 

thermocouple showing that a flame was present in this region. 

A database of computed nozzle exit profiles was generated for several cases, 

providing boundary conditions for the simulation of the coaxial free-jet and a 

Figure 7-6: Static temperature profiles at the nozzle exit
179 

benchmark for validation of non-intrusive laser diagnostics (such as dual-pump 

CARS), and other instrumentation. All species mass fraction are uniform at the exit. 

Figure 7-6 shows temperature profiles obtained for the values of Me and Mf for which 

CARS data have been acquired. 

Table 7-1summarizes the numerical results obtained at the nozzle exit on the 

centerline for several parameters of interest, for the conditions in which CARS 

measurements have been taken. For the supersonic cases the exit pressure is slightly 

above atmospheric, therefore the jet is under-expanded; expansion waves will depart 

from the nozzle exit and a system of expansion and compression waves will be 

generated. 

Table 7-1: Centerline values at the nozzle exit 

7.3 Experimental Set-Up 

The laboratory-scale supersonic burner has been installed in the CARS laboratory 

at NASA Langley Research Center. Four Hastings flow-meters are used to measure

the mass flow-rates. A 2500 standard liter per minute (SLPM) flow-meter measures 

the air-flow, two 1000 SLPM flow-meters measure the H2 central jet flow, and the coflow, and a 300 SLPM flow-meter measures the O2 flow. The nominal accuracy of 

the flow-meters is 1% of the full scale, which is 25 SLPM for the air flow, 10 SLPM 

for H2 and 3 SLPM for O2. A set of experiments was performed to verify the factory 

flow-meter calibration. In each experiment 2 flow-meters were connected in series so 

Me Mf ρ(kg/m3

) u(m/s) M TKE(m2/s2) P(atm) T(K) O2 N2

1 7 0.188 787 0.952 8236 1.003 1681 0.230 0.569

1.6 6 0.283 1068 1.542 13708 1.030 1183 0.231 0.625

1.6 7 0.221 1189 1.538 17070 1.022 1458 0.231 0.569

2 6 0.345 1263 1.929 18816 1.063 1050 0.231 0.625
180 

that the same amount of flow was passing through them, and the measured flow rates 

were compared. Observed discrepancies in between the two readings were within 1% 

of the full scale. The flow-meters are calibrated for atmospheric pressure at the outlet, 

but during a facility run the pressure at the exit of the flow-meters is much higher (up 

to 140 psi). To verify the effect of the outlet pressure on the mass flow rates accuracy, 

two flow-meters were connected in series, with a valve in between so that the desired 

pressure at the exit of the upstream flow-meter is obtained, where the downstream 

was discharging to atmospheric pressure. Increasing the outlet pressure, the reading 

decreases, but the error is below 1% of the full scale. The flow-rates were not 

adjusted to correct for this effect.

Pressure measurements are taken by means of wall static taps in the combustion 

chamber (reported in Table 7-2) and of the co-flow nozzle. A FLIR Model SC4000-

MWIR infra-red (IR) camera, with sensitivity in the 3-5 μm range and an electronic

exposure time set nominally to 12 μs was used to obtain IR images of the jet. 

The laboratory-scale burner is mounted on a three-axis translation stage, remotely 

controlled through Labview. The capability of moving the flow field, rather than the 

optical set-up as in Ref.[72], simplifies the CARS instrument. 

Table 7-2: Mass flow-rates, computed and measured pressure for the combination of 

Me and Mf tested

Mass Flow Rates (SLPM) Total pressure (atm)

Me Mf Air O2 H2 H2 co-flow Φ Computed This work Ref.[27] 

0.75 7 310.8 115.4 135.0 120.0 0.5 N/A 1.35 N/A

1.00 7 426.1 123.9 185.1 120.5 0.5 1.745 1.68 1.75

1.60 6 939.8 182.8 266.6 483.0 1 4.015 4.0 4.06

1.60 7 741.9 221.0 322.3 419.1 1 3.915 3.88 3.93

2.00 6 1273.0 242.0 361.0 666.0 1 7.809 7.12 7.36
181 

The enthalpy of the vitiated air center-jet (expressed in terms of a nominal Mf) can 

be varied between 5 and 7 by changing the flow-rates of air, O2 and N2. For the sonic 

and subsonic case only for the Mf=7 case combustion is complete inside the 

burner.[27] Table 7-2 shows the flow rates required for the conditions tested for this 

work. The column labeled Φ indicates the equivalence ratio of a homogeneous 

mixture of only the H2 co-flow and the vitiated air center-jet. For the mixing case, 

120 SLPM of N2 replaces the H2 in the co-flow. The last three columns offer a 

comparison between the computed total pressure and measurements in the burner 

obtained during the test described in this work (during which CARS spectra were 

collected), and a previous set of tests described in Ref.[27]. The reduced total 

pressure could be caused by a reduced total mass flow rate, or reduced temperature 

Figure 7-7: Infra-red image of the supersonic combusting jet
182 

rise in the burner. Both could be consequences of inaccuracies in the mass flow rates. 

Measurements of the nozzle throat diameter using calibrated pin gauges, revealed that 

the Me=2 nozzle throat is between 1.9% and 2.2% larger than the design value, 

explaining the large discrepancy in the total pressure for that case. Throat erosion was 

considered a possible cause for the total pressure reduction, but measurements 

performed after this test showed no difference from what was reported in Ref.[27] 

IR-images of the free combusting jet for various combination of Me and Mf were 

collected. Figure 7-7 shows an IR image of the supersonic-combusting free jet. The 

flame is attached to the burner at the interface between the co-flow and the ambient 

air, and this is the case for all the test conditions of Table 7-2. For the case with 

Me=1.6 and Mf=7 auto-ignition occurred; in the other cases the flame was ignited with 

an electric spark lighter. Once ignited, the flame propagated upstream in the co-flowambient-air mixing layer, attaching to the co-flow nozzle exit. Local extinction is 

visible less than two nozzle diameters from the exit. The image shows asymmetry 

with respect to the centerline. As it will be shown in Chapter 8, the co-flow rate is not 

uniform through the co-flow nozzle. The asymmetry could be caused by small errors 

in centering the nozzle with respect to the annulus, thereby increasing the co-flow 

nozzle exit area on one side, and reducing it on the other. Efforts were made in 

centering the nozzle correctly, and visual inspection did not show significant 

asymmetry, yet the IR image and the DP-CARS measurements still show asymmetric 

co-flow. Another possible explanation for the asymmetry is that the center jet nozzle 

exterior surface, which forms the interior surface of the co-flow nozzle, is slightly 

asymmetric. 
183 

CHAPTER 8 - DP-CARS Measurements in the 

Laboratory-Scale Supersonic Combusting 

Jet

8.1 Introduction

The dual-pump CARS (DP-CARS) instrument has been applied to obtain 

measurements in the flow-field provided by the laboratory-scale supersonic burner 

described in the previous chapter. The goal of the test was to demonstrate the 

capability of the DP-CARS instrument in a flow relevant to the study of supersonic 

combustion, and to provide a database for the validation of computational fluid 

dynamics (CFD) models applied in the simulation of compressible mixing layers. 

DP-CARS provides instantaneous, spatially resolved, simultaneous measurements 

of temperature and mole fractions. Mean, variances, co-variances and histograms are 

obtained from the single shots measurements, providing the CFD modelers with 

quantities never measured before in similar flows. Several test cases have been 

considered, both reacting and not, to isolate the effects of the compressibility, of the 

enthalpy, and of the heat release, on mixing in a compressible shear layer. 

This chapter begins with a brief review of published works on compressible 

mixing layer to provide the necessary background to correctly interpret the DP-CARS 

measurements. The test matrix is described, and the challenges encountered during 

the data acquisition discussed. Measured nozzle exit profiles are compared to the 

results of the numerical simulations presented in Chapter 7. DP-CARS measurements 

for the mixing case are illustrated and when possible compared to previously 
184 

published results. Finally, DP-CARS data for the combustion cases are presented, and 

the role of the heat release on mixing discussed.

8.2 The Compressible Shear Layer

The flow provided by the facility described in chapter 7, was developed to 

provide further insight in the physics of compressible mixing layer. This is a key 

issue in designing a scramjet engine, and adequate CFD models needs to be 

developed to compute these flows and validated. Published experimental studies of 

compressible shear layers involve several techniques, including Pitot pressure 

measurements, [13-19] gas sampling, [22] laser Doppler velocimetry, [15, 181] 

Schlieren imaging [14, 15, 28], planar laser-induced fluorescence (PLIF) and planar 

laser Mie scattering (PLMS). [182] To my knowledge, this is the first successful

application of the DP-CARS technique to measurements in a compressible shear 

layer. In this section, the discussion is limited to key aspects of the flow physics, to 

provide a framework for the interpretation of the DP-CARS results. In depth reviews 

of works on compressible shear layers can be found in Ref. [183] and [184]. 

Early experimental studies of supersonic jets expanding in a quiescent medium 

are summarized in a review work by Birch. [185] All those experiments show a 

decreasing spreading-rate of the shear layer with increasing Mach number. The 

spreading-rate reduction was attributed to the lower density ratio associated with the 

higher Mach number. Brown [186] investigated the effect of the density ratio on lowspeed planar shear layers by using different combinations of gases to simulate density 

ratios similar to what observed in supersonic shear layers. The study showed that the 

effect of a decrease in the density ratio on the spreading-rate is much smaller than 
185 

measured in compressible shear layers. Brown showed that compressibility effects, 

and not changes in the density ratios were responsible for the reduced spreading-rate 

reported in Ref. [185]. 

Ortwerth [187] and Oertel [188] observed large coherent structures in supersonic 

shear layers and suggested that instabilities of these large scale structures govern the 

growth of the shear layer. Experimental studies [15, 181, 182] show that for 

increasing compressibility, these coherent structures become more three-dimensional, 

less coherent and the turbulent fluctuations are reduced. Since these large structures 

are critical for the mixing, compressibility needs to be defined in a reference system 

moving with these coherent eddies. This concept was first introduced by Bogdanoff 

[189] and Papamoschou [19] with the definition of a compressibility parameter, the 

convective Mach number (Mc), that is the Mach number of the jet in a reference 

system moving with the large eddies. The definition of this quantity, introduced for 

planar shear layers between two flows at different speeds, can be extended to an 

axisymmetric jet spreading in a quiescent gas. Under the assumption of null total drag 

force on the eddies, the convective Mach number can be expressed as: 

1 1

2 4

(1 )

(1 )

j u

c

M

M

ρ γ

λ

λ λ

−

− =

+

(8-1) 

where Mj is the center jet Mach number, λu, λρ, λγ are the ratios of velocity, density and 

specific heat ratio between the freestream (numerator) and the center jet 

(denominator). 

Papamoschou [19] observed that the rate of growth of the shear layer thickness 

(based on Pitot measurements), normalized by its incompressible value, drops 
186 

drastically as the convective Mach number is increased up to 0.8, and then it stays 

roughly constant. This also implies that at higher convective Mach numbers, mixing 

is reduced. 

Slessor [190] plotted the results of several experimental studies [15, 16, 19, 28, 

181] as function of the convective Mach number, and showed that the data do not 

collapse well. In particular, larger discrepancies between the expected behavior and 

the experimental values were found in presence of large density ratios and when one 

of the two streams is subsonic. Based on the observation that the compressibility is an 

energy transfer mechanism (kinetic and thermal), Slessor proposed an alternative 

compressibility parameter Π defined as: 

1

max i

i

u

a

  γ − Π =   ∆

   

(8-2) 

where a is the speed of sound, γ the ratio of specific heat, and Δu the speed difference 

between the two gases. The quantity in brackets is evaluated for both streams, and the 

greater of the two values is selected in computing Π. The parameter coincides with 

the convective Mach number for density ratios close to 1, but differs largely (3 times 

larger than Mc for λs=0.1 or 10) otherwise. Much better collapse of the data is 

achieved when using this parameter as shown in Figure 4 of Ref.[190] . The flowfields examined in this chapter have velocity ratio close to zero (supersonic jet in 

quiescent air), and density ratio between 4 and 7; therefore, the compressibility 

parameter Π is a better choice than the convective Mach number to evaluate the 

compressibility effects. 
187 

All the experimental works agree that increasing the compressibility reduces the 

spreading-rate, makes the coherent structure increasingly three-dimensional, and 

reduces the turbulent fluctuations. Insight on the fundamental mechanism driving the 

observed phenomena has been provided in recent years by direct numerical 

simulations (DNS) as the one performed by Pantano [191]. In this work, the authors 

show that a reduction in turbulent production is responsible for the decrease in the 

spreading-rate. The reduction in turbulent production is ultimately caused by the 

finite speed of sounds in compressible flows, which limits the propagation of pressure 

fluctuations across the shear layer, and disrupts the agglomeration of the turbulent 

eddies.[191] 

The flow-field complexity increases in presence of chemical reaction and heat 

release. In the incompressible case, the dominant effect is displacement caused by the 

heat release. The heat release slows the development of the large-scale structures and 

the resulting entrainment of the reactants. The spreading-rate and the turbulent shear 

stresses decrease with increasing heat release for both incompressible and 

compressible flows. These effects have been observed experimentally[192] and in 

DNS simulations.[193, 194] 

Publicly available experimental data for reacting compressible shear layers are 

scarce, and more data are desirable to improve RANS and LES models. Accurate 

quantitative measurements of multiple parameters, capable of providing converged 

statistics (mean, variances, and co-variances) are needed. The data set collected with 

the DP-CARS instrument described in the previous chapters is the first containing 
188 

simultaneous measurements of temperature and all major species mole fraction in a 

compressible turbulent shear layer. 

8.3 DP-CARS Data Acquisition and Test Matrix

DP-CARS data have been acquired for 5 combinations of exit Mach number (Me) 

and flight Mach number (Mf), for both mixing and combustion cases as illustrated in 

Table 8-1. 

Table 8-1: Test cases for DP-CARS measurements. M indicates a mixing test case, C a 

combustion test case.

Mf↓\Me→ 0.75 1 1.6 2

6 M/C M

7 M M/C M/C

Mf is varied by changing the mass flow-rates of air, O2 and H2 in the burner, Me, 

by selecting the appropriate SiC nozzle, and mass flow-rates. The three nozzles differ 

by throat area, but have the same exit diameter (10 mm). The co-flow was either H2

(combustion case) or N2 (mixing case). For the combustion case, the H2 co-flow was 

set to be in stoichiometric ratio with the O2 from the center jet. The N2 co-flow was 

constant and equal to 120 SLPM in all the mixing test cases. 

The test cases were selected so that the effect of each variable (compressibility, 

enthalpy, and heat release) could be isolated. For the lower exit Mach numbers 

(Me=0.75 and 1) combustion in the burner was not complete for Mf<7 as observed in 

Ref.[27]. A combustion test case for Me=2 and Mf=6 was attempted but the large 

amount of heat released prevented successful data acquisition. (Warm combustion 
189 

products mixed with air recirculating within the laboratory caused excessive beam 

steering, preventing acceptable CARS data quality, and radiant heating of the optical 

system caused problems with maintaining optical alignments. See discussion Section 

8.4.) 

The laboratory-scale supersonic burner is mounted on a three-axis translation 

stage, which allows changing the position of the measurement volume with respect to 

the flame. As shown in Figure 8-1, measurement locations reported here are in a 

reference system having the origin at the center of the nozzle, at its exit plane. The z

axis is orthogonal to the nozzle exit plane, the y direction parallel to the Nd:YAG 

laser beam. Data have been acquired along five lines parallel to the x-axis and at z = 

1, 15, 35, 65 and 100 mm downstream of the nozzle exit, as shown in Figure 8-1. This 

orients the CARS probe volume orthogonal to the direction of the maximum 

temperature gradient, reducing spatial averaging effects (see Chapter 6 and 8). In 

addition, data have been collected along two lines parallel to the y-axis and 1 mm and 

Figure 8-1: Infra-red image of the supersonic combusting jet. Green circles are the 

measurement locations
190 

100 mm downstream of the nozzle exit. Data along this direction are obtained to 

evaluate the effect of the probe volume length on the measurements, and to evaluate 

the symmetry of the flame. The number of points varies for each line between 27 and 

39. Each location along the z = 65 and 100 mm lines and along the centerline (x=0) is 

visited 4 times (replications), where points along the z = 1, 15 and 35 mm lines were 

visited only once. For each replication, 250 single shot spectra were acquired. For 

each condition, ~ 100,000 spectra were collected. Closer to the nozzle exit, the 

accuracy of the means, variances and co-variances computed from the CARS 

measurements is limited by the steep gradients, rather than by the sample size (error 

associated to the spatial averaging larger than sampling error), therefore a single 

replication was deemed sufficient. Further downstream the gradients are smoother, 

CARS measurements more accurate, and therefore increasing the sample size was 

helpful in obtaining better statistics. For given test conditions (Me, Mf, mixing or 

combustion) the test matrix is fully randomized. All the test cases using the same 

nozzle were done sequentially to avoid disassembling and reassembling the burner 

several times. 

Data acquisition is controlled through a Labview graphical interface, which drives 

the translation stage and the CARS instrument (laser, camera, pulse generator, 

rotation stage for the wave-plate). Before starting the supersonic jet, background 

spectra were collected in ambient air and in argon, providing the spectra for the 

background subtraction and non-resonant normalization described in Chapter 3. The 

origin of the reference system is determined experimentally immediately before the 

data acquisition. The distance between the nozzle exit and the measurement volume 
191 

was determined by placing a piece of black-painted aluminum on the nozzle and 

marking it with the laser. A micrometer was then used to determine the distance 

between the nozzle exit and the laser mark. With the supersonic burner running at the 

test conditions, CARS signal intensity in the O2 spectrum was recorded at several 

locations along the x and y-axis, 1 mm from the nozzle exit. Since O2 is not present in 

the co-flow, this allows determining the location of the nozzle centerline, with respect 

to the CARS measurement volume. The process was automated, and was performed 

daily before starting the data acquisition. The accuracy of this approach is within 1 

mm. Once the origin had been determined, the DP-CARS data acquisition started. 

The Labview software reads a position from a text file containing all the randomized 

locations, moves the translation stage to that location, reduces the energy of the 

Nd:YAG laser to avoid detector saturation if necessary, acquires 250 single shots and 

then moves to the next location. No further input from the operator is needed once the 

acquisition has begun. The automation of the data acquisition process was critical in 

increasing the amount of data that could be collected in a single test day. Once the 

test matrix was completed, background spectra and CARS spectra in argon were 

acquired again to take into account shift in the broadband dye laser spectrum (details 

and limitation of this approach are illustrated in Chapter 3). A typical test lasts 4-5 

hours during which the burner operates continuously. The test was monitored from a 

control room across a hallway from the laboratory. Here the operator could monitor 

the peak CARS signal intensity and the advancement of the test along the test matrix 

(through the Labview interface), the crossing and focusing of the beams through the 
192 

beam-viewing system placed after the measurement volume, the correct operation of 

the burner and the translation stage through the IR camera. 

The collected data were analyzed as described in Chapter 3, and returned 

instantaneous measurements of temperature, and N2, O2 and H2 mole fractions. A 

post-processing algorithm written in Matlab rejects spectra having a poor fit, based on 

a quality-of-fit parameter obtained in output from the fitting code. The postprocessing algorithm merges all the data collected at a single location, and computes 

mean, standard deviation, covariance and skewness for all the measured quantities. A 

single text file containing the measurement locations and all the computed statistics is 

obtained in output for each test case. 

8.4 Additional Challenges in DP-CARS Data Acquisition in the 

Laboratory-Scale Supersonic Free Jet

Data acquisition in the supersonic jet presented some additional challenges 

compared to acquisition in the steady, laminar Hencken burner flame. Beam steering 

effects due to turbulence and vibrations were expected, and the beam shaping 

technique demonstrated in Chapter 3 was implemented to mitigate this issue. Figure 

8-2 is a video of typical motion of the laser beams traversing the supersonic jet. The 

camera is imaging the three beams, slightly before their intersection, so that the 

Nd:YAG (the elliptical beam on the right) is separated from the overlapped 

broadband (in red) and the narrowband (blue-white color in the image). The video 

shows movements of the overlapped beams with respect to the Nd:YAG that would 

have prevented the beam from crossing and generate the CARS signal if the Nd:YAG 
193 

beam was not elliptical. The axis ratio used for the Nd:YAG beam for this test is ~4:1 

and the data yield (percentage of the shots that produces acceptable measurements) is 

97% for the mixing case, and 95% for the combustion case. The test is a successful 

application of the beam shaping technique in an actual test environment. 

 In addition to the random motion, a drift of the laser beams’ alignment with time

was observed. The large amount of heat released by the supersonic jet caused an 

increase of the room temperature and of all optical elements in the proximity of the 

jet. Changes in temperature of the mirrors cause steering of the beams, degradation of 

the beam overlap, and consequent signal reduction. (Note that the signal reduction 

does not change the results, since it is the relative intensity of the CARS spectrum 

that matters, not the absolute.) Such drift was monitored using the beam viewing 

system placed after the measurement volume, while the Labview interface was 

monitoring the CARS signal level. Periodically the test had to be interrupted, so that 

the relative position between the lasers could be restored. Using the Nd:YAG beam as 

Figure 8-2: Beam steering caused by turbulence in the 

laboratory-scale supersonic free jet. 

Click on the figure to start the video
194 

reference, the dye lasers position was restored with respect to this beam by remotely 

controlling two mirrors (mounted on New-Focus pico-motors mounts); one is placed 

on the laser cart and adjusts the broadband dye laser, the other which adjusts the 

superimposed dye lasers is placed immediately before the focusing lens. Note that a 

sideways drift of the location of the measurement volume with time was not corrected 

by this system, though the error induced by this drift is estimated to be a fraction of 

the length of the probe volume. 

Analysis of the CARS data was the same as described in Chapter 3. The long test 

duration, the increase in the room temperature, and in the dye temperature, were 

responsible for changes in the dye lasers spectral output. Chapter 3 includes a detailed 

discussion on the consequences of the spectral changes in the broadband dye laser 

profile, how it affects the measurements accuracy, and how to minimize its effects.

The frequency of the narrowband dye laser changed in time during the data 

acquisition because of the temperature increase in the room. The shift was monotonic, 

and changes up to 0.8 wavenumbers were observed for the combustion cases. The 

frequency difference between the two pump beams (the Nd:YAG and the narrow 

band dye laser) is not a fitting parameter, but an input required for the theoretical 

library. For this reason for each test day, four libraries of theoretical spectra were 

generated, with different values of the offset between the two pumps, one for each 

hour of testing. 
195 

8.5 Measurements at the Nozzle Exit

In this section the results of measurements taken at the most upstream location (z 

= 1 mm) for |x| < 5 mm are described. Measurements at the centerline are relatively 

steady and are used to evaluate the repeatability of the measurements, which is useful 

for determining their capability to resolve turbulent fluctuations. Experimental 

measurements along x are compared to their numerical counterparts. Experimental 

profiles along y are shown to illustrate the effect of the CARS probe volume length 

on the measurement accuracy. A strategy that uses the nozzle exit profile to obtain a 

better estimate of the measurement locations is described.

For each test condition, the location on the centerline, 1 mm downstream of the 

nozzle exit is visited 4 times (4 replications) and 250 single shot spectra are acquired 

at each passage. The length of the CARS probe volume is not a significant issue since 

numerical simulations indicated that the temperature at the nozzle exit is uniform. 

Table 8-2 shows the average and the standard deviation of temperature, N2 and O2

Table 8-2: Measurements and confidence intervals at the nozzle exit on the centerline 

for Me=1.6, and Mf=7, and H2 co-flow. The values in brackets are the 1% confidence 

interval

Run Tav(K) Tsd(K) N2av(%) N2sd(%) O2av(%) O2sd(%)

A 1392±11 63 [57,72] 49.9±0.3 2.0 [1.8, 2.3] 20.2±0.2 1.2 [1.1, 1.4]

B 1394±10 62 [56, 70] 50.1±0.4 2.9 [2.6, 3.2] 20.0±0.2 1.3 [1.2, 1.5]

C 1387±10 63 [56,71] 50.6±0.4 2.8 [2.5, 3.1] 20.0±0.2 1.1 [1.0, 1.3]

D 1407±10 60 [53, 68] 50.3±0.5 3.0 [2.7, 3.4] 20.1±0.2 1.3 [1.1, 1.4]

Pooled 1395±25 62 [59, 67] 50.2±0.8 2.7 [2.6, 2.9] 20.2±0.3 1.2 [1.2, 1.3]
196 

mole fraction computed for each replication (250 single shots) for the combustion 

case with Me=1.6 and Mf=7. The data span an acquisition time of approximately 4 

hours. The values following the means in Table 8-2 are the 99% confidence intervals 

defined for the mean as:[195] 

1 /2 t sn / ± −α (8-3) 

where n is the number of shots, s the estimated standard deviation, t1-α/2 is the 99.5th

percentile of a t distribution with n-1 degrees of freedom. Similarly for the standard 

deviation the confidence interval is given by:[195] 

2 2 2 2

1 /2 /2 [( 1) / ,( 1) / ] ns ns − − χ χ −α α (8-4) 

where χ

2 is the chi-square distribution with n-1 degrees of freedom. Analysis of 

variance (ANOVA) shows that the temperature between runs is significantly different 

(for a significance level α=1%) but there is no significant difference between the mole 

fraction measurements. Although there is a statistically significant difference between 

the temperatures measured in each run, there is no trend with time. Small changes in 

the mass flow-rates probably cause the run-to-run variations. The measured standard 

deviations instead are independent of the time. The row labeled “pooled” contains the 

average over all the measurements taken at a single location. Since there is a 

significant difference between the runs, then it would be incorrect to compute the 

interval of confidence as in Eq. (8-3) using as n the total number of acquisition. 

Instead the 1% interval of confidence is based on the 4 averages over each run, and is 

larger (2.5 times) than that computed over a single run, as expected since it includes 

the variation between runs. For the rest of this work, unless specified, “pooled” 

averages will be shown.
197 

The variance of the pooled results can be expressed as sum of the variance due to 

variations between runs ( 2 σ Between ) and within a single run 2 σ Within . The variance within a 

single run can be further decomposed in the contribution due to the turbulence in the 

flow and the contribution due to instrument error. 

22 2 2 2 2

Pr ( ) σσ σ σ σ σ Total Between Within Between Turbulence ecisi = += + + on (8-5) 

For the data of Table 8-2 2 2 σ σ Between ~ 1.5% Total . Based on measurements in the Hencken 

burner, for a temperature of 1355 K and an O2 mole fraction of 21%, the temperature 

standard deviation due to the instrument precision is 25 K. At the centerline, the 

instrument precision is responsible for ~ 15% of the total variance. The estimated 

temperature standard deviation due to the turbulence alone is 57 K. For the N2 mole 

fraction the total standard deviation is 2.7 % of the total mole fraction, where in the 

Hencken burner for similar conditions it was 2.1%. Turbulence contributes to 45% of 

the total variance and the estimated standard deviation of N2 due to the turbulence is 

1.8%. Similarly for O2 the turbulence contribution to the variance is 76% of the total 

and the standard deviation is 1.1%. These results show that the DP-CARS instrument 

is capable of resolving the temperature fluctuations due to the turbulence at this 

location, but it performs worse for the mole fraction fluctuations. 
198 

Table 8-3 is analogous to Table 8-2 but obtained for the mixing case. The two 

data sets were collected on different days. The average temperature is ~22 K lower 

and the temperature standard deviation is the same. Mole fraction of N2 and O2 are 

within the 1 % interval of confidence determined for the combustion case. This shows 

that there is no significant difference in the pooled statistics between data taken in 

different days. 

Figure 8-3 shows the temperature profiles of the center jet measured 1 mm from 

the nozzle exit and compare it to the CFD results presented in the previous chapter. 

The experimental results are systematically lower (~5%) than the prediction and the 

curvature is greater. The lower exit temperature could indicate that the numerical 

solution underestimated the heat transfer, or that the actual equivalence ratio in the 

burner differs from its nominal value. The higher curvature is likely a consequence of 

the CARS probe volume length; 90% of the CARS signal is generated over a length 

of 1.5 mm, which is longer than the shear layer between the center-jet and the coTable 8-3: Measurements and confidence intervals at the nozzle exit on the centerline 

for Me=1.6, and Mf=7, and N2 co-flow. The values in parenthesis are the 1% confidence 

interval

Run Tav (K) Tsd (K) N2av(%) N2sd(%) O2av(%) O2sd(%)

A 1382±11 64 [57,72] 49.2±0.4 2.7 [2.4, 3.0] 19.9±0.2 1.2 [1.1, 1.4]

B 1372±10 62 [55, 70] 50.4±0.4 2.9 [2.6, 3.3] 20.0±0.2 1.3 [1.1, 1.4]

C 1373±10 60 [56,71] 50.4±0.5 3.1 [2.8, 3.5] 20.1±0.2 1.1 [1.3, 1.6]

D 1365±10 62 [54, 68] 49.9±0.4 2.7 [2.4, 3.0] 20.3±0.2 1.3 [1.2, 1.5]

Pooled 1373±20 62 [55, 70] 50.2±0.8 2.9 [2.7, 3.1] 20.1±0.4 1.3 [1.2, 1.4]
199 

flow. CARS signal is a strong function of temperature, with much stronger signal 

generated in the colder co-flow and quiescent air region. 

The measured temperature is not an average along this distance, but it is biased 

toward lower values of temperature. As consequence of the CARS probe volume 

length and of the signal temperature dependence, the instrument artificially decreases 

the steepness of the flame front. The closed symbols in Figure 8-3 are measurements 

for variable x, having the probe volume oriented in direction orthogonal to the 

temperature gradient. Open symbols are measurements along y, with the probe 

volume oriented in the direction of the maximum gradient, therefore more subject to 

Figure 8-3: Comparison of numerical and experimental temperature profiles at the 

nozzle exit for 4 combinations of Me and Mf
200 

the averaging effect. The measurements are overlapped in proximity of the centerline, 

but moving toward the edge of the jet, temperatures taken along y (open symbols) 

drop more quickly because the probe volume includes larger portions of the co-flow. 

Figure 8-3shows that the DP-CARS measurements are inaccurate in presence of steep 

gradients, tend to overestimate the thickness of the shear layer, and not predict 

correctly its location. Orienting the probe volume in direction orthogonal to the 

temperature gradient mitigates this deleterious effect, thus most of the CARS data 

were taken in lines along x. 

In turbulent flows, the measurement fluctuations are indicative of the turbulence 

level. Since the probe volume cannot resolve the smallest turbulence scales, the 

CARS signal will integrate over these finer structures; colder regions produce 

stronger signal, therefore the measured temperature is biased toward lower values.

Furthermore, the spatial averaging reduces the intensity of the measured fluctuations. 

[196] Also mole fractions are biased toward the mole fractions associated to the lower 

temperature. 
201 

Figure 8-4 shows the nozzle exit profiles for the mole fraction measurements. In 

terms of total mole fraction the measured N2 is systematically lower, (up to 1%), 

where O2 is systematically higher (up to 1.5%). Measurements in the Hencken burner 

showed accuracy within 0.5% for O2 and within 1% for N2. Errors in the division by 

the non-resonant spectrum can potentially cause inaccuracies up to 1% on O2 and 

2.5% on N2, but no evidence of incorrect normalization was found in the fitted 

spectra. The lower burner pressure (see Table 7-2) and exit static temperature, and the 

increased O2 mole fraction suggest that less O2 burned in the burner. Errors in the 

mass flow-rates are the most likely cause for the discrepancy. 

Figure 8-4: Comparison of numerical and experimental mole fraction profiles at the 

nozzle exit for 4 combinations of Me and Mf
202 

In order to compare experimental and computational results, it is necessary to 

know the exact location at which the data have been collected. In section 8-3 the 

procedure to determine the location of the nozzle center in the reference frame of the 

translation stage is described. The algorithm relies on quickly analyzing just a few 

samples of unprocessed spectra. This can potentially lead to errors of 1 mm or more. 

The profiles of temperature and mole fractions obtained near the nozzle exit, 

combined with the assumption of symmetry of the center jet allow for a more precise 

determination of the nozzle center. An improved estimate of the origin (x=0, y=0) 

location with respect to the actual centerline can be obtained by fitting temperature 

profiles in the core of the jet (over a region of ±3.3 mm for the mixing case, ±4.6 mm 

for the combustion case) with a quadratic function; the vertex of the fitted parabola 

provides the actual location of the centerline. As an example, for Me=1.6 and Mf=7 

the values determined along x are -0.016 mm for the mixing, and -0.05 for the 

combustion, therefore they are negligible. On the other hand, along y the centerline is 

0.55 mm from the origin of the reference system for the mixing data, and 0.06 mm for 

the combustion data. This approach allows accurate determination of the location of 

the measurement points, for a more faithful comparison to CFD simulations. Based 

on the results of this approach, the data presented in this work have been shifted so 

that the centerline coincides with the z axis of the reference system.

8.6 Mixing Study

This section discusses the measurements acquired for the mixing case, that is for a 

constant flow of 120 SLPM of N2, and variable Mf and Me. Since the co-flow has low 
203 

speed, and small total mass flow rates, the flow can be treated as jet in quiescent air. 

Four exit Mach numbers are considered (0.75, 1, 1.6 and 2) and for Me=1.6, flight 

Mach number (Mf) of 6 and 7 are compared. Parameters that characterize the flow are 

the velocity ratio λu, the density ratio λρ, the convective Mach number (Mc) and the 

Slessor compressibility parameter Π. Table 8-4 shows the values of these parameters 

for the test cases considered. The velocity ratio is 0, assuming that the supersonic jet 

is mixing with quiescent air. The mean values obtained from the DP-CARS 

measurements are shown, and compared to what it was expected, based on the 

published results discussed in section 8-2. The spreading-rates are estimated, and the 

effect of compressibility and of the density ratio is identified. Standard deviations and 

co-variances plots are presented and discussed. 

8.6.1 Mean Values

Figure 8-5 shows the DP-CARS average measurements of temperature and mole 

fractions, as a function of the radial distance x at different heights, z, for the two 

Table 8-4: Values of the velocity ratio (λu), density ratio(λρ), convective Mach number 

Mc, and Slessor`s compressibility parameter Π for the conditions tested

Me Mf λu λρ Mc Π

0.75 7 0 6.5 0.52 1.33

1 7 0 6.2 0.7 1.73

1.6 6 0 4.0 1.04 2.25

1.6 7 0 5.2 1.08 2.53

2 6 0 3.7 1.28 2.63
204 

mixing cases with Me=1.6. The black triangles are for Mf =6 (Mc=1.05), the red circles 

for Mf=7 (Mc=1.08). The average at each location is computed over the total number 

of replications and repetitions (pooled average). The error bars represent ± one 

standard deviation, and include fluctuations due to the instrument precision, the 

turbulence in the flow, and the small contribution due to the run-to-run variations, as 

discussed in the previous section. The exit temperature of the center jet is higher for 

Mf=7 because of the higher total enthalpy and so is the density ratio (λρ=5.2 for Mf=7, 

4.0 for Mf=6). For Mf=7 the heat transfer from the flow inside the burner to the SiC 

nozzle and to the co-flow (acting as coolant) is larger than for Mf=6; therefore the N2

co-flow is hotter for the higher enthalpy case. There is no significant difference in the 

O2 mole fraction between the two cases. The N2 mole fraction in the center jet is 

lower and H2O higher for Mf=7 because more H2 had to be burned to achieve the 

desired enthalpy. No H2 lines were visible in the spectra, indicating that the 

combustion is complete at the nozzle exit, as predicted from the CFD simulation. The 

co-flow is pure N2, but the CARS system measures mole fraction of ~97%, and O2

mole fraction of ~1%. This is a systematic error of the DP-CARS system. A likely 

cause of this error is that the fitting algorithm does not allow for mole fraction greater 

than 1, and uses lower order interpolation in proximity of 1, biasing the error toward 

lower mole fraction. Also small errors in the background subtraction can contribute. 

At 1 mm from the exit, the boundaries between the co-flow jet and the center jet and 

between the co-flow and the ambient air are well defined. Notice that the temperature 

of the co-flow jet is not exactly symmetric, but it is lower for positive x. The co-flow 

is asymmetric with higher mass flow rates for positive values of x. 
205 

Figure 8-5: Average temperature and mole fractions at different heights for Me=1.6 and 

Mf=6 and 7. Error bars indicate ± one standard deviation
206 

At 15 mm downstream of the nozzle exit, the center of the supersonic jet is 

largely unaltered, although a growth of the shear layer is detectable. The low speed 

N2 co-flow, as expected, mixes more efficiently with the ambient air, as can be 

observed in the N2 and O2 mean profiles. O2 mole fractions up to 15% are recorded 

because of the entrained air in the co-flow jet. The asymmetry in the co-flow 

volumetric flow rates is evident from the N2 and O2 profiles. Water, present only in 

the center jet, is a good indicator of jet spreading and mixing. The DP-CARS 

instrument is unable to measure water vapor directly, but the water mole fraction is 

computed by subtracting the measurements of N2 and O2 from one, assuming that all 

other species are negligible. The instrument accuracy in measuring mole fractions is 

lower at low temperature, where the O2/N2 ratio is measured incorrectly (see Chapter 

6) and the sensitivity to background subtraction is higher. This problem is more 

evident for the Me=1.6, Mf=6 case. It was the first data set acquired, and not enough 

background spectra were collected. 

Further downstream, 35 mm from the nozzle exit, the co-flow is no longer 

distinguishable from the entrained air. The shear layer is growing, but the mixing is 

limited to the outer region of the supersonic jet. The asymmetry is no longer evident, 

suggesting that the co-flow constitutes only a small portion of the entrained mixture.

For z > 65 mm the entrained mixture has reached the centerline, causing a 

reduction in temperature, and water mole fraction, and an increase in N2 mole 

fraction. The O2 mole fraction is uniform, where the N2 maintains a wake profile. The 
207 

water mole fraction is spreading outward, indicating the spreading of the supersonic 

center jet. 

The mean values plots show no major differences in the behavior of the jet for the 

two flight Mach numbers. This was expected because the convective Mach number is 

approximately the same for both cases (Mc=1.05 and 1.08 for Mf=6 and Mf=7, 

respectively). The results confirm that the density ratio plays only a small role in the 

mixing of a supersonic jet, as it had already been observed by Brown. [186] 

Figure 8-6 compares mean measurements collected for constant Mf=6, and Me=1.6 

(black symbols), and Me=2 (magenta symbols), corresponding to Mc=1.05 and 1.28, 

respectively. The overall behavior of the flow is the same as described above. The 

change in convective Mach number produces some significant differences in the 

mixing. The mean profiles show that the N2-air mixture penetrates sooner in the 

supersonic jet for lower values of Mc. Up to 65 mm from the nozzle exit the profiles 

obtained for the lower convective Mach number are wider both in temperature and 

H2O mole fraction. Curiously the temperature profiles at 100 mm match almost 

perfectly, but the same is not observed for the water mole fraction that maintains a 

wider profile at lower Mc. Increasing the convective Mach number reduces the mixing 

and the spreading-rate in the upstream region (see section 8-6-3 for details on the 

spreading rate) . 

Figure 8-7 shows the results obtained for constant Mf=7 and Me=0.75, 1 and 1.6 

corresponding to values of Mc=0.53, 0.69, and 1.08. For the Mf=0.75 case data were 

collected only along three lines (z=1, 65 and 100 mm) and replications were limited 

to the centerline and to a subset of radial locations. 
208 

Figure 8-6: Average temperature and mole fractions at different heights for Mf=6 and 

Me=1.6 and 2.Error bars indicate ± one standard deviation
209 

During preliminary tests performed with the mass flow rates that provide Mf=7 for 

Me=0.75, a high pitch whistle was heard, pressure changes observed in the burner and 

severe fluctuations of the flame were visible in the IR image. This was likely a 

symptom of combustion instabilities. To remove the high pitch whistle the air flow 

rate was reduced to 285.8 SLPM (from the nominal 310.8) and the O2 flow rate 

increased to 115.4 (from 90.4). The high pitch noise was effectively removed during 

most of the test, but occasionally was still heard. This explains the different O2 mole 

fraction values measured for this test case with respect to the other Mf=7 cases. The 

temperature and H2O profiles show some distortions near the center jet 65 mm and 

100 mm from the nozzle exit. This has been observed only for the Me=0.75 case and 

it is probably consequence of combustion instabilities. 

The temperature and H2O plots in Figure 8-7clearly show the compressibility 

effect in reducing the shear layer spreading-rate and the mixing. In particular, for the 

sonic and subsonic cases the air has penetrated the jet up to the centerline already at 

35 mm from the nozzle exit.
210 

Figure 8-7: Average temperature and mole fractions at different heights for fixed Mf=7 

and, Me=0.75, 1 and 1.6. Error bars indicate ± one standard deviation
211 

Figure 8-8 a) plots the difference between the centerline and the freestream

temperature as function of the downstream distance (expressed in nozzle diameters). 

The difference is normalized by its value measured 1 mm from the nozzle exit. Figure 

8-8 b) shows the same quantity except computed for N2. Increasing the convective 

Mach number the penetration of the entrained air is delayed to locations further 

downstream, consistent with what has been reported in the literature and discussed in 

Section 8-2. 

All sonic and supersonic flow curves show a relatively flat region (up to 3.5 

diameters), followed by a drop in the normalized difference indicating that the 

entrained surrounding air has reached the centerline. The figure also shows that the 

variation in this normalized quantity is not linear with the z coordinate, and its slope 

increases with the distance from the exit. Notice a small reduction of the temperature 

and N2 difference for z/D = 1.5, and then a subsequent increase to its original value 

for z/D = 3.5. Previous computational analysis shows that the nozzle is not pressure 

matched, but slightly under-expanded, and a system of expansion and compression 

Figure 8-8: Normalized temperature (a) and N2 mole fraction (b) difference as function 

of the normalized z coordinate 
212 

waves is generated. The pressure along the centerline is therefore not uniform, but 

this is neglected in the DP-CARS data analysis which assumes in the calculation of 

theoretical spectra that the pressure is constant (pressure changes the spectra; for 

example using a pressure of 1 atm instead of 1.03 atm at the nozzle exit for Me=1.6 

and Mf=6 causes an error of 9 K in temperature, and ~ 0.17% (of the total 

composition) in O2 and N2). 

8.6.2 Mole Fraction of Gases Based on their Provenance

For a better understanding of the flow physics, it is helpful to know at each location 

the mole fraction of gases originating from the center-jet, the co-flow, and the 

freestream. V, C, and A are the mole fractions of these contributions. 

222

2

2 2

V aN bO cH O

C N

A dN eO

= ++

=

= +

(8-6) 

where the coefficients a, b, c are measured at the centerline, 1mm from the nozzle 

exit, d=0.78, e =0.208. By definition 

VCA ++=1 (8-7) 

The atomic mole fractions of N, O and H in a generic mixture (V, C, A) can be 

expressed as 

( ) ( )

( )

( ) ( )

( ) ( )

2 22

223 2 2

2 2

223 2 2

2

223 2 2

N

O

H

aV C dA

x

a b cV C d e A

b c V eA

x

a b cV C d e A

cV

x

a b cV C d e A

+ + = ++ + + +

+ + = ++ + + +

= ++ + + +

(8-8) 
213 

At each location xN, xO and xH can be computed from the measured molecular mole 

fractions (H2O is computed by difference). 

2

222

2 2

222

2

222

2

223

2

223

2

223

N

N

N O HO

O HO

O

N O HO

H O

H

N O HO

x

x

x xx

x x

x

x xx

x

x

x xx

= + +

+ = + +

= + +

(8-9) 

Equating Eq. (8-8) to Eq. (8-9) a system of 3 equations in 3 unknowns is obtained, 

but only 2 of the three equations are linearly independent. Replacing one of the 

linearly dependent equations with Eq. (8-7), a system of three independent equations 

in three unknowns is obtained. The system of equations is solved for (V,C,A) at each 

location. Results obtained using this procedure are displayed in Figure 8-9. 

The algorithm seems to correctly identify the center-jet, the co-flow and the 

ambient air at the nozzle exit. The lack of accuracy in the DP-CARS measurement

when only one species is present, and for cold air spectra was previously discussed. In 

these cases the water mole fraction is systematically high, and since molecules 

containing H atoms are present only in the center jet, this error causes a 

systematically higher value of the center jet mole fraction, where it should be 0. This 

effect is evident 1 mm from the nozzle exit in the co-flow region. Figure 8-9a) shows 

a comparison between data collected for Me=1.6 and Mf=6 (full symbols), and 

Mf=7(open symbols). The two plots are almost identical, with the lower enthalpy case 

spreading slightly faster than the higher enthalpy one. The results confirm that 

changes in density ratio are relatively unimportant. The plot shows the fast mixing of 
214 

the co-flow with the ambient air 15 mm from the base, where the N2 co-flow is less 

than 50% of the total composition. Above 15 mm the co-flow becomes only a minor 

constituent of the total composition in any location, as increasing amounts of air are 

entrained. Notice that most of the co-flow gas stays confined outside the original 

diameter of the central jet (|x|> 5 mm). For z=65 mm and above the air has penetrated 

up to the centerline, consistently with observations in the previous section. The figure 

clearly shows that the incompressible shear layer between the co-flow and the 

freestream grows much faster than the compressible shear layer between the 

supersonic center-jet and the co-flow. 

Figure 8-9: Mole fractions of gases based of their provenance
215 

Figure 8-9 b) shows the same quantities measured for varying convective Mach 

number. The plot clearly shows that compressibility, through the convective Mach 

number, plays the key role in determining the mixing between the center-jet and the 

co-flow. Air penetrates the center jet sooner at lower convective Mach numbers and 

the jet spreading-rate decreases with increasing Mach number, as previously 

observed. 

8.6.3 Spreading Rate

From the average temperature and mixture fraction profiles shown in the previous 

sections it is possible to determine the jet diameter and the width of the shear layer as 

a function of the downstream distance z. Temperature and mixture fraction radial 

profiles are normalized as follows: 

(,) (,) (0, )

freestream

norm

freestream

Txz T

T xz

T zT

− = − (8-10) 

(,) (,) (0, ) normV xz V xz

V z = (8-11) 

Tfreestream is the temperature in the core of the co-flow jet for z = 1 mm, and the 

freestream air temperature (300 K) everywhere else. V indicates the mole fraction of 

the gas originated in the center jet (vitiated air). The jet diameter δR is defined as the 

distance between the two locations where the normalized temperature drops to 0.1. 

The shear layer width δT is defined as the distance between the radial locations where 

the normalized temperature is 0.9 and 0.1. Two values of δT are obtained, one for 

positive and one for negative values of x, and the shear layer width is defined as the 

average of these two values. Similarly, another shear layer width δV can be defined 
216 

based on the 20% and 90% thresholds in the center-jet mole fraction profile. The 

choice of the thresholds to define the shear layer width and the jet radius is arbitrary, 

and other choices are possible. The x locations of the thresholds have been 

determined based on a quadratic interpolation. 

Figure 8-10 shows the width of the jet and of the shear layer according to the 

definitions given, as function of the distance z from the nozzle exit. As a general 

trend, increasing the convective Mach number, the computed width decreases, 

consistently with previous works. Notice that the slope of the curves changes after the 

turbulent shear layer has reached the centerline of the jet. The spreading-rate is here 

defined as the slope of the curves of Figure 8-10 for 15 ≤ z ≤ 65 mm. Values of the 

shear layer width measured 1mm from the exit are unreliable, because the length of 

Figure 8-10: Jet diameter (δR), shear layer width based on the normalized 

temperature (δT) and on the center-jet mole fraction (δf) as function of the distance 

from the nozzle exit, expressed in nozzle diameters
217 

the probe volume cause a reduction of the steepness of the measured profile, and 

therefore larger shear layers widths. Past 65 mm the shear layer has reached the 

centerline, and the physics of the process is different. The spreading-rate contains 

both the effects of the density ratio, and of compressibility. The two effects can be 

decoupled by normalizing the spreading-rate by its incompressible value, that can be 

estimated based on a spatial growth model, as in Ref.[197]. 

'

0

(1 )(1 ) (1 ) / (1 )

1

2(1 ) 1 2.9(1 ) / (1 )

u

u u u

C ρ ρρ

δ

ρ

λλ λ λ

δ

λ λ λ λ

−+ − +  

=   − + ++ −  

(8-12) 

where λu and λρ are the velocity and density ratio, respectively and Cδ a constant, 

which depends on the definition of the width, on the facility, the inflow conditions 

and other details. Figure 8-11 compares the measured normalized growth rate to the 

value predicted using a fitting curve proposed by of Slessor [190]: 

2 0.5

0

' (1 4 ) 'δ

δ

− = +Π (8-13) 

The curve is a best fit of several experimental results, expressed as function of the 

compressibility parameter Π. The value of Cδ is set so that the spreading-rate for 

Π=2.53 matches the value obtained from the fitted curve. This is arbitrary, but it 

forces the agreement at Π=2.53, and then agreement over the other values of Π 

indicates consistency with the theory. The range over which Π is varied is small (1.33 

to 2.63) but this is the best that can be done with the present data. Figure 8-11 shows 

that Eq.(8-13) correctly predicts (within 10%) the relation between the 

compressibility parameter and the spreading rate. The agreement is surprisingly good, 

considering the CARS smoothing effect on gradients. Notice that at the lower values 
218 

of the compressibility parameter Π, the width based on the center-jet mole fraction is 

higher than that computed based on temperature.

8.6.4 Standard Deviation and Co-Variances

The DP-CARS system allows for instantaneous measurements at a 20 Hz rate, 

therefore higher order statistics (variances, and co-variances) can be obtained from 

repeated measurements at each location. 1000 single shots acquisitions are available 

along the centerline, and for lines at z = 65 and 100 mm, 250 shots elsewhere. The 

standard deviations reported in this section contain contributions from the flow 

turbulence, the instrument precision, and the flow repeatability, as illustrated in 

section 8-5. In general, large values of standard deviations are encountered in the 

shear layer, where entrained gases from the hot center-jet and the quiescent air are 

Figure 8-11: Normalized growth rates as function of the compressibility parameter 

Π, compared to Slessor`s fitting curve
219 

mixing. Temperature-N2 co-variance (<T, N2>) is also shown. Large negative values 

of the co-variance indicate that the high temperature measurements are correlated to 

low measurement of mole fractions. Peaks in the standard deviation profile, coupled 

to negative peaks in <T, N2> indicate where mixing of the co-flow-air mixture (colder 

and with more N2) with the center jet occurs. 

Figure 8-12 shows the effect of the enthalpy Mach number on the standard 

deviations. The plots show small fluctuations at the outer edge, corresponding to the 

relatively quiescent freestream ambient air, and relatively low fluctuations in the 

center core of the jet. The temperature standard deviation (σT ) of the center jet 

depends on the enthalpy content. Removing the contribution from the instrument 

precision and the flow repeatability, the component due to the turbulence on the 

centerline is 42 K for Mf = 6, and 57 K for Mf = 7 (3.7% and 4.1% of the centerline 

temperatures). Local maxima in the standard deviations can be found at the interface 

between the co-flow and the center jet, and the co-flow and the quiescent air, 

indicating some degree of entrainment in the co-flow. Moving downstream the region 

of higher standard deviation becomes broader and of higher intensity. Up to 35 mm, 

the temperature standard deviation profiles in the shear layer are approximately the 

same for the 2 cases, except for higher fluctuations at higher Mf . At 65 mm the 

standard deviation for x = 0 is increased signaling that the mixing layer has reached 

the centerline. For z = 65 mm the effect of the flight Mach number is significant and 

the two profiles are very different. For Mf = 6 the standard deviation profile is more 

flat and has lower amplitude than for Mf = 7. The standard deviation presents a valley 

at the centerline much more pronounced for the higher enthalpy case. 
220 

Figure 8-12: Temperature and mole fractions standard deviation, and temperature, N2

co-variance (<T, N2>) at different heights for Me=1.6 and Mf=6 and 7 
221 

Similar considerations apply to the N2 standard deviation, with the only difference 

that the valley at the centerline has disappeared for both cases at z = 100 mm. The O2

standard deviation profile at 1 and 15 mm from the nozzle exit is an indicator of the 

mixing of the co-flow with the jet and the ambient air. Past 15 mm from the nozzle 

exit, the co-flow has approximately the same O2 content of the center jet; therefore, 

the σO2 profile flattens. The large negative values of the <T, N2> co-variance indicate 

intense mixing. Again, profiles are identical up to 35 mm, then they differentiate, 

with larger (negative) values and more pronounced valleys and peaks for the higher 

enthalpy case. 

Figure 8-13 and Figure 8-14 show the effect of compressibility on the standard 

deviations and on <T, N2>. Figure 8-13 compares results for Mf=6 and Me=1.6 (back 

triangles) and Me=2 (magenta diamonds). At the jet exit, there are no significant 

differences. Mean values plots showed improved mixing for the lower exit Mach 

number in the upstream region (up to 35 mm). This is reflected in the standard 

deviation plots, where the regions having standard deviation above the center-line 

value is larger, and the peak standard deviation higher. The <T, N2> co-variance plots 

show the same behavior. 100 mm from the base, the mean temperature plots are 

almost identical for the two cases, but the standard deviation is different, with the 

Me=1.6 case having a higher standard deviation, and more negative co-variance. 

Figure 8-14 compares the standard deviations and the <T, N2> co-variance for 

values of Me = 0.75, 1 and 1.6 and the higher flight Mach number, Mf = 7. Again, for 

higher compressibility, standard deviations peaks are lower, and the width of the 

region having standard deviations above the centerline value is smaller. Moving 
222 

downstream, past the location where the shear layer reaches the centerline, the 

standard deviation at the centerline increases, and the peak standard deviation moves 

toward the centerline. Past the location where the peak standard deviation occurs at 

the centerline, the profile flattens and the peak standard deviation starts dropping. 
223 

Figure 8-13: Temperature and mole fractions standard deviation, and temperature, N2

co-variance (<T, N2>) at different heights for Mf=6 and Me=1.6 and 2
224 

Figure 8-14: Temperature and mole fractions standard deviation, and temperature, N2

co-variance (<T, N2>) at different heights for Mf=7 and Me=0.75, 1 and 1.6
225 

As discussed in the background section, turbulence production is lower at higher 

compressibility. Figure 8-15 a) plots the temperature standard deviations at x = 0 

normalized by the average centerline temperatures. Before the shear layer reaches the 

centerline, the normalized temperature standard deviation is in the 4-4.5% range for 

all cases. Once the shear layer reaches the centerline the normalized standard 

deviation increases for all cases but the slope depends on Mc. Increasing Mc, the 

normalized standard deviation at the centerline decreases, consistently with the 

reduction in turbulence production observed in other experimental and numerical 

studies. Once the location of the peak standard deviation has reached the centerline, 

its amplitude begins decreasing as observed for Mc=0.52, and Mc=0.7. 

Similarly, Figure 8-15 b) shows the peak standard deviation normalized by the 

difference between the center jet temperature at the given z location, and the 

quiescent air temperature. This quantity increases moving downstream the flow, and 

generally decreases at higher compressibility. It differs from the normalized 

centerline standard deviation since it does not decrease after the location of the peak 

Figure 8-15: Normalized standard deviation on the centerline, and normalized peak 

standard deviation as function of the distance from the nozzle exit, expressed in 

nozzle diameters
226 

standard deviation reaches the centerline, but keeps a roughly linear behavior up to 10 

diameters from the nozzle exit. Another difference is that the behavior is not 

monotonic with the convective Mc number, suggesting that also the density ratio has a 

significant role in the evolution of this quantity. In particular increasing the density 

ratio appears to reduce the normalized peak standard deviation. 

8.7 DP-CARS Results: Combustion Case

In this section, the results obtained for the combustion test cases are presented. 

Three conditions were tested, as described at the beginning of Section 8-3. Two of 

these have Me=1.6 and a Mf=6 and 7 respectively for the center jet, and the third has

Me=1 and Mf= 7. For the supersonic cases the H2 co-flow was in stoichiometric ratio 

with the O2 in the center jet, although H2 can react with the O2 in either the quiescent 

air or the center jet. For the sonic case the H2 co-flow was 120 SLPM, corresponding 

to an equivalence ratio of 0.5 with the O2 in the center-jet.

8.7.1 Means, Standard Deviations and Co-Variances for the Combustion 

Test Cases 

Figure 8-16 shows the mean temperatures, N2, O2 and H2 mole fractions for the 

three combustion cases. Figure 8-17 shows the standard deviations for the same 

quantities. Figure 8-18 and Figure 8-19 shows the co-variances <T, N2>, <T, O2>, 

<T, H2>, <N2, O2>, < N2, H2> and <O2, H2>.
227 

Figure 8-16: Mean temperature and mole fractions at different heights for the 

combustion test-cases
228 

Figure 8-17: Temperature and mole fractions standard deviations at different heights 

for the combustion test-cases
229 

Figure 8-18: Co-variances at different heights for the combustion test-cases 
230 

Figure 8-20 to 8-25 re-propose some of the plots shown above, but rearranged so 

that each figure contains profiles for a given value of z. This arrangement of the plots 

is more convenient for the discussion of the results that follows

Figure 8-20 shows the mean temperature and mole fractions, the temperature and 

the N2 standard deviation, and the temperature-mole fractions co-variances obtained 

at z = 1 mm. Profiles at the nozzle exit (z = 1 mm, and |x |< 5 mm) have already been 

compared to their mixing counterparts, and to CFD predictions in Figure 8-3 and 

Figure 8-4, and previously discussed. Moving further out in the radial direction, the 

DP-CARS probes the H2 co-flow. Temperature was high enough so that two H2

rotational lines, S(5) and S(6), were detected. When possible, it is preferable to 

Figure 8-19: <O2, H2> and <N2, H2> at different heights for the combustion test-cases
231 

extract the temperature from the N2 spectra, but for this region, only temperature 

measurements from the two H2 lines were possible. No data are available for the 

accuracy and precision of these measurements. The average temperature in the coflow is ~700 K for the supersonic cases, and ~850 K for the sonic case. The measured 

H2 mole fraction in the pure H2 co-flow is between 0.95 and 1, and the instrument 

correctly measures a null mole fraction of N2 and O2. Past 7.4 mm from the center, 

mixing between the co-flow and ambient air occurs. The sharp peaks in temperature 

and H2O mole fraction profiles at the interface between the air and the co-flow (x ≈ 

±8.9 mm) indicate that combustion has occurred. 

Figure 8-20: Mean, standard deviations and co-variances for z = 1 mm, combustion 

cases
232 

This is consistent with the observation that the flame is flame attached to the 

burner in the IR image (see Figure 8-1). Notice that the flame for the sonic case is 

broader than what is observed for the supersonic cases. Large peaks of temperature 

standard deviations occur near the peak temperature (x ≈ ±9.5 mm), and are likely 

caused by flame fluctuations. 

Additional local peaks of mean temperature and H2O are found at the interface 

between the co-flow and the center-jet (x = -5.4 mm) for the two higher enthalpy 

cases (Mf=7). Measurements at these locations present very large fluctuations, up to 

690 K in temperature. Examining the evolution with time of the single shots 

measurements, it was found that the first shots were from high temperature fuel rich 

mixtures, and the rest from much colder spectra. Movement of the translation stage 

during the data acquisition could explain this behavior. Another possibility is that 

sparks produced by the focused laser beams ignites the mixture, but the flame cannot 

self-sustain. The behavior is consistent for all the other standard deviation peaks in 

Figure 8-20, except for the peaks at the interface with the quiescent air.

 The inability of this instrument to resolve sharp temperature gradients must be 

taken into account in interpreting the CARS results near the peaks. In addition, only 

250 shots are available at each location shown in Figure 8-20, limiting the accuracy 

of the standard deviation and co-variance estimates. For these reasons, the profiles of 

standard deviation and co-variances shown in Figure 8-20 are only qualitatively 

useful. 

Figure 8-21 shows the mean temperature and mole fractions, the temperature and 

the N2 standard deviation, and the temperature-mole fractions co-variances obtained 
233 

for z = 15 mm. The temperature profiles are significantly different in the three cases 

examined. For Me=1 (blue squares), the flame front has moved toward the center jet, 

with peak temperatures at x=-5.4 and 5.9 mm. Ambient air has penetrated further in 

the co-flow providing the oxidizer to feed the combustion. At the peak temperature 

location, the N2 mole fraction is ~ 46 %, where O2 is completely depleted. 

Peak temperature gradients are much less than for z = 1 mm, therefore useful 

quantitative information can be obtained from the variances and co-variances. In 

particular, the temperature-mole fraction co-variances can be used to determine where 

the combustion is occurring. As already observed for z = 1 mm, near the temperature 

peaks the standard deviations are very high (up to 400 K for σT) because of flameFigure 8-21: Mean, standard deviations and co-variances for z = 15 mm, combustion 

cases
234 

front fluctuations. Between the temperature peak and the freestream the temperaturemole fraction co-variances (<T, O2> and <T, N2>) are negative with a peak for x = -

6.4 mm and x = 6.9 mm. Negative co-variances mean that an instantaneous lower 

temperature typically corresponds to higher values of mole fractions. This indicates a 

region in which combustion products (higher temperature, lower mole fractions), mix 

with the colder freestream. Moving toward the centerline, <T, N2> becomes positive, 

while <T, O2> and <T, H2> are negative. The change in the sign of <T, O2> is an 

indicator of the combustion. Instantaneous high temperature are associated to high 

values of N2 and low values of O2 and H2, that is for entrained air that has reacted

with the H2 co-flow. 

Proceeding further toward the centerline, the mean temperature reaches a 

minimum and then rises to the center-jet plateau value. In this region <T, N2> and <T, 

O2> are positive, where <T, H2> is negative, as consequence of the mixing between 

the vitiated air in the center-jet (higher T, N2 and O2) and the H2 co-flow. The sign of 

the co-variance indicates that combustion is not occurring in this region. 

For |x| ≤ 2.7 mm the measurements are identical (within the accuracy of the 

instrument) to what is measured at z=1 mm. This constitutes the core of the sonic jet, 

that is completely unaffected by the co-flow and the entrained air. 

The temperature profile for Me=1.6 and Mf=7 (red circles), is quite different. The 

main features are a strong asymmetry and a local extinction of the flame for negative 

x, also visible in the IR images. For positive x, the mean temperature profile is similar 

to the one observed for the sonic case, with the only difference being a lower peak 

temperature. As in the previous case the location of the peak temperature moves 
235 

toward the center, from x=9.5 mm to x=6.4 mm (x=5.9 mm for Me=1). The 

temperature profile between the peak temperature and the freestream appear almost 

overlapped to that measured in the sonic case. At the peak temperature location the 

mole fraction for N2 and H2 are 22% and 77% respectively, where for the sonic case 

they are 41% and 21%. The mean equivalence ratio is therefore higher in the 

supersonic case, lowering the peak temperature. Notice that the difference is not the 

consequence of the different compressibility, but of the much higher H2 flow rate in 

the co-flow. 

For negative x there is no peak in the temperature profile, but a smooth rise from 

ambient air to the center jet plateau. Single-shot spectra show simultaneous presence 

of O2 and H2, indicating that the combustion is not sustained in this region. For x = -

6.9 the average temperature is 1270 K, but the time history of the single shots 

temperatures shows high temperatures for the first 4 seconds of acquisition and lower 

thereafter. A spark caused by the lasers itself could have ignited the flow, but 

conditions were inadequate to sustain the combustion, as suspected for those other 

anomalous location in the lower plane. 

For the lower enthalpy case (Mf=6) the temperature profile for negative x shows 

local extinction similar to what is observed for Mf=7; for positive x the flame is fuel 

rich and it has not moved toward the centerline as for the other cases, the equivalence 

ratio is lower and the peak temperature higher. The reason for this difference is 

unclear.
236 

For z=35 mm. shown in Figure 8-22, combustion between the H2 co-flow and the 

ambient air occurs for both positive and negative values of x for all cases. The sonic 

case now shows a lean flame with an O2 mole fraction of 7% and a peak temperature 

of 1974 K. H2 is almost completely depleted. The valley, between the peak 

temperature and the center-jet plateau has disappeared. The σT profile shows a peak at 

the interface between the center-jet and the co-flow flame (x = ±4.5 mm), and another 

at the interface between the co-flow flame and the free stream (x = ±8.5 mm). 

Negative peaks of <T, O2> are present at the interface of the co-flow with the 

freestream and the center-jet. Although this hints to combustion between the oxidizer 

from the sonic jet and the H2 in the co-flow, it is not certain because the sign of <T, 

Figure 8-22: Mean, standard deviations and co-variances for z = 35 mm, combustion 

cases
237 

N2> and <T, H2> cannot be determined (their value is lower than the measurement 

uncertainty). 

The two supersonic test cases have profiles that are asymmetric, as consequence 

of the non-uniform flow rate across the co-flow nozzle. For negative values of x the 

profiles resemble what is observed for the sonic case, although the co-flow flame is 

still fuel rich, the peak temperature is lower, and it is reached further away from the 

centerline. 

For positive values of x the profiles resemble what is observed for the sonic case 

at z = 15mm. In particular, the location where the temperature peaks is further away 

from the centerline, and there is a valley between the center-jet plateau and the peak 

temperature. The flame is richer (31% at the peak temperature location for Mf=6) and 

at lower temperature than for negative values of x. 
238 

Further downstream, 65 mm from the nozzle exit the supersonic cases differ 

drastically from the sonic one. In the sonic case most of the H2 was depleted at 35 

mm from the nozzle exit, (because of lower Φ), thus no further heat is released 

moving downstream. The high temperature co-flow entrains gas from the colder 

center jet, and quiescent air lowering its temperature and increasing its O2 content. 

The interface between the flame and the core of the center jet moves further toward 

the center but does not reach the centerline, as can be observed in the σN2 and <T, O2> 

profiles. The temperature profile at the interface with the freestream, almost identical 

for all test cases in presence of heat release, is now completely different for the sonic 

case

Figure 8-23: Mean, standard deviations and co-variances for z = 65 mm, combustion 

cases; note change in horizontal scale from Figs. 8-16 through 8-18
239 

For the supersonic cases H2 is still available and combustion occurred between z= 

35 and z= 65 mm. The flow is still dominated by the heat release, and the same 

features observed for z = 35 mm appear for z = 65 mm. The asymmetry with respect 

to the centerline is increasingly evident, as a consequence of the increasing difference 

in the released heat. The shear layer between the co-flow and the supersonic jet has 

penetrated most of the jet core, but it has not reached the centerline. At the interface 

between the higher temperature, H2 rich co-flow, and the colder center-jet rich in O2

and N2, <T, N2> is positive, <T, O2> and <T, H2> negative. This is evidence of 

combustion between the gases coming from the center jet, and the fuel rich co-flow. 

For z=100 mm the mean profiles for the sonic nozzle show that the shear layer has 

Figure 8-24: Mean, standard deviations and co-variances for z = 100 mm, combustion 

cases
240 

reached the centerline, causing a temperature increase, and a decrease in the N2 and 

O2 mole fractions. For increasing distances from the centerline the temperature

decreases and the N2 mole fraction increases monotonically but the standard deviation 

plots shows a peak marking the interface with the ambient air. The O2 mean profile 

presents a local maximum at the centerline, then it drops in the co-flow region and 

finally rises to its ambient air value. 

For the supersonic case, since H2 was still available for combustion, the flow 

profiles resemble what is observed for z=65 mm. The only difference is that the peak 

temperature is increased and the interface between the core of the center jet and the 

co-flow flame has moved further toward the center, as can be deduced from the 

location of the σT, σN2 and <T, O2> peaks and valleys locations. As consequence, an 

increase in the centerline temperature is observed. The flame is even more 

asymmetric with respect to the centerline, because of the increasingly different 

amounts of heat is released. Further downstream the asymmetry is expected to grow 

since on one side the H2 has been almost completely depleted, where on the other is 

still present in significant amount (up to 13%). 

8.7.2 Effect of Heat Release

Comparing the results for the mixing and the combustion test cases, it is evident 

that the presence of reactions dramatically changes the flow field. In the mixing case 

the shear layer reaches the centerline 65 mm from the nozzle exit (z/D = 6.5), but this 

does not occur until further downstream in presence of combustion as shown in 

Figure 8-25 a). The figure shows, for both the mixing and the combustion cases, the 
241 

normalized temperature difference defined as the difference between the temperature 

and the freestream temperature, divided by the same difference computed at the 

nozzle exit (same of Figure 8-8 a)). Similarly the temperature standard deviation on 

the centerline, as a percentage of the mean temperature, stays approximately constant 

until 65 mm, but is significantly higher 10 diameters downstream of the nozzle exit as 

shown in Figure 8-25b). Heat release delays the entrainment of the co-flow in the 

center jet, reducing the mixing, and causing the different behavior in the mixing and 

combustion cases. 

Better understanding of the effect of the heat release on the mixing, is possible by 

looking at the gas composition at each location in terms of their provenance. 

Following the same strategy described in section 8.6.2 it is possible to determine the 

mole fraction of gases originated in the center-jet, the co-flow and the quiescent air. 

The only difference is that in this case reactions can occur and convert H2 and O2 into 

Figure 8-25: Normalized mean temperature difference (a) and normalized temperature 

standard deviation on the centerline (b) as function of the normalized z coordinate 
242 

water. This does not affect the previous strategy since it is based on a balance of 

atomic species. Eq. (8-6) to (8-9) modified for H2 co-flow become: 

222

2

2 2

V aN bO cH O

C H

A dN eO

= ++

=

= +

(8-14) 

where the coefficients a, b, c are measured at the centerline, 1 mm from the nozzle 

exit, d=0.78, e =0.208. By definition 

VCA ++=1 (8-15) 

The atomic mole fractions of O and H in a generic mixture (V, C, A) can be expressed 

as: 

( )

( ) ( )

( ) ( )

2 2

223 2 2

2 2

223 2 2

O

H

b c V eA

x

a b cV C d e A

cV C

x

a b cV C d e A

+ + = ++ + + +

+ = ++ + + +

(8-16) 

At each location, xO and xH can be computed from the measured molecular mole 

fractions (H2O is computed by difference). 

2 2

22 22

2 2

22 22

2

2223

2 2

2223

O HO

O

N O H HO

HO H

H

N O H HO

x x

x

xxxx

x x

x

xxxx

+ = +++

+ = +++

(8-17) 

As shown previously the equation for xN is linearly dependent on the other 2, so it is 

not necessary. 

Figure 8-26 compares the results obtained for the 3 combustion cases. The 

different flight and exit Mach numbers do not greatly affect the profile of the mole 

fraction originated from the center jet, except at the most downstream location, where 
243 

the sonic case shows a lower value of the center-jet mole fraction on the centerline. 

The profiles for the gases that originated in the co-flow and the ambient air show 

larger differences; the ambient air penetrates further in the co-flow and in the center 

jet for the sonic case, since the H2 co-flow is present in larger quantities for the 

supersonic cases. As discussed in the previous section, these differences are a 

consequence of the lower H2 flow rate, rather than the different compressibility. This 

is a striking difference with respect to the mixing case where the compressibility 

significantly reduces the mixing.

Figure 8-27 compares the results for the sonic combustion case to its mixing 

counterpart. A direct comparison is meaningful because the co-flow rates are the 

same. At z = 15 mm the profiles look similar, but less air is entrained in the co-flow 

because of the heat release. Further downstream, the diameters of the center-jet and of 

the co-flow jet are increased because of the heat release. The rise in temperature 

reduces the density; because there is no axial pressure gradient that can accelerate the 

flow, the velocity is constant, and therefore the jet area must increase. Mixing is 

reduced as can be seen by the reduced amount of entrained air in the combustion case. 

Figure 8-28 shows the locations where the mole fractions of gas coming from the 

center jet are 20% and 80% of their value on the centerline. The plot clearly shows 

for the combustion cases a higher growth rate of the center-jet (20% lines further 

away from the centerline), and reduced mixing (80 % lines closer to the centerline), 

as a consequence of the heat release. 
244 

Figure 8-26: Composition by gas provenance for the combustion cases
245 

Figure 8-27: Composition by gas provenance for Me=1 and Mf=7. Comparison between 

mixing and combustion
246 

8.7.3 Histograms

In addition to average and standard deviations, histograms have been obtained at each 

location to provide additional information to the CFD modelers. Showing all the 

histograms would not be practical (it would require ~ 10000 plots), therefore only an 

example is shown here to explain how they have been obtained and to describe what 

additional information they provide. At each measurement location and for each 

variable, the post-processing code divides the measurement range in several bins, and 

counts the number of measurements falling in each bin. A bar-plot of these quantities 

Figure 8-28: Locations where the mole fractions of gas coming from the center jet are 

20% and 80% of their value on the centerline for Me=1, and Mf=7
247 

returns a histogram as shown in Figure 8-29. The choice of the bin width is based on 

Scott`s rule:[198] 

3

3.5

w

n

σ = (8-18) 

where w is the bin-width, σ is the estimated standard deviation, and n the number of 

samples. This choice of the bin-width is appropriate for data that have a Gaussian 

distribution. 

Figure 8-29 shows histograms of temperature measurements at the nozzle exit (x 

= 0 and z = 1 mm, in the lower panel) and in a combustion region downstream (x = 

14.7 and z = 100 mm, in the upper panel). The temperature histogram in the lower 

Figure 8-29: Histograms of temperature at x=0, z=1 mm (lower panel) and at x=14.7

mm, z=100 mm (upper panel). The black continuous lines are fit to a Gaussian (lower 

panel) and to the sum of 2 Gaussian (in blue and green)
248 

panel has a Gaussian distribution (black curve, R2

=0.99). The temperature histogram 

obtained in the combustion region downstream has a much larger standard deviation 

(285 K) than is observed at the nozzle exit (62 K), and does not follow a Gaussian 

distribution (dotted curve in figure, R2=0.77). Instead it has a bimodal distribution 

(black continuous line, R2

=0.97), given by the sum of a Gaussian centered at 1500 K 

(blue curve) and another Gaussian centered at 1986 K (green curve). The bimodal 

distribution indicates fluctuations of the flame front. The temperature histogram in the 

combustion region shows temperature ranging from 400 to 2400 K in a single 

location. Removing spectra that saturate the detector from the analysis, as in Ref. [66, 

72], would have neglected those lower temperature shots introducing errors in the 

average and in the standard deviation estimates

8.8 Discussion

Two major drawbacks reduce the usefulness of the data set. The first is the length 

of the DP-CARS probe volume, and the non linear dependence of the signal 

amplitude with the temperature. Consequently, the accuracy of the measurements in 

proximity of steep temperature gradients is compromised (biased toward lower 

temperature) and the turbulent fluctuations are underestimated. The small size of the 

burner exacerbates the issue. Care must be used in interpreting the CARS 

measurements in proximity of steep temperature gradients. 

The second major issue with the dataset is the asymmetry of the co-flow nozzle. 

This is a minor issue for the non reacting case, where air is rapidly entrained in the 

co-flow, mitigating the effects of the asymmetry. For the reacting case, the different 
249 

flow-rates directly affect the amount of heat released that is the governing factor in 

the flow evolution. The difference in the total amount of heat released increases 

proceeding downstream, and so does the flow asymmetry. 

Nevertheless, there is no other data set providing statistics on temperature and 

mole fractions in compressible shear layers, nor in compressible reacting shear layers.

The data set can be a useful tool in the development of CFD turbulence model for 

compressible shear layer. High fidelity, time dependent CFD simulations, for 

example LES simulations, could be post-processed to account for the spatial 

averaging inherent to the CARS technique, allowing this limitation of the dataset to 

be mitigated. 
250 

CHAPTER 9 -Conclusion

9.1 Summary

Research on CARS for supersonic combustion applications has been an ongoing 

effort at NASA Langley Research Center for the past 25 years.[6, 12, 66, 67, 69, 70, 

72] A dual-pump (DP) CARS instrument, based on previous works from O’Byrne [6] 

and Tedder [66, 72], was developed to provide measurements in supersonic 

combustion experiments. The instrument allows instantaneous and spatially resolved, 

simultaneous measurements of temperature, N2, O2 and H2 absolute mole fraction in 

H2-air flames. The instrument was applied to measurements in a laboratory-scale 

supersonic combusting free jet.

The development of the instrument was focused on the resolution of several issues 

relevant to measurements in a H2-air supersonic combusting free jet and more in 

general to supersonic combustion experiments.[6, 66, 72] Most components of the 

instrument hardware have been upgraded and several new features have been added. 

CFD validation requires large amounts of data, therefore efforts were made to 

increase the acquisition rate, and reduce the data processing time. The increase in the 

acquisition rate (compared to Ref.[66, 72]) is obtained by several changes in the 

Labview data acquisition software, to eliminate the need of any input from the 

operator once the acquisition begins. Several algorithms have been developed that 

provide more accurate (better background subtraction, non-resonant normalization, 

and improved pixel-to-frequency conversion) and faster processing of the raw CARS 

data. A new, faster and more precise fitting algorithm, developed by Cutler [107] was 
251 

used to fit the processed CARS spectra. Overall, the entire data analysis process is at 

least 10 times faster than in previous CARS experiments at NASA Langley Research 

Center. A faster analysis of CARS data allows identifying unforeseen issues during a 

test campaign and solving them before the bulk of the data is acquired. For example 

the need of an improved procedure for the background subtraction was found during 

the initial tests in the laboratory-scale supersonic combusting jet, and additional 

background spectra were added afterwards. 

In previous experiments,[66,72] beam steering proved to be a major obstacle to 

the successful acquisition of CARS data in supersonic free jets. A combination of a 

planar BOXCARS phase matching configuration and shaping of one of the laser 

beams was investigated as a tool to mitigate the reduction of CARS signal caused by 

the refraction of the pump and Stokes beams as they pass through unsteady density 

gradients produced by turbulent flows. The signal loss is due both to beam wandering 

(relative displacement of the beams) and beam spreading (increase in the size and 

distortion of the shape of the beams at the focal plane). The technique results in a 

signal that is insensitive to displacement in the plane of the beams, and less sensitive 

to “out-of-plane” displacement. The spatial resolution is not affected by this 

technique. The approach was tested in two experiments, the first in which the beams 

were deflected by movements of a mirror and the second by a turbulent flow of 

helium and air. The beam shaping method proved to be effective in mitigating the 

effects of beam steering in both experiments. The amount of data rejected because of 

low signal-to-noise ratio was reduced by a factor 10 in the experiment involving the 

helium jet. The low data yield sometimes reported in turbulent measurements can be 
252 

overcome by this technique. Finally, a model of the beam interaction/signal 

generation process was developed and validated by comparison with the experimental 

results. The beam shaping approach is then applied to measurements in the 

laboratory-scale supersonic free jet, where beam steering is a significant issue. For 

CARS systems in which unused laser energy is available, the technique has no 

significant disadvantages while if the laser energy is limited, a compromise must be 

struck between the level of irradiance and the amount of ellipticity at the pump beam 

focus. 

The typical length of the CARS probe volume (1-2 mm) affects the accuracy of 

measurements in presence of steep temperature gradients, and determines the size of 

the smallest turbulent structure that can be resolved. Options to reduce the CARS 

probe volume length have been investigated. Improving the spatial resolution of 

CARS in combustion measurements is challenging since the intensity of the CARS 

signal is proportional to the square of the probe volume length. So decreasing the 

probe volume length by increasing the beam crossing angle decreases the signal 

below acceptable levels. Increasing the laser irradiance also increases the CARS 

signal, but high irradiance effects may perturb the CARS spectra. A systematic study 

was conducted to determine the effect of Stark broadening and stimulated Raman 

pumping (SRP) on dual-pump CARS spectra of N2, O2 and H2. Since these effects are 

not easily modeled and they are not typically included in fitting routines, they lead to 

errors in measurements of absolute concentration when these spectra are fitted to 

theory. Stark broadening alters the linewidth and amplitude of all transitions. Errors 

can be avoided by limiting the total irradiance at the measurement volume. SRP alters 
253 

the population difference between the lower and upper state of a transition, reducing 

the peak CARS signal and raising the level of the higher vibrational bands in room 

temperature air spectra. Errors in measured temperature and absolute and relative 

concentrations of resonant species can be caused by SRP. Such effects can be avoided 

by limiting the product of the pump and Stokes laser beam irradiances. 

To explain the effects of high irradiance perturbations on CARS spectra, simple 

theoretical models from the literature are discussed and compared with experimental 

results. Experimental CARS spectra, collected in ambient air, fuel-lean and fuel-rich 

flames for several values of irradiance, are examined. Perturbations to the spectra are 

discussed and their effect on concentration and temperature measurements quantified. 

Both SRP and Stark broadening effects are present in the acquired spectra. Errors in 

O2 concentration measurements up to 50% are observed. Other researchers, based on 

theoretical considerations, determined that Stark broadening may not be significant if 

the computed Stark shift is less than the Raman linewidth. This simple criterion is 

validated experimentally for O2 and N2, limiting the total irradiance to 250 GW/cm2

at 1180 K and atmospheric pressure. Hydrogen spectra are particularly sensitive to 

Stark broadening, and small perturbations are observed even at the lowest total 

irradiance level tested (170 GW/cm2). Measurements of concentration were observed 

to be much more sensitive to Stark broadening than are measurements of temperature. 

It is also shown that the characteristic SRP time has to be an order of magnitude 

larger than the laser pulse length to completely avoid errors in concentration 

measurements, but it is sufficient that it is only greater or equal to the pulse length to 

mole fraction of the pump-Stokes irradiance product for N2 and O2 concentration 
254 

measurements is 2 x 103 GW2

/cm4, and for temperature it is 2 x 104 GW2/cm4. The 

study not only proved that the spatial resolution could not be reduced by increasing 

the laser irradiance, but also that high irradiance perturbation effects were present in 

previous experiments at NASA Langley. In particular the systematically lower H2/N2

reported separately by O’Byrne[6, 72] and Tedder [72] was a consequence of the 

Stark broadening. This finding was very important because removed a major source 

of systematic error in the H2 mole fractions measurements.

In providing data for CFD validation, it is important to determine accuracy, 

precision and spatial resolution of the measurements. Significant improvements in the 

accuracy and precision of the instrument have been achieved. Results from validation 

measurements in a Hencken burner are discussed and the instrument accuracy and 

precision estimated. Calibration of the optical diffusion coefficient and the third order 

non-resonant susceptibility reduced systematic errors. The accuracy of the mole 

fractions measured for temperatures above 600 K is 0.5, 1.5 and 1% of the total 

composition for O2, N2 and H2, respectively. Uncertainty in the non-resonant 

spectrum is responsible for additional errors up to 3% of the measured mole fractions, 

and up to 1% of the measured temperature. The precision of the temperature 

measurements, determined from the standard deviation of the measured temperature 

over 500 acquisitions, is a function of temperature and composition, and lies between 

1.8 and 3.3%. Absolute mole fraction precisions are between 0.5 and 1.8% for O2, 1.5 

and 3.4% for N2, where these percentages are given as a fraction of the total 

composition. The precision of H2 mole fraction measurements is ~10% of the 

measured value. 
255 

Results from a numerical study show that accurate temperature and species mole 

fraction measurements are possible when a portion of the spectra saturates the 

camera. The error is within 1% for the degree of detector saturation expected in the

measurements of the laboratory-scale supersonic combusting jet. This approach is 

highly preferable to the removal of the saturated spectra from the dataset because it 

does not introduce significant bias, and extends the range of temperature that the 

instrument is capable of measuring. The probe volume length has been measured 

experimentally, and 90% of the CARS signal is generated over a 1.7 mm length. 

In summary the DP-CARS development efforts described in this work, have: 

• Increased the data acquisition rate and the data yield

• Reduced the data processing time 

• Developed a technique to mitigate the effects of beam steering without 

affecting the spatial resolution

• Determined thresholds for high irradiance perturbation effects (Stark 

broadening and SRP) , found in Stark broadening the source of systematic 

errors in earlier H2 mole fraction measurements

• Provided better instrument accuracy through improvements in the 

theoretical modeling 

• Provided better instrument precision thanks to higher spectral resolution 

and new fitting algorithm

The DP-CARS instrument has been used to collect data in a laboratory-scale 

supersonic free jet flame for several values of exit and flight Mach numbers. The flow 

consists of a center-jet of hot vitiated air and a co-flow of N2 for mixing study, or H2
256 

for combustion studies. Approximately 800,000 CARS spectra were collected and 

analyzed. The signal to noise ratio was sufficiently high at all the locations tested, and 

data yield > 95% was achieved. Averages, variances, co-variances, and histograms 

have been obtained at each location probed. Measured standard deviations are 

consistently larger (2x or more) than what was measured in laminar flames under 

similar conditions. Therefore, the instrument was capable of estimating temperature 

fluctuations due to the turbulence in this flow. 

The experimental results for the non-reacting test cases showed that increased 

compressibility reduces the shear layer spreading rate, and the turbulence 

fluctuations, in agreement with what was observed in previous experimental work. 

The DP-CARS measurements in the reacting test cases showed that the heat released 

from the combustion strongly limits the growth of the co-flow shear layer, and the 

mixing of the center jet. Examination of the standard deviation and of the covariances profiles proved to be very useful in determining where significant mixing 

and combustion are occurring. The experimental results were in agreement with what 

was previously observed or predicted, but the relevance of the acquired data-set lays 

in providing accurate quantitative measurements of the distributions of mean and 

fluctuation parameters (i.e. variances covariances, pdfs). 

Two major drawbacks reduce the quality of the data set. The first is the significant 

length of the DP-CARS probe volume, which leads to spatial averaging and to errors 

in the measurements in proximity of steep temperature gradients (biased toward lower 

temperature) and underestimated turbulent fluctuations. The small size of the burner 

exacerbates this issue. Care must be used in interpreting the CARS measurements in 
257 

the proximity of steep temperature gradients. Spatially resolved CFD simulations 

could be post-processed for direct comparison to the results. 

The second major issue with the dataset is the asymmetry of the co-flow nozzle. 

This is a minor issue for the non-reacting case, where the co-flow rate is low and air 

is rapidly entrained in the co-flow, mitigating the effects of the asymmetry. For the 

reacting case, the different flow-rates affect directly the amount of heat released that 

is the governing factor in the flow evolution. The difference in the total amount of 

heat released increases proceeding downstream, and so does the flow asymmetry. 

Nevertheless, there is no other data set providing statistics on temperature and 

mole fractions in compressible shear layers. The data set can be a useful tool in the 

development of CFD turbulence model for compressible shear layer. 

9.2 Future Work

The DP-CARS instrument has been moved to the University of Virginia, and DPCARS data are currently being acquired in a Dual-Mode Scramjet Combustor.[105] 

After this test campaign the instrument will be moved back to NASA Langley 

Research Center for measurements in the Durable Combustor Rig in the Direct 

Connect Supersonic Test Facility. 

Further instrument development to improve the accuracy and the precision is 

recommended. The changes in the spectral shape and peak wavelength of the 

broadband dye laser during the data acquisition were responsible for errors in the 

mole fraction measurements. Improvements are possible if spectra of the broadband 

dye laser are collected on a separate spectrometer each time CARS data are collected. 
258 

It is then possible to determine the relationship between the broadband dye laser 

spectral shape, and the non-resonant spectra, and to properly account for changes in 

the broadband dye laser with time. This method requires a second spectrometer, and a 

mapping from the spectral shape of the dye laser to the corresponding non-resonant 

profile. 

As an alternative a CARS non-resonant profile can be collected simultaneously to 

the resonant CARS signal.[106] Generating two CARS signals in two different probe 

volumes would require roughly twice the laser energy if the non-resonant medium is 

argon. On the other hand, a strong non-resonant CARS signal can be obtained in a 

solid with laser energies that are few orders of magnitude less. The low energy 

collected for the beam viewing system would be sufficient to generate a non-resonant 

signal in a 1 mm (or thicker) thick microscope slide. A strong non-resonant signal 

could be generated by placing the microscope slide at the image of the crossing 

location generated by the beam viewing system. It has the same crossing of the main 

probe volume, but much lower irradiance. The non-resonant signal can then be sent 

on the path of the main CARS signal, but slightly misplaced in the vertical direction 

so that it would appear on the upper or lower bin. The microscope slide could be 

mounted on a remotely controlled translation stage, so that the non-resonant signal 

level can be controlled by changing the portion of the probe volume inside the solid. 

This is necessary to compensate for the signal reduction when the Nd:YAG energy is 

reduced to avoid detector saturation. This system would allow for a shot-to-shot 

normalization, completely removing the uncertainty related to the changes in the 

broadband dye laser. 
259 

Further improvement in the modeling can help in reducing the systematic errors. 

The low temperature test cases may benefit from theoretical models that include the 

collisional narrowing effect. A furnace, providing a controlled temperature and a 

known composition (air) is a good validation test-case to evaluate the effect of 

alternative linewidth models. Additional validation measurements for H2 at lower 

temperature than are used for this test are also needed to evaluate if the exponential 

law for the optical diffusion coefficient is appropriate at lower temperatures.

The laboratory-scale supersonic combusting jet is an interesting test case for CFD 

validation, and there are several additional studies that can be accomplished using 

variations of the CARS technique described here. The nozzle and the co-flow annulus 

of the laboratory scale supersonic burner have been redesigned to remove the 

asymmetry in the flow. This problem greatly affected the combustion cases, and I 

recommend repeating some of the measurements, after implementing the 

improvements to the CARS system discussed above. Combustion cases using 

ethylene as co-flow and applying Tedder`s WIDECARS [85] for simultaneous 

measurements of temperature, N2, O2, CO, CO2, C2H4 and H2 are planned. To 

implement the technique it is necessary to replace the oscillator of the broadband dye 

laser, with the version designed by Tedder [199], to replace the dye, and the 

spectrometer grating (from 2400 lines/mm to 1200 lines/mm). 

Spatial resolution was another limitation of the data presented here. Tests in the 

larger scale facility alleviate the issue, and the beam shaping technique developed for 

this test would mitigate the beam steering effects that compromised the previous 

attempt.[72] Improved spatial resolution for the combustion cases is limited by the 
260 

high irradiance perturbation effects, and a probe volume length shorter than 1.5 mm is 

challenging with a planar BOXCARS configuration. Improvements are instead 

possible for the mixing cases. Lower temperature implies higher signal, therefore 

smaller measurement volumes are achievable. In addition, there is no H2 in the flow, 

and the second hot band does not appear. This allows moving the N2 and O2 spectra 

closer to each other and to the peak of the broadband dye laser. For this test case it is 

recommended to reduce the width of the dye laser, so that more energy is available 

for the CARS process (remember that Stark broadening is determined by the total 

irradiance, so a narrower broadband dye laser would contribute more to the CARS 

and the SRP process, but not to the Stark broadening). 

Also the effect of the beam steering on the length of the measurement volume 

should be investigated. For example, the measurement of the probe volume length 

described in Chapter 6.8 could be repeated in presence of the beam steering generated 

by the helium jet of Chapter 4.4 

The use of a modeless dye lasers as Stokes beam was previously attempted but 

did not provide the expected precision improvements. [66] This was a consequence of 

the lower irradiance of the laser and of the decreased spectral bandwidth. The N2

portion of the spectra happened to be at the edge of the modeless Stokes laser, where 

the mode noise is larger and the spectral energy lower. The use of a modeless dye 

laser should be considered for the mixing test-case. Since the N2 and O2 spectra can 

be put close to each other, the reduced bandwidth is no longer an issue. The use of the 

modeless dye laser combined with simultaneous acquisition of a resonant and a nonresonant CARS signal, would also allow removal of the mode noise that is a major 
261 

noise source in CARS, allowing even higher improvement in precision as discussed 

in Ref.[106]. 
262 

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914 2011. 
REPORT DOCUMENTATION PAGE Form Approved

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Contractor Report

 4. TITLE AND SUBTITLE

Dual-Pump CARS Development and Application to Supersonic 

Combustion

5a. CONTRACT NUMBER

NNX08AB31A, NNX07AC32A

 6. AUTHOR(S)

Magnotti, Gaetano; Cutler, Andrew D.

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 NASA Langley Research Center The George Washington University 

Hampton, Virginia 23681-2199 1 Old Oyster Point

 Newport News, Virginia 23602

 

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14. ABSTRACT

A dual-pump Coherent Anti-Stokes Raman Spectroscopy (CARS) instrument has been developed to obtain simultaneous measurements of

temperature and absolute mole fractions of N2, O2 and H2 in supersonic combustion and generate databases for validation and development 

of CFD codes. Issues that compromised previous attempts, such as beam steering and high irradiance perturbation effects, have been 

alleviated or avoided. Improvements in instrument precision and accuracy have been achieved. An axis-symmetric supersonic combusting 

coaxial jet facility has been developed to provide a simple, yet suitable flow to CFD modelers.Approximately one million dual-pump CARS 

single shots have been collected in the supersonic jet for varying values of flight and exit Mach numbers at several locations. Data have been 

acquired with a H2 co-flow (combustion case) or a N2 co-flow (mixing case). Results are presented and the effects of the compressibility 

and of the heat release are discussed.

15. SUBJECT TERMS

CARS; CFD validation; Experiments; Fluid mechanics; Gas dynamics; Laser Diagnostics; Scramjets; Supersonic jets; 

Supersonic mixing; Supersonic shear layers

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