ABSTRACT 
 
 
 
 
Title of Document: THE ROLE OF DENSITY GRADIENT IN 
LIQUID ROCKET ENGINE COMBUSTION 
INSTABILITY 
  
 Amardip Ghosh, PhD, 2008 
  
Directed By: Professor Kenneth H. Yu, Department of 
Aerospace Engineering  
 
 
 
Experimental and analytical studies were conducted to investigate key physical 
mechanisms responsible for flame-acoustic coupling during the onset of acoustically 
driven combustion instabilities in liquid rocket engines (LREs). Controlled 
experiments were conducted in which a turbulent Hydrogen-Oxygen (GH2-GO2) 
diffusion flame, established downstream of a two-dimensional model shear coaxial 
injector was acoustically forced by a compression driver unit mounted in a transverse 
direction and excited through a broad range of frequencies (200Hz-2000Hz) and 
amplitudes. Characteristic interactions between flame and acoustics visualized 
through OH* and CH* chemiluminescence imaging and dynamic pressure 
measurements obtained using high frequency dynamic pressure transducers indicated 
that small acoustic disturbances could be amplified by flame-acoustic coupling under 
certain conditions leading to substantial modulation in spatial heat release 
fluctuations. Density gradient between fuel and oxidizer was found to significantly 
  
affect the way acoustic waves interacted with density stratified flame fronts. The 
particular case of an asymmetric flame front oscillation under transverse acoustic 
forcing indicated that baroclinic vorticity, generated by the interactions between 
misaligned pressure gradient (across the acoustic wave) and density gradient (across 
the fuel oxidizer interface) could further amplify flame front distortions. Asymmetric 
interaction between flame and acoustics is shown to occur preferentially on flame 
fronts where controlled waves from the compression driver travel from lighter fluid to 
denser fluid and the amount of interaction between flame and acoustics is shown to 
depend strongly on the density ratio between the fluids on either sides of the flame 
front. This observation is in agreement with the baroclinic vorticity mechanism and a 
variant of the classical Rayleigh-Taylor instability mechanism. The results provide 
the first known experimental evidence that baroclinic vorticity could play a role in 
triggering flame-acoustic interactions associated with LRE shear coaxial injectors. 
Parametric studies investigating the sensitivity of flame-acoustic interaction on key 
physical parameters that govern shear coaxial injector operations (including density 
ratio, velocity ratio, momentum ratio and chemical composition of the fuel) were 
conducted by varying the parameter of interest independently while holding the other 
parameters relatively constant. Density ratios ranging from 1 to 16, velocity ratios 
ranging from 3.02 to 5.27, momentum ratios ranging from 0.67 to 2.12 and fuel 
mixtures ranging from pure Hydrogen to 10%-90% GH2-GCH4 combination were 
tested. It is shown that in the ranges considered, flame-acoustic interaction is most 
sensitively affected by density ratio changes. Spectral measurements of flame front 
oscillations using local chemiluminescence measurements further revealed the non-
  
linear nature of the interaction process : a flame system forced at 1150 Hz gave rise 
not only to 1150 Hz oscillations but also triggered flame oscillations occurring at 
substantially lower frequencies. Analytical models were developed to interpret and 
predict acoustic modes of a combustion chamber containing a density stratified 
flowfield subjected to transverse acoustic disturbances. Incorporating both the known 
phenomenon of jet mixing length and the new experimental result of preferential 
excitation, the models allow different resonant behaviors to occur for separate regions 
of the combustor bounded by sudden changes in density. For isothermal experiments 
where the flow temperatures were known, calculated Eigen frequencies were in good 
agreement with measured frequencies. Overall, the identification of fuel-oxidizer 
density ratio as a critical parameter in flame acoustic coupling and the identification 
of baroclinic vorticity as a potential mechanism in flame acoustic coupling are 
significant because a  reduction in the density gradient between fuel and oxidizer 
could be used as a control mechanism to improve flame stability in liquid rocket 
engines.  
 
 
 
 
 
 
 
 
 
 
  
 
 
 
THE ROLE OF DENSITY GRADIENT IN LIQUID ROCKET ENGINE 
COMBUSTION INSTABILITY   
 
 
 
By 
 
 
Amardip Ghosh 
 
 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
2008 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Associate Professor Kenneth H. Yu, Chair 
Professor Ashwani K. Gupta 
Associate Professor David Akin 
Associate Professor Christopher Cadou 
Associate Professor Arnaud Trouv? 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Amardip Ghosh 
2008 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ii 
 
Dedication 
 
 
 
To my parents for their continuing support and blessings and great faith in all my 
efforts and endeavors. 
 
 
 
 
 
 
 
 
 
 
 iii 
 
Acknowledgements 
 
 I am grateful to Dr. Kenneth Yu, my faculty advisor and the director of the 
space vehicle research institute for his many valuable suggestions and constructive 
criticisms, both in the course of the research and in the writing of this dissertation. 
His simple yet keen insight into the nature of various fluid mechanical processes has 
significantly changed my way of looking at experimental data. Between the times 
when I started off with this project and now when I am about to finish I feel that this 
has made me a substantial change in my ability as a researcher. I am grateful to Dr. 
Arnaud Trouv? and Dr. Tingguang Ma of the Fire Protection Engineering department 
who worked closely in developing numerical simulations corresponding to some of 
my experiments. I am grateful to my family here in Timonium and all my friends here 
at College Park who made life in the lab and on campus enjoyable. Thanks are due to 
Ipshita Chakraborty, Mike Krasel and Colin VanDercreek for proofreading my thesis, 
Rebanta Chakraborty for always being curious about my research in particular and 
my life in general, Qina Diao for helping me in conducting many of the experiments 
reported in this work, Vivek Gautam for reminding me in the early days of my 
research that my work was good but not enough, Abhishek, Anand, Siddharth and 
Sachin for making life at 7422 W Park more like that of a family, Anna Obizhaeva 
for offering her help in improving the quality of my slides for presentation and 
Ranjeeta Pal for being an affectionate sister and checking on me every now and then. 
I am grateful to my committee members for their time and critical evaluation. This 
research was supported by NASA SVTI with Claudia Meyer as program manager. 
 
 iv 
 
The support is gratefully acknowledged. I am grateful to my parents, whose 
supportive role in my education and upbringing is beyond words.  Finally, I am 
grateful to the humble towns of Hyattsville and College Park, for giving me the 
chance to live learn and grow. 
 
 v 
 
Table of Contents 
 
 
Dedication.....................................................................................................................ii 
Acknowledgements......................................................................................................iii 
Table of Contents..........................................................................................................v 
List of Tables..............................................................................................................viii 
List of Figures...............................................................................................................x 
Nomenclature.............................................................................................................xxi 
Chapter 1: Introduction.................................................................................................1 
1.1 Background and Motivation................................................................................1 
1.2 Key Physical Mechanisms..................................................................................6 
1.2.1 Baroclinic Vorticity Driven Instability........................................................6 
1.2.2 Rayleigh-Taylor Instability..........................................................................7 
1.2.3 Richtmyer-Meshkov Instability...................................................................7 
1.3 Technical Objectives...........................................................................................8 
1.4 Scope of the Present Work..................................................................................9 
Chapter 2: Literature Review......................................................................................13 
2.1 Thermoacoustic Instabilities in Combustion Systems......................................13 
2.1.1 Introduction................................................................................................13 
2.1.2 Historical Developments............................................................................15 
2.1.3 Rayleigh?s Criterion...................................................................................17 
2.1.4 Representative Work in the Area...............................................................20 
2.2 Combustion Instability in Liquid Rocket Engines............................................24 
2.2.1 Introduction................................................................................................24 
2.2.2 Representative Work in the Area...............................................................26 
2.2.3 Prior Research involving Shear-Coax Injector Element............................33 
2.3 Acoustically Driven Instabilities.......................................................................35 
2.3.1 Introduction................................................................................................35 
2.3.2 Unsteady Atomization under Acoustic Oscillations..................................35 
2.3.3 Unsteady Vaporization under Acoustic Oscillations.................................38 
2.3.4 Flame Response under Acoustic Oscillations............................................39 
Chapter 3: Review of Key Physical Mechanisms.......................................................43 
3.1 Baroclinic Vorticity Driven Instabilities.......................................................43 
3.2 RM and RT instability of acoustically accelerated interfaces.......................46 
3.3 Jet Preferred Mode and Wake Mode Instabilities.........................................50 
Chapter 4: Experimental Apparatus and Techniques..................................................53 
4.1 Introduction.......................................................................................................53 
4.2 Description of Apparatus..................................................................................54 
4.2.1 Combustor Geometry.................................................................................54 
4.2.2 Inlet Section................................................................................................55 
4.2.3 Supply System for Fuel and Oxidizer........................................................56 
4.2.4 Acoustic Driver..........................................................................................56 
4.3 Instrumentation and Diagnostics.......................................................................56 
4.3.1 Schlieren Imaging......................................................................................56 
 
 vi 
 
4.3.2 Phase Sensitive OH*/CH* Chemiluminescence Visualizations................57 
4.3.3 Dynamic Pressure Measurements..............................................................58 
4.3.4 High Speed Cinematographic Imaging......................................................59 
4.3.5 Hotwire Measurements..............................................................................59 
4.3.6 OH* / CH* Chemiluminescence Oscillation Measurements.....................59 
4.3.7 Other Lab Equipments...............................................................................60 
4.4 Flow Rate Calculations.....................................................................................61 
4.5 Injection Arrangement.......................................................................................62 
4.6 Firing sequence for reacting flow experiments.................................................63 
4.6.1 Ignition.......................................................................................................63 
4.6.2 Extinction...................................................................................................64 
Chapter 5 :  Experimental and Analytical Characterization of Chamber Acoustics 
using Broad-Band Forcing..........................................................................................66 
5.1 Preliminary Experiments...................................................................................67 
5.2 Model Development..........................................................................................68 
5.2.1 Full Mixing Model / Well Stirred Reactor Model......................................71 
5.2.2 Jet Mixing Length Model...........................................................................72 
5.2.3 Acoustically Driven Entrainment Model...................................................73 
5.3 Comparison of Isothermal Case Data with Model............................................75 
5.4 Extension to Density Stratified Reacting Flows...............................................76 
Chapter 6:  Acoustic Excitation of Density Stratified Non-Reacting Flow Fields.....77 
6.1 Acoustic Modes.................................................................................................78 
6.1.1 Characteristic Acoustic Frequencies..........................................................78 
6.1.2 Acoustic Excitation at Characteristic Frequencies.....................................78 
6.2 Hydrodynamic Modes.......................................................................................82 
6.2.1 Characteristic Hydrodynamic Frequencies................................................83 
6.2.2 Acoustic Excitation at Characteristic Hydrodynamic Frequencies............85 
Chapter 7: Acoustic Excitation of Chemically Reacting Flow Fields........................87 
7.1 Characteristic Flame Acoustic Interactions.......................................................87 
7.2 Baroclinic Vorticity as a Potential Mechanism.................................................89 
7.2.1 Pressure Amplitude Change Experiment...................................................92 
7.2.2 Density Ratio Change Experiment.............................................................93 
7.2.3 Density Gradient Reversal Experiment......................................................95 
7.2.4 Further Considerations for the Density Ratio Variation Tests...................98 
7.3 Estimation of Growth Rates for the Flame Perturbations...............................104 
7.4 Parametric Studies...........................................................................................105 
7.4.1 Dimensional Analysis..............................................................................105 
7.4.2 Effect of Density Ratio.............................................................................108 
7.4.3 Effect of Velocity Ratio...........................................................................109 
7.4.4 Effect of Momentum Ratio......................................................................110 
7.4.5 Effect of Chemical Composition of Fuel.................................................112 
7.5 Spectral Measurements and High Speed Imaging...........................................114 
7.5.1 High Speed Imaging Results....................................................................114 
7.5.2 PMT tube OH* Chemiluminescence oscillation results..........................115 
Chapter 8: Summary and Conclusions......................................................................119 
8.1 Summary of key tasks.....................................................................................119 
 
 vii 
 
8.2 Summary of important findings......................................................................121 
8.2.1 Qualitative characterization of flame-acoustic interactions.....................121 
8.2.2 Identification of new physical mechanism...............................................123 
8.2.3 Sensitivity analysis and measurements....................................................125 
8.2.4 Non-linear response in flame-acoustic interaction...................................129 
8.2.5 Model development..................................................................................129 
8.3 Concluding remark..........................................................................................132 
Appendices................................................................................................................133 
Appendix A: Images..............................................................................................133 
Appendix B: Tables...............................................................................................221 
Appendix C: Gas Properties..................................................................................230 
Bibliography..............................................................................................................231 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 viii 
 
List of Tables 
 
 
Table 3.1. Location of pressure taps. y-axis is streamwise, x-axis is transverse. 
Table 5.1. Comparison of measured spectral peak frequencies and calculated 
resonance frequencies for no-flow with quiescent air. 
Table 5.2. Flow conditions for the different test runs for model development. 
Table 5.3. Comparison of measured spectral peak frequencies and calculated 
resonance frequencies for isothermal flow conditions. 
Table 5.4. Comparison of measured spectral peak frequencies under reacting flow 
conditions. 
Table 7.1. Test conditions for flame response to acoustic forcing at characteristic 
frequencies. 
Table 7.2. Test conditions for the density ratio variation experiments. 
Table 7.3. Test conditions for the reversal of density gradient experiments. 
Table 7.4. Test conditions for change in flame heat release experiments. 
Table 7.5. Test conditions for variation in jet momentum experiments. 
Table 7.6. Flow conditions for the simultaneous measurement of pressure and 
chemiluminescence oscillations. 
Table 7.7. Test conditions for velocity ratio experiments. 
Table 7.8. Test conditions for variation in jet momentum through variation in jet 
densities. 
Table 7.9. Test conditions for variation in jet momentum through variation in jet 
velocities. 
 
 ix 
 
Table 7.10.  Test conditions for flame-acoustic experiments using GH2-GCH4 
blended fuel and Oxygen. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
List of Figures 
 
Figure 1.1. Schematic showing typical flow field in the neighborhood of a LOX- GH2 
shear coaxial injector. 
Figure 3.1. Baroclinic interactions between pressure gradient and density gradient at a 
density stratified interface. (a) Destabilizing interaction. (b) Stabilizing interaction. 
Figure 3.2. RT unstable configurations. (a) Single-mode case. (b) Multi-mode case 
 ( After Kumar, 2003). 
Figure 3.3. RT instability, single wavelength initial perturbation (After Youngs 1984). 
Figure 3.4. Richtmyer-Meshkov instability (After Sunhara et al.,1996). 
Figure 3.5. Jet preferred mode instability. 
Figure 3.6. Wake mode instability.  
Figure 4.1. (a) Physical model. (b) Schematic of the shear-coax injector rig. All 
dimensions are in inches. 
Figure 4.2. Schematic view of shear coax combustor. (a) Overall setup (b) Near 
injector region showing pressure tap locations. All dimensions are in inches. 
Figure 4.3. Physical setup. 
Figure 4.4. Physical model of inlet to combustor. 
Figure 4.5. Schematic showing dimensions for inlet to combustor. All dimensions are 
in inches. 
Figure 4.6. Schematic showing position and size of through holes for bolts for fixing 
the side plates between which the center piece is sandwiched. All dimensions are in 
inches. 
 
 xi 
 
Figure 4.7. Schematic showing side plate with injection location for gases. All 
dimensions are in inches. 
Figure 4.8. Schlieren setup. (a) Laboratory arrangement. (b) Schematic. 
Figure 4.9. Kistler dynamic pressure sensor locations. cf. Table 3.1. for location of 
pressure taps. All dimensions are in inches. 
Figure 4.10. Injection arrangement for reversal of density gradient test. (a) Normal 
configuration. (b) Reversed configuration. 
Figure 4.11. Injection arrangement for the different tests. (a) Effect of density ratio. 
(b) Effect of velocity ratio. (c) Effect of chemical composition of fuel. 
Figure 5.1. Pressure spectrum at (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap#4 . No-
flow conditions. Chamber is excited with band limited white noise forcing. 
Figure 5.2. Pressure spectrum of no flow quiescent air excited with white noise 
redrawn from previous figure. Tap #4.  
Figure 5.3. Pressure spectrum of isothermal case excited with white noise.  Density 
ratio = 14.5.  (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4. 
Figure 5.4. Pressure spectrum of isothermal case excited with white noise.  Density 
ratio = 11. (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4. 
Figure 5.5. Pressure spectrum of isothermal case excited with white noise.  Density 
ratio = 7. (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4. 
Figure 5.6. Schematic showing distribution of acoustic media in a combustor. 
Figure 5.7. Schlieren visualization showing three different acoustic regions of the 
combustor. Regions 1 and 3 are product dominated and can have different resonant 
 
 xii 
 
behaviors in the longitudinal direction because they are bounded from each other by 
interfaces with sudden density changes.  
Figure 5.8. Comparison of experimental and predicted values of resonant frequencies 
for isothermal case. 
Figure 5.9. Pressure spectrum of reacting flow case excited with white noise.  Density 
ratio = 14.5. (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4. 
Figure 5.10. Pressure spectrum of reacting flow case excited with white noise.  
Density ratio = 11.  (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4. 
Figure 5.11. Pressure spectrum of reacting flow case excited with white noise.  
Density ratio = 7.  (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4. 
Figure 6.1. Flow arrangement. Band limited (100Hz ? 10KHz) white noise forcing is 
applied from the left. Center jet of air is at 6m/s and co-flowing Helium jets are at 
18m/s. 
Figure 6.2. Pressure spectrum of isothermal case excited with white noise.  He-18m/s-
Air-6m/s-He-18m/s. (a) Tap #1 , (b) Tap #2, (c) Tap #3, (d) Tap#4. 
Figure 6.3. Pressure spectrum of isothermal case excited with white noise redrawn 
from previous figure (Tap #4). He-18m/s-Air-6m/s-He-18m/s. 
Figure 6.4(a). Baseline case, no forcing, exposure ? 30?s, He-18m/s-Air-6m/s-He-
18m/s. 
Figure 6.4(b). Flow response to forcing  from left at 200 Hz, 40vpp, exposure ? 30?s, 
He-18m/s-Air-6m/s-He-18m/s. 
Figure 6.4(c). Flow response to forcing from left at 234.4 Hz, 40vpp, exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s. 
 
 xiii 
 
Figure 6.4(d). Flow response to forcing from left at 400.4 Hz, 40vpp, exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(e). Flow response to forcing from left at 500 Hz, 40vpp, exposure ? 30?s, 
He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(f). Flow response to forcing  from left at 625 Hz, 40vpp, exposure ? 30?s, 
He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(g). Flow response to forcing from left at 771.5 Hz, 40vpp, exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(h). Flow response to forcing from left at 820.3 Hz, 40vpp, exposure ? 30?, 
He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(i). Flow response to forcing from left at 947.3 Hz, 40vpp, exposure ? 30?s, 
He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(j). Flow response to forcing from left at 1016 Hz, 40vpp, exposure ? 30?s, 
He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(k). Flow response to forcing from left at 1094 Hz, 40vpp, exposure ? 30?s, 
He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(l). Flow response to forcing from left at 1094 Hz, 50vpp, exposure ? 30?s, 
He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.4(m). Flow response to forcing  from left at 1250 Hz, 50vpp, exposure ? 
10?s, He-18m/s-Air-6m/s-He-18m/s. 
Figure 6.4 (n). Flow response to forcing from left at 1850 Hz, 50vpp, exposure ? 
10?s, He-18m/s-Air-6m/s-He-18m/s. 
 
 xiv 
 
Figure 6.4 (o). Flow response to forcing from left at 2676 Hz, 50vpp, exposure ? 
10?s, He-18m/s-Air-6m/s-He-18m/s. 
Figure 6.5.  Acoustic regions of the combustor. Tap #1 measures acoustic signature in 
Region 1 while Tap #4 measures acoustic signature in Region 3.  
Figure 6.6. Comparison of pressure spectrum between Tap #1 and Tap #4 of 
isothermal case excited with white noise. He-18m/s-Air-6m/s-He-18m/s. 
Figure 6.7. Schematic for wake mode instability calculation.  
Figure 6.8. (a) Injection arrangement (b) Hotwire probe location. 
Figure 6.9. Frequency response of velocity in unforced and forced cases (monotone 
excitation). 
Figure 6.10. Frequency response of velocity in unforced and forced cases (broadband 
excitation). 
Figure 6.11(a). Baseline, no forcing, exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.11(b). Flow response to forcing from left at 429.7 Hz, 4 Vpp. Exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.11(c). Flow response to forcing from left at 429.7 Hz, 12 Vpp. Exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.11(d). Flow response to forcing from left at 429.7 Hz, 16 Vpp. Exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.11(e). Flow response to forcing from left at 429.7 Hz, 20 Vpp. Exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.11(f). Flow response to forcing from left at 429.7 Hz, 30 Vpp. Exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 xv 
 
Figure 6.11(g). Flow response to forcing from left at 429.7 Hz, 40 Vpp. Exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 6.11(h). Flow response to forcing from left at 429.7 Hz, 50 Vpp. Exposure ? 
30?s, He-18m/s-Air-6m/s-He-18m/s.  
Figure 7.1. Flow arrangement for the GH2 / GO2 / GH2 turbulent diffusion flame 
system. VO2 = 6 m/s, VH2 = 18 m/s, ReO2 = 4900. Acoustic forcing is from the left. 
Figure 7.2. OH* chemiluminescence showing natural instabilities in an unforced GH2 
/ GO2 / GH2 turbulent flame. VO2 = 6 m/s, VH2 = 18 m/s, ReO2 = 4900. 
Figure 7.3. Pressure spectrum from Tap #4 under band limited (100Hz-10kHz) white 
noise excitation (9 watts).  
Figure 7.4. OH* chemiluminescence at various phases of oscillation (00, 900, 1800 and 
2700) of a GH2 / GO2 / GH2 turbulent flame forced at 300 Hz from the left. VO2 = 6 
m/s, VH2 = 18 m/s, ReO2 = 4900. D is the width of the center jet = 0.75 inch. 
Figure 7.5. OH* chemiluminescence at various phases of oscillation (00, 900, 1800 and 
2700)  of a GH2 / GO2 / GH2 turbulent flame forced at 1150 Hz from the left. VO2 = 
6 m/s, VH2 = 18 m/s, ReO2 = 4900. D is the width of the center jet = 0.75 inch. 
Figure 7.6.  Contour plots showing flame response to an increasing set of acoustic 
forcing amplitude. VO2 = 4.5 m/s, VH2 = 13.5 m/s, ReO2 = 3700. Forcing is increasing 
from left to right and top to bottom, 0 watts, 4.5 watts, 5.3 watts, 7 watts, 9.6 watts 
and 12.5 watts.                  
Figure 7.7(a). Instantaneous OH* chemiluminescence images showing a monotonic 
decay of oscillations as density ratio between fuel and oxidizer is decreased from 15.9 
to 5. VO2 = 4.5 m/s, VH2 = 13.5 m/s, ReO2 = 3700. 
 
 xvi 
 
Figure 7.7(b). Contour plots of ensemble averaged OH* chemiluminescence images 
showing a monotonic decay of oscillations as density ratio between fuel and oxidizer 
is decreased from 15.9 to 5. VO2 = 4.5 m/s, VH2 = 13.5 m/s, ReO2 = 3700. 
Figure 7.8.  Normalized intensity for flame across the width of the combustion 
chamber for different oxidizer-fuel density ratios at an axial location y/D=4.7. At a 
given axial  location, width of flame, ?(y) =| ro- ri |, where the horizontal line 
corresponds to an intensity of 10% of the maximum. 
Figure 7.9. Measured flame brush thickness at various density ratios and axial 
locations. 
Figure 7.10.  Flame brush thickness as a function of density ratio and acoustic forcing 
amplitude. 
Figure 7.11. UV filtered flame image showing natural instabilities in an unforced 
Hydrogen-in-the-center turbulent diffusion flame. VO2/N2 = 17.8m/s m/s, VH2 = 5 m/s, 
ReH2 ~ 600, ReO2/N2 ~ 8800.  
Figure 7.12(a). UV filtered images at various phases of oscillation (00, 900, 1800 and 
2700) of a Hydrogen-in-the-center turbulent diffusion flame forced at 300 Hz (at 30 
Vpp) from the left. VO2/N2 = 17.8m/s m/s, VH2 = 5 m/s, ReH2 ~ 600, ReO2/N2 ~ 8800.  
Figure 7.12(b). UV filtered images at various phases of oscillation (00, 900, 1800 and 
2700) of a Hydrogen-in-the-center turbulent diffusion flame forced at 580 Hz (55Vpp) 
from the left. VO2/N2 = 17.8m/s m/s, VH2 = 5 m/s, ReH2 ~ 600, ReO2/N2 ~ 8800.  
Figure 7.13. Dynamic pressure distribution across the flames. Pressure Tap #1 is 
closest to the speaker. 
Figure 7.14. Variation of density ratio and heat release rate with molar dilution. 
 
 xvii 
 
Figure 7.15. Comparison of flame-acoustic interaction under similar forcing and heat 
release, conditions (15 kW) but different density ratios. OH* chemiluminescence 
images. Density ratios from left to right are as 7.0 or 15.2, 7.0 and 15.2 respectively. 
Figure 7.16. Growth rate of flame perturbation thickness as a function of streamwise 
location 
Figure 7.17. Variation of density ratio and jet momentums with molar dilution. 
Momentum Total = Momentum, center Jet + 2x Momentum, Co-Flow Jet. 
Figure 7.18. Outer jet momentum = 0.0055 kg.m/s2, center jet momentum = 0.0047 
kg.m/s2. Density ratio between oxidizer and fuel is ~ 8. Acoustic forcing is from the 
left and is held fixed at 15.8 Watts.   
Figure 7.19. Outer jet momentum = 0.0055 kg.m/s2, center jet momentum = 0.0036 
kg.m/s2. Density ratio between oxidizer and fuel is ~ 2. Acoustic forcing is from the 
left and is held fixed at 15.8 Watts. 
Figure 7.20. Pressure spectrum at Tap #1 (a) and at Tap #4 (b) for reacting flow-fields 
under white noise excitation for density rations 16, 10 and 6. 
Figure 7.21. Location of pressure measurement and OH* chemiluminescence 
oscillation measurement ports. 
Figure 7.22. Comparison of local OH* chemiluminescence fluctuations responding to 
pressure oscillation at density ratio=14.5.  The sensors are located horizontally at x=-
0.67d (left column) and x=0.67d (right column), and vertically at (a) y=5d, (b) y=3d, 
(c) y=1d. 
Figure 7.23. Comparison of local OH* chemiluminescence fluctuations responding to 
pressure oscillation at density ratio=3.  The sensors are located horizontally at x=-
 
 xviii 
 
0.67d (left column) and x=0.67d (right column), and vertically at (a) y=5d, (b) y=3d, 
(c) y=1d. 
Figure 7.24. Classical RT mode instability analysis yields wavelength-dependent 
growth rate. 
Figure 7.25. Amplification in growth rates as function of acoustic cycle. 
Figure 7.26. Measured flame brush thickness at various density ratios and streamwise 
locations. 
Figure 7.27. Instantaneous OH* chemiluminescence images showing flame 
perturbations affected by fuel-oxidizer velocity ratio. Fuel oxidizer velocity ratios are 
in increasing order from left to right and from top to bottom. Velocity Ratios are as  uf 
/ uo=3.02, uf / uo=3.36, uf / uo=3.64, uf / uo=4.01, uf / uo=4.51, uf / uo=5.03 and uf / 
uo=5.27. 
Figure 7.28. Time averaged OH* chemiluminescence images showing flame 
perturbations affected by fuel-oxidizer velocity ratio. Fuel oxidizer velocity ratios are 
in increasing order from left to right and from top to bottom. Velocity ratios are as  uf 
/ uo=3.02, uf / uo=3.36, uf / uo=3.64, uf / uo=4.01, uf / uo=4.51, uf / uo=5.03 and uf / 
uo=5.27. 
Figure 7.29. Measured flame brush thickness at various velocity ratios and 
streamwise locations. 
Figure 7.30. Flame perturbations affected by fuel-oxidizer momentum ratio involving 
no change in velocity ratio. uf / uo =  3,?o / ?f = 6, ?o / ?f = 5, ?o / ?f = 4, ?o / ?f = 3, ?o / ?f 
= 2, Jo/Jf =1.99, Jo/Jf =1.67, Jo/Jf =1.33, Jo/Jf =1.00, Jo/Jf =0.67. 
 
 xix 
 
Figure 7.31. Flame perturbations affected by fuel-oxidizer momentum ratio involving 
no change in density ratio. ?o / ?f = 7.99, uf / uo=3.36, uf / uo=3.64, uf / uo=4.01, uf / 
uo=4.51, uf / uo=5.27; Jo/Jf =2.12,  Jo/Jf =1.80, Jo/Jf =1.49, Jo/Jf =1.18, Jo/Jf =0.86. 
Figure 7.32. Flame perturbations affected by non-dimensionalized fuel-oxidizer 
momentum difference.  (a) Momentum change through velocity change. (b) 
Momentum change through density change. 
Figure 7.33. Lifted flame using 100% CH4. No acoustic excitation. (a) Instantaneous 
CH* chemiluminescence image (b) Instantaneous OH* chemiluminescence image (c) 
Average CH* chemiluminescence image (d) Average OH* chemiluminescence 
image.  
Figure 7.34.  50% CH4, 50% H2 fueled flame acoustically excited from left at 1150 Hz 
(a) Instantaneous CH* chemiluminescence image (b) Instantaneous OH* 
chemiluminescence image (c) Average CH* chemiluminescence image (d) Average 
OH* chemiluminescence image.  
Figure 7.35. Measured flame brush thickness at various fuel compositions and axial 
locations. 
Figure 7.36. High-speed imaging showing a typical vortex pairing event when the 
GO2 / GH2 turbulent flame is forced at 1150 Hz. VO2 = 4.5 m/s, VH2 = 13.5 m/s., 
Center jet width, D = 0.75 inch. 
Figure 7.37. Time domain and frequency domain measurement of OH* 
chemiluminescence oscillations using PMT. Probe location (x, y) = (-0.375?, 0.375?) 
is shown by the circle on the flame image. VO2 = 4.5 m/s, VH2 = 13.5 m/s., Center jet 
width, D = 0.75 inch. Forcing is from left at 1150 Hz. 
 
 xx 
 
Figure 7.38. Time domain and frequency domain measurement of OH* 
chemiluminescence oscillations using PMT. Probe location (x, y) = (-0.375?, 2.25?) 
is shown by the circle on the flame image. VO2 = 4.5 m/s, VH2 = 13.5 m/s., Center jet 
width, D = 0.75 inch. Forcing is from left at 1150 Hz. 
Figure 7.39. Time domain and frequency domain measurement of OH* 
chemiluminescence oscillations using PMT. Probe location (x, y) = (-0.375?, 3.75?) 
is shown by the circle on the flame image. VO2 = 4.5 m/s, VH2 = 13.5 m/s., Center jet 
width, D = 0.75 inch. Forcing is from left at 1150 Hz. 
Figure 7.40. Time domain and frequency domain measurement of OH* 
chemiluminescence oscillations using PMT. Probe location (x, y) = (-1.375?, 3.75?) 
is shown by the circle on the flame image. VO2 = 4.5 m/s, VH2 = 13.5 m/s., Center 
jet width, D = 0.75 inch. Forcing is from left at 1150 Hz. 
Figure 7.41. Instantaneous OH* chemiluminescence image for a GH2/GO2/GH2 
flame forced at 1150 Hz from left (a) and OH* oscillation as picked up by PMT 
sensor at location marked ?A? (b) and ?B? (c). OH* oscillations are large when 
acoustic waves from driver are passing from lighter H2 to denser O2. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 xxi 
 
 
Nomenclature 
   
.
m = Mass flow rate 
a = Speed of sound 
? =   Vorticity 
?    = Density                                                                  
u = Velocity 
J = Momentum  
Y = Mole fraction 
n   =    Number of moles   
?  = Excited flame brush thickness 
D = Width of center jet 
x = Distance in transverse direction 
y = Distance in streamwise direction 
?  = Density 
p = Pressure 
T =  Temperature 
Re = Reynolds number 
St =  Strouhal number 
f =  Frequency 
L =  Length of Combustor 
MW = Molecular weight 
 
 xxii 
 
chem?  = Characteristic chemistry time scale 
Q = Heating rate (Joules/Mole)      
? = Dynamic viscosity 
?  =    Kinematic viscosity 
? = Ratio of specific heats 
*A  = Choked orifice area 
R = Gas specific gas constant  
op  = Stagnation pressure 
oT  = Stagnation temperature 
I = Intensity 
 
 
Subscripts: 
o =  Oxidizer 
f =  Fuel 
a =  Ambient 
u = Universal 
p = Products 
max = Maximum 
 
Abbreviations 
LRE =  Liquid Rocket Engine 
LOX =  Liquid Oxygen 
 
 xxiii 
 
GO2 = Gaseous Oxygen 
GH2 = Gaseous Hydrogen 
GCH4 = Gaseous Methane 
PMT    =   Photo-Multiplier-Tube 
RT    =   Rayleigh-Taylor (Instability) 
RM    =  Richtmyer-Meshkov (Instability) 
KH    =  Kelvin-Helmholtz (Instability) 
VK          = Von Karman 
FFT      =  Fast Fourier Transform 
FPS    =  Frames Per Second 
Vpp     = Volts Peak-to-Peak (Acoustic Forcing Amplitude) 
UV     = Ultra Violet 
RMS     = Root Mean Square
 
 1 
 
Chapter 1: Introduction 
1.1 Background and Motivation 
 Combustion instabilities remain among the most challenging problems 
encountered in power and propulsion systems in which, large amplitude pressure 
oscillations, driven by in phase heat release ( Rayleigh 1945; Chu 1956; Putnam  and 
Dennis 1954; Culick 1987) adversely affect the stability and survival of the flame, 
produce intense vibrations, enhance heat transfer rates (Rupe and Jaivin, 1964) and in 
certain extreme cases lead to catastrophic failures (Williams 1984; Putnam 1971; 
Candel 1992; Clayton and Rogero 1965).  
 In confined geometries where combustion occurs inside a combustion 
chamber, interactions leading to such instabilities take place as a result of acoustic, 
vortical, and/or entropy coupling (Lieuwen 2003). Acoustic coupling, in particular, 
involves the interaction of the flame with standing and/or traveling pressure waves, 
and has been studied both experimentally (Crump et al. 1986; Yu et al. 1991; Broda 
et al. 1991, Cohen et al. 2003; Lieuwen 2002) and theoretically (Marble and Candel 
1978; Flandro et al. 2004; Lieuwen 2003; Subbaiah 1983; Lieuwen 2001; Zambon 
and Chelliah 2006).  Under certain circumstances, small amplitude acoustic 
disturbances can cause large amplitude heat release oscillations. Self-sustaining 
oscillations can eventually be excited if the phase relation between the modulated 
burning rate variations and pressure oscillations is favorable, as per the Rayleigh?s 
criteria (Rayleigh, Lord, 1945; Sreenivasan and Raghu 2000).  
 
 2 
 
 For liquid rocket engines in particular, transverse modes? of the chamber 
(tangential and radial modes) are known to interact with combustion heat release 
resulting in high-frequency high-amplitude pressure oscillations (Culick and Yang 
1995; Rubinsky 1995). Combustion instabilities characterized by such pressure 
oscillations are extremely destructive and the hardest ones to control (Crocco et al. 
1960; Reardon et al. 1964). Male et al. (1954), for instance, report severe heat 
transfer rates, sometimes high enough to lead to destructive burnouts of entire thrust 
chamber assemblies during such instabilities. Reardon (1961), reports peak-to-peak 
values as high as 300% (of the steady chamber pressure) in the amplitudes of purely 
transverse modes. Clayton and Rogero (1965) report high amplitude tangential mode 
rotating detonation like pressure waves excited during resonant combustion of a 
20,000 lbs thrust laboratory liquid rocket engine. Ebrahimi et al. (2000) report severe 
vibrations (greater than 1000g) that can practically impair operability of sensitive 
guidance instruments.  
 The interaction between transverse pressure waves and the flow field in the 
vicinity of the injector is critical to the instability problem. Acoustic fluctuations, for 
instance, in the neighborhood of the injector affect injection, atomization, 
vaporization, mixing and subsequent combustion of propellants and thereby influence 
the combustion characteristics and stability behavior of the entire engine.  The role of 
a superimposed oscillatory field on unsteady atomization has consequently been 
                                                 
? Transverse modes of instability dominate the rocket engine environment for various reasons. Firstly, 
most of these engines have a low length-to-diameter ratio (Fischbach et al. 2007) that allows transverse 
modes of comparable frequencies to be excited. Secondly, the exhaust nozzle dampens longitudinal 
modes to a greater extent as compared to the tangential modes (Oefelein and Yang 1993). Thirdly, 
shock waves perpendicular to the engine axis introduce additional dissipation for the longitudinal 
waves but not for the transverse ones (Maslen and Moore 1956). 
 
 
 3 
 
investigated by several researchers in the past (cf. Cold flow experimental studies by 
Miesse (1955), Reba and Brosilow (1960), Buffum and Williams (1967); reacting 
flow experiments by Heidmann (1965) and Ingebo (1966), Lecourt and Foucaud 
(1987); Analytical studies by Clark (1964), Buffum and Williams (1967), Heidmann 
and Groeneweg (1969)). Unsteady vaporization under the influence of acoustic 
oscillations has also been studied by various investigators (cf. Wieber and Mickelsen 
(1960), Heidmann and Wieber (1966), Crocco et al. (1967), Abramzon and Sirignano 
(1988), Chiang, Raju and Sirignano (1989), Anderson and Winter (1992), Fichot, 
Harstad and Bellan (1993)). Combustion response to acoustic oscillations has been 
studied extensively and a detailed review is presented in section 2.3.4.. Various fluid 
mechanical and chemical processes that occur near the injector are more sensitive to 
velocity fluctuations that are parallel to the injector faceplate than to fluctuations that 
are normal to it. Also, because of higher densities near the injector faceplate, acoustic 
pressure amplitudes of purely tangential modes are found to be significantly higher 
near the injector than near the nozzle (Kim and Williams 1998) which  contributes to 
an increase in the sensitivity of acoustic instabilities to the characteristics of flames 
near the injector. With the near injector region containing practically most of the 
mechanisms that lead to instability, (Oefelein and Yang 1993) such sensitivity often 
closes feedback loops and allows the transverse modes to grow through conditions 
favorable for positive thermo-acoustic coupling.  
 Although most injectors would be subjected interactions of this kind, for 
purposes of this research, the scope was restricted to flame acoustic interactions 
occurring in the near field of the shear coaxial injector. Such injectors, used for 
 
 4 
 
instance in the Space Shuttle Main Engine (SSME), consist of a center jet of liquid 
Oxygen (LOX) surrounded by an annular co-flow of high speed gaseous Hydrogen 
(GH2) (Fig. 1.1). Once injected into the chamber, the LOX jet is atomized and 
vaporized, and a diffusion flame is formed between GH2 on one side and GO2 on the 
other. At this initial stage of flame development, any physical mechanism that causes 
flame-acoustic coupling may cause modulations in spatial heat release fluctuation 
which in turn could allow pressure oscillations in the chamber to couple with it and 
drive the combustor unstable. Various fluid mechanical and chemical processes that 
occur near the shear coaxial injector could promote such instabilities. The shear layer 
between the fuel and the oxidizer, in the neighborhood of the injector is subjected to 
wake and jet mode instabilities that could be amplified by certain modes of acoustic 
oscillations in the chamber. Large difference in velocity between fuel and oxidizer 
makes the interface susceptible to Kelvin-Helmholtz (KH) instability and variants 
thereof (Rehab et al. 1997). The presence of a reacting interface between fuel and 
oxidizer which can be driven cellular under certain conditions makes it susceptible to 
thermo-diffusive instabilities (Matalon 2007, Kim et al. 1996). Interactions with finite 
amplitude steep fronted pressure waves? generated through the excitation of chamber 
acoustics makes the density stratified interface between fuel and oxidizer susceptible 
to baroclinic vorticity driven instabilities. A variant of the Richtmyer-Meshkov (RM) 
instability arising from the passage of finite amplitude steep fronted pressure waves 
through the density stratified interface and a variant of the classic Rayleigh-Taylor 
(RT) instability arising from the acoustic acceleration of the density stratified 
                                                 
? The flow of combustion energy to the acoustic waves may supersede the losses leading to the 
formation of non-linear large amplitude shock type steep fronted waves (Ebrahimi et al. 2000). 
 
 5 
 
interface can also be triggered (Taylor 1950; Richtmyer 1960; Meshkov 1969; 
Markstein and Squire 1955). Direct Numerical Simulation (DNS) of violent folding 
of flame fronts under flame acoustic interaction driven RT instability has recently 
been reported (Petchenko et al. 2006). Once instability is excited through any of the 
competing processes, small amplitude acoustic disturbances can cause large 
amplitude fluid movement leading to significant modifications in flame surface area. 
This in turn can lead to a modulation of heat release oscillations driven at the acoustic 
excitation frequencies. Self-sustaining oscillations can eventually be excited if the 
phase relation between the modulated burning rate variations and pressure oscillations 
is favorable, as per the Rayleigh?s criteria. 
 Unfortunately, although the shear coaxial injector is widely used in liquid 
rocket engines to deliver fuel and oxidizer into the combustion chamber (Hulka and 
Hutt 1995; Vingert et al. 1995) there is no definitive knowledge regarding which 
among several competing processes ultimately cause combustion instability in rocket 
motors that use them (Glogowski et al. 1994). Small changes in injector geometry 
and associated flow field variables like fuel-oxidizer velocity ratio, momentum ratio, 
injection temperature and injection pressure drop have been found to have significant 
effect on the overall stability of the engine (Hulka and Hutt 1995). However, physics-
based understanding of such correlations are often not satisfactory. Consequently, 
passive control strategies involving the use of baffles, resonance rods or some 
modification of geometry that were introduced since the early days of rocket engine 
development are still in use (Culick and Yang 1995). The present work is motivated 
by this apparent shortcoming. As a part of this research, flame acoustic interactions in 
 
 6 
 
the near-field of a shear coaxial injector is studied experimentally with the goal of 
identifying physical mechanisms that could play key role during the onset of 
acoustically driven instabilities in liquid rocket engines using such injectors.  
1.2 Key Physical Mechanisms 
 In this study, particular attention is given to interactions between density 
stratified fuel oxidizer interfaces and pressure waves passing through them. As 
already noted in section 1.1, such interactions give rise to various fluid mechanical 
instabilities that need to be critically considered for finding physics based 
mechanisms relevant to the LRE combustion instability problem. It is interesting to 
note that although the density stratification of the shear coax flowfield is well 
recognized and the acoustically charged nature of rocket engine combustor is well 
understood, a study of the interplay between them has not been critically considered 
in evaluating instability mechanisms in liquid rocket engines. In this thesis, it is 
shown that under the acoustic environment of the rocket engine, the density gradient 
between fuel and oxidizer becomes a critical parameter affecting flame acoustic 
interaction. The interaction could take place through the excitation of intermittent 
baroclinic vorticity driven instability, Rayleigh-Taylor instability and in extreme 
cases through the excitation of the Richtmyer-Meshkov instability.  
1.2.1 Baroclinic Vorticity Driven Instability? 
 Baroclinic vorticity is generated when a pressure wave interacts with a density 
stratified interface between two fluids in such a way that the pressure gradient 
                                                 
? For a detailed discussion, see section 3.1 
 
 7 
 
associated with the former is misaligned with the density gradient associated with the 
latter. In the context of the liquid rocket engine, such instability can be generated by 
the interactions between misaligned pressure gradient (across the acoustic wave) and 
density gradient (across the fuel oxidizer interface). Due to presence of large density 
gradients across fuel-oxidizer interfaces and large amplitude pressure waves within 
the combustion chamber, the strength of such vorticity in the near field of the injector 
can be significant. 
1.2.2 Rayleigh-Taylor Instability? 
 When an interface separating two fluids of different densities is accelerated 
such that the acceleration is directed from the denser fluid to the lighter fluid, the 
interface separating the two fluids become unstable with initial perturbations growing 
exponentially in time. The same configuration with acceleration directed in the 
opposite direction is stable with interfacial perturbations remaining bounded in time. 
In the context of the liquid rocket engine, the density stratified fuel-oxidizer interface 
can be acoustically accelerated giving rise to such instability. 
1.2.3 Richtmyer-Meshkov Instability? 
 The Richtmyer-Meshkov instability occurs when a density stratified interface 
is impulsively accelerated (say by the passage of a shock wave). It differs in two 
primary ways from the Rayleigh-Taylor instability. Firstly, RM instability does not 
depend on the direction of the acceleration and secondly, the initial interfacial 
                                                 
? For a detailed discussion, see section 3.2 
? For a detailed discussion, see section 3.2 
 
 8 
 
perturbations grow linearly in time. In the context of the liquid rocket engine, 
acoustic waves can undergo wave amplification and wave steepening resulting in 
steep fronted shock-like waves that can interact with the density stratified fuel-
oxidizer interface giving rise to RM instability?.  
1.3 Technical Objectives 
The technical objectives of this work are as follows: 
1. To study the basic physics of acoustically driven combustion instabilities in 
liquid rocket engines (LREs) that use shear-coaxial injectors.  
2. To characterize flame-acoustic interactions in GH2-GO2 diffusion flames 
during the onset of combustion instability involving a 2D model shear-coaxial 
injector. 
3. To assess the relative importance of hydrodynamic and acoustic modes in 
affecting instability and to study if a hydrodynamic-acoustic coupling 
mechanism is operative during the onset of instability. 
4. To model the relative importance of relevant flow-field parameters affecting 
flame acoustic interaction in LREs. Parameter space will be limited to four 
primary variables : fuel-oxidizer density ratio, fuel-oxidizer velocity ratio, 
fuel-oxidizer momentum ratio and chemical composition of the fuel. 
                                                 
? In practical configurations, an interaction somewhere midway between the RT and RM instabilities 
might be expected in the LRE flowfield. It should be noted that for both RT and RM instabilities, the 
basic mechanism for amplification of initial perturbations is still the baroclinic generation of vorticity. 
 
 
 9 
 
5. To assess the feasibility of actively controlling combustion instability in LREs 
by gaining key insight into various processes and parameters relevant to the 
instability problem. 
6. To build a detailed dataset for model validation on flame-acoustic coupling as 
a function of relevant injection parameters such as fuel-oxidizer density ratio, 
fuel-oxidizer velocity ratio, fuel-oxidizer momentum ratio and fuel 
composition. 
1.4 Scope of the Present Work 
 Overall, the set of experiments conducted as a part of this study involved an 
oversimplification of phenomenon associated with real rocket engines. Firstly, in our 
experiments gaseous Oxygen was used instead of cryogenic Oxygen. Secondly, 
chamber pressure was atmospheric, which in the case of engines like that of Ariane 5 
(Vulcain) could be anywhere around 100 bar. Thirdly, our study dealt with a single 
element injector whereas real rocket engines have hundreds of coaxial injectors 
forming a showerhead covering the motor back plane. Finally, the confinement effect 
provided by the geometry of the combustor used in this study is different from the 
confinement experienced in real engines.  
 However, although the absence of a dominating LOX core prevented the 
characterization of dynamic response of atomization, vaporization, mixing and 
combustion of the LOX jet to acoustic perturbations, it provided a convenient way of 
eliminating instability mechanisms associated with the atomization and the 
vaporization processes and allowed probing into instability mechanisms associated 
specifically with the flame acoustic interaction process. It should be observed here, 
 
 10 
 
that even in liquid rocket engines, by the time the flame is formed downstream of the 
injector, it (the flame) essentially sits between vaporized Oxygen and gaseous 
Hydrogen.  This observation is substantiated by Oefelein and Yang?s (1997) 
observation that in cases involving high heating rates, intermolecular forces are 
reduced which can favor diffusion dominated processes to occur which causes 
diffusion of the liquid core into the co-flowing gas even before substantial 
atomization of the liquid core has occurred. The central jet of liquid Oxygen in such 
cases vaporizes into a continuous fluid in the presence of extremely large density 
gradients and a well mixed diffusion flame is formed at the interface of the two fluids. 
The two-dimensional model was chosen mainly for ease of diagnostics so that 
processes could be studied in detail and data could be generated for model 
validations. Since the acoustic output of the driver unit was limited, the model 
experiments were conducted at scaled-down conditions, ensuring relatively strong 
level of acoustic excitation compared to the level of natural turbulence fluctuations. 
Consequently, the design retained some of the dominant aspects of fluid behavior 
occurring in real engines and the results obtained from this study should facilitate an 
understanding of the real problem under consideration.  
 
The scope of this study is summarized below : 
1. A single element 2D shear-coax injector rig with a transversely mounted 
acoustic driver unit will be used to simulate flame acoustic interactions that 
could occur near the injector plate of a typical liquid rocket engine with  shear 
coax injectors. Carefully controlled flame experiments will be conducted on 
 
 11 
 
turbulent Oxygen-Hydrogen diffusion flames (ReO2? ~ 5500 - 7300) 
acoustically forced at frequencies ranging from 200Hz to 2000Hz.  
2. Experiments will be restricted to the study of flame acoustic interactions 
involving fuel and oxidizer in their gaseous forms. Gaseous fuel would 
essentially mean GH2 (gaseous Hydrogen) sometimes diluted with inert gases 
like Helium and Argon and non-inert gases like Methane. Gaseous oxidizer 
would essentially mean GO2 (gaseous Oxygen) sometimes diluted with inert 
gases like Helium, Argon or Nitrogen.  
3. Periodic vortex structures in the interface between reactants will be visualized 
using phase locked schlieren technique while the time dependant heat release 
patterns will be characterized using OH* and CH* chemiluminescence at 
different phases of the acoustic forcing. Hotwire measurements will be 
conducted to measure natural frequencies in the shear layer for non-reacting 
flow conditions. Dynamic pressure sensors will be used to capture pressure 
oscillations and acoustic modes of the chamber. PMT tube with suitable filters 
will be used to measure frequency of flame oscillations.  
4. Parametric studies will be conducted to see the partial dependency of flame 
excitability to different flow-field variables under given external 
perturbations. Effects of changing density ratio, velocity ratio, momentum 
ratio and chemical composition of the fuel on flame-acoustic interaction will 
be  studied. Density ratios ranging from 1 to 16, velocity ratios ranging from 
3.02 to 5.27, momentum ratios ranging from 0.67 to 2.12 and fuel mixtures 
                                                 
? Re based on width of center jet (0.75in) and velocity of center jet of Oxygen at 4.5m/s and 6 m/s 
respectively. 
 
 12 
 
ranging from pure Hydrogen to 10%-90% GH2-GCH4 combination will be 
tested. 
 
 
 
 
 
 
 
                                                                     
  
 
 
   
 
 
 
 
 
 
 
 13 
 
Chapter 2: Literature Review 
2.1 Thermoacoustic Instabilities in Combustion Systems 
 The first part of this literature review addresses research performed in the 
broad area of combustion instability. Although systems, ranging from industrial 
burners and land based gas turbine engines to aero engines and rockets, are extremely 
different in their constructional and operational details, the fundamental aspects of the 
instability problem remain the same. In fact, much of the fundamental understanding 
gained from the study of combustion instability in other systems has proven valuable 
to the understanding of combustion instability in liquid rockets (Culick and Yang 
1995). An overall review of combustion instability with an historical overview is 
therefore presented to introduce the reader to combustion instabilities in general. The 
particular case of instabilities in liquid rocket engines will be covered in a separate 
section.   
2.1.1 Introduction 
 In the early years of solid rocket motor development, test firings were often 
accompanied by unexpected changes in the mean pressure levels and large amplitude 
structural vibrations. The role of acoustic waves inside the combustor as responsible 
for such erratic behavior was indicated by researchers  (e.g., Boys and Schofield 
1943; Grad 1949) and later established experimentally (e.g., Swanson 1951; Smith 
and Sprenger 1953). Large amplitude pressure oscillations with frequencies close to 
the natural resonant modes of the chamber were observed to be excited in these tests.  
 
 14 
 
 In the years that followed, various studies on instabilities in propulsion 
systems ranging from the liquid and solid rocket engines (e.g., Crocco and Cheng 
1956;  Price 1959; Tsuji and Takeno 1965; Zinn and Powell 1971) to the  jet  engine 
afterburners (Langhorne 1988; Bloxsidge et al. 1988) and ramjet engines (Yang and 
Culick 1986; Schadow and Gutmark 1992; Hedge et al. 1987; Yu et al. 1987; Yu et 
al. 1991; Schadow et al. 1987) revealed that a complex feedback type interaction 
between heat release oscillations and acoustic disturbances in the combustion 
chamber essentially led to the excitation of the large amplitude pressure oscillations. 
These oscillations, when excited in the combustor, were found to affect the stability 
and survivability of the flame, produce intense structural vibrations and thermal 
stresses, reduce engine life and in certain extreme cases lead to catastrophic failures?. 
Similar instabilities were also observed in the combustion chambers of industrial 
burners (Putnam 1971) and gas turbine engines (Kydd 1969; Keller 1995; Lieuwen 
1999; Mongia et al. 2003).  
 Although the details of the interaction process between flame and acoustics 
that led to such instabilities were remarkably complex, the basic phenomenological 
nature of the interaction process was somewhat intuitive. Unsteady combustion 
generated sound (Chu 1953; Zinn 1986; Dowling 1992; Candel et al. 2004). In cases 
where combustion took place in a confined region, like a typical combustor, the 
generated sound reflected from the boundaries of the combustor and interacted with 
the flame system, thereby modulating the source of which they themselves were a 
product of.  Such interactions, under certain conditions, caused more unsteady heat 
                                                 
? In the case of pulse combustors, however, these oscillations are desirable since they lead to enhanced 
rates of heat transfer and/or evaporation (Margolis 1993) and reduces the emission of pollutants like 
NOx , CO and soot (Candel 1992). 
 
 15 
 
release, for example, through changes in fuel-air ratio (Richards and Janus 1998), 
through hydrodynamic instabilities (Poinsot et al. 1987, Renard et al. 2000), or 
through flame area variations. In the nonlinear form, heat release modulations 
sometimes arose from interactions between shock waves and combustion (Rudinger 
1958). When the pressure oscillations and the heat release oscillations were 
sufficiently in phase with one another, amplification in the amplitude of the pressure 
waves eventually occurred as per the Rayleigh?s criterion leading to combustion 
instability. A brief description of this criterion is provided in section 2.1.3.  
2.1.2 Historical Developments 
 Although technological interest in combustion instability was spurred by the 
rocket engine programs of the 1930s, combustion driven acoustic oscillations were 
observed by Higgins (cf. Tyndall 1867) as early as 1777. In what became famous as 
the ?singing flame? experiment, Higgins found that a Hydrogen diffusion flame 
placed inside a closed or an open ended tube could produce sound, given, the fuel 
supply line and the surrounding tube were of certain specific lengths. Later, LeConte 
(cf. Tyndall 1867) observed the ?Dancing Flame?, where a naked flame was seen to 
pulse with the audible beats of music. In 1850, German physicist C. Sondhauss (cf. 
Feldman et al. 1966, Raun et al. 1993) observed sound produced by heating the glass 
bulb of a glass tube having an opening at one end and glass bulb at the other.  Rijke 
(1859) discovered that an audible sound was produced when metal gauze placed in 
the lower half of an open ended vertical tube was heated. He observed that the 
oscillations were strongest when the gauze was located a quarter of the tube length 
from the bottom. He also observed that if the metal gauze was placed in the upper 
 
 16 
 
half of the tube and heated, instead of driving acoustic oscillations, a dampening of 
the oscillations occurred. In a similar apparatus called the Bosscha Tube, (cf. Howe 
1998) oscillations were found to be driven when a refrigerated gauze was placed in 
the upper quarter. Extensive reviews on Rijke oscillations are given by Feldman 
(1968), Raun et al. (1993), and Bisio and Rubatto (1999). Early observations on 
oscillatory combustion were also made by Mallard and Le Chatelier (cf. Mallard and 
Le Chatelier 1883). 
 The discovery of the Rijke tube phenomena was an important milestone in the 
scientific study of combustion instabilities. Although Rijke?s own explanation was 
not sufficient to explain the interplay between heat and sound as observed in his own 
experiments, it spurred a significant amount of interest in combustion driven 
instabilities among the scientific community of his time. Moreover, it provided an 
easy yet excellent setup for which acoustic oscillations could be modeled analytically 
and generated experimentally in terms of acoustic modes and sound pressure levels 
(SPL) (McQuay et al.  2000). Possibly the first theoretical investigation of the 
interaction between pressure waves and combustion was made by Lord Rayleigh 
around 1878 (cf. Rayleigh 1945) in his explanation of Rijke tones. He proposed that 
thermoacoustic oscillations are encouraged when heat fluctuates in phase with 
pressure perturbations.  Popularly known as the Rayleigh?s criteria, it stated that : 
 
?If heat be periodically communicated to, and abstracted from, a mass of air 
vibrating in a cylinder bounded by a piston, the effect produced will depend upon the 
phase of the vibration at which the transfer of heat takes place. If heat be given to the 
 
 17 
 
air at the moment of greatest condensation or to be taken from it at the moment of 
greatest rarefaction, the vibration is encouraged. On the other hand, if heat be given 
at the moment of greatest rarefaction, or abstracted at the moment of greatest 
condensation, the vibration is discouraged?.  
2.1.3 Rayleigh?s Criterion 
 The Rayleigh criterion is commonly described by the following inequality: 
 
 
 
p? and q? are unsteady pressure and heat release oscillations, respectively, ? is the 
period of oscillation, V is the combustor volume (control volume) and ? is the wave 
energy dissipation rate. Thermoacoustic instability occurs when the inequality in the 
above equation is satisfied. The LHS of the inequality describes the total mechanical 
energy added to the oscillations by the heat addition process per cycle and the RHS 
describes the total energy dissipated by the oscillation per cycle. Normally, the 
acoustic dissipation in combustors can be assumed very small (? ? 0) and under this 
assumption, the above equation further simplifies into the following inequality:  
 
 
 
 
 18 
 
This inequality essentially indicates that when p? and q? are sufficiently in phase with 
one another, the combustor will be driven unstable whereas when p? and q? are 
sufficiently out of phase with one another, the effect will be a stabilizing one. It is to 
be noted that the integrals are also spatial, meaning that both effects, destabilizing and 
stabilizing, can occur in different locations of the combustor, and at different times, 
and the stability of the combustor will be decided by the net mechanical energy added 
to the combustor. Rayleigh himself did not indicate how he arrived at such a 
generalized statement.  Noting this shortcoming, Putnam and Dennis (1953) derived a 
mathematical proof for the phasing requirement between pressure and heat release 
oscillations. It was essentially a thermodynamic proof that was accomplished by 
extending a ?customary derivation? of the wave equation for acoustic motions. 
Neglecting the damping forces, Putnam and Dennis put Rayleigh?s Criteria in a very 
precise form: that ?a component of the rate of heat input must be in phase with the 
pressure to drive the oscillation?. In a paper that appeared a year latter (cf. Putnam 
and Dennis 1954), the now well known expression  
 
                                                     ?
cycle
Hpdt > 0                                                        (2..1) 
    
appeared wherein combustion driven oscillations were expected to occur if the 
inequality was satisfied. Here H was the heat release rate and p was the fluctuating 
component of pressure. In a latter work that appeared in 1971 (cf. Putnam 1971) 
Putnam presented an extensive account of various ways in which the Rayleigh?s 
criterion could be used to suppress combustion instability in industrial systems. 
 
 19 
 
 Noting that Putnam?s derivation (Putnam and Dennis 1953) was more 
mathematical than physical, Chu (1956) derived expression (2.1) for the stability of 
systems with heat sources based on the conservation equations. He stated that ?a 
dynamical system will start to oscillate with increasing amplitude only if energy is 
fed into the system in such a way that there is a net increase of the total mechanical 
energy of the system after each cycle of oscillation. The vibration is finally 
maintained at a given level when the mechanical energy fed into the system per cycle 
of oscillation is just equal to the sum of that dissipated by viscosity and that radiated 
away from the system per cycle of oscillation. ?In a latter paper, Chu (cf. Chu 1965) 
used the concept of ?energy in a small disturbance? to derive a generalized form of the 
Rayleigh?s criterion. He also discussed the effects of body forces, heat and material 
sources in promoting the instability and pointed out certain limitations of the 
Rayleigh?s criterion for the stability of systems with heat sources.  
 Culick contributed significantly to the mathematical representation of the 
Rayleigh?s criteria. He (cf. Culick 1976) derived an expression for the energy 
addition to the acoustic mode by considering conservation equations resulting in the 
following equality. 
                                            
 
where p? is the pressure perturbation; '
.
Qis the fluctuation of the heat release rate; ?  
is the gas constant; po is the mean ambient pressure; V is the chamber volume; and T 
is the cycle period. The above expression is an explicit formulation of the Rayleigh?s 
 
 20 
 
criterion indicating that instability is excited when heat release fluctuates with the 
pressure perturbation.  Culick (1987) also performed a detailed analysis of the 
criterion including linear and non-linear thermoacoustic oscillations and arrived at an 
?explicit rendition of Rayleigh?s criterion in a more general form than commonly 
used? given by the following expression for ?energy? for the nth mode. 
 
 
 
If the energy ( )(tn?? ) for the nth mode is positive, then heat addition tends to drive 
the nth mode.  
2.1.4 Representative Work in the Area 
 Since the existing literature on combustion instability is enormous and 
adequate summarization is beyond the scope of this work only a few representative 
works will be cited so as to give the reader familiarity with the important 
developments in this area throughout the last several decades.   
 Gaydon and Wolfhard (1960) provided a brief but interesting review of early 
literature on unstable flames. Studies on the influence of sound on both diffusion 
flames and premixed flames due to Rayleigh, Brown, Tollmien, Zickendraht, Dubois, 
Hahnemann, Ehret, Loshaek et al. were summarized. Toong et al. (1965) studied 
mechanism responsible for triggering, amplification and suppression of acoustic 
waves, due to the presence of flames and suggested that the interaction between 
 
 21 
 
acoustic waves and flame oscillations could occur through both linear and non-linear 
mechanisms. Instability of the traveling Tollmien-Schlichting wave was highlighted 
as a possible mechanism responsible for the self-sustained oscillations of diffusion 
flames. Price (1969) reviewed contemporary advances in solid propellant combustion 
instability in rocket engines. A basic case of instability where the combustor is 
modeled as a closed right cylinder with combustion occurring at the side walls and 
gas oscillations taking place in the first axial standing mode was elaborated. The solid 
burning surface was treated as an acoustically active surface that fed energy into the 
bulk of gas in the combustor. Effects of mean flow were neglected. Marxman and 
Wooldridge (1969) looked into the driving mechanism of high amplitude axial mode 
combustion instability in solid-rocket combustion. The case of a shock wave 
oscillating along the axis was considered. The effect of burning rate perturbation 
induced by the pressure pulse accompanying the shock on the shock wave itself was 
analyzed. Sirignano (1969) treated axial-mode shock-wave oscillations in solid 
rocket-engines and suggested an analytical way of inferring about the combustion 
process inside the combustor from experimental observation of non-linear pressure 
traces during oscillatory operation. Thring (1969) discussed combustion oscillations 
in industrial combustion chambers and classified them into three broad categories: 
combustion roar, Helmholtz resonator oscillations and acoustic oscillations.  Zinn in 
his comments to this paper (cf. Thring 1969) observed the similarity of the various 
types of instabilities mentioned by Thring to those observed in solid and liquid rocket 
engines and suggested a universal way of classifying combustion instabilities arising 
in various systems. Barr?re and Williams (1969) compared combustion instability 
 
 22 
 
found in various types of combustors and defined three classes of instabilities: 
chamber instabilities, system instabilities and intrinsic instabilities. Chamber 
instability was further classified into three categories: acoustic instabilities, shock 
instabilities and fluid-dynamic instabilities.  Kydd (1969) performed analytical and 
experimental work on combustion instability in gas turbine engines and showed that 
inlet pressure drop and the phasing between heat release rate and inlet flow velocity, 
both, could have significant effects on the overall stability of the combustor. Pariel 
and Martin (1969) studied combustion instability in industrial hearths and used 
Rayleigh?s criteria to show how the location of a velocity antinode (or node) with 
respect to the flame, could influence combustion instability. A time delay parameter 
that related the time delay of combustion to the period of oscillation in the 
combustion was introduced. Deckker and Sampath (1971) studied the role of the 
Tollmien-Schlichting waves in the vibration of enclosed laminar diffusion flames and 
indicated that the vibrations were sustained when pressure oscillations and heat 
release oscillations were appropriately phased as per the Rayleigh?s criterion. They 
demonstrated that wave like structures on the interface between the central and 
annular jet could be amplified if the velocity shear between the center and the co-flow 
jets was sufficiently high. Williams (1984) provided a fundamental description of 
combustion instabilities in solid and liquid rocket engines and discussed elaborately 
on mechanisms responsible for amplification and damping. Hydrodynamic and 
diffusive instabilities, non linear effects and oscillatory burning in liquid propellant 
rocket motors were also discussed. This book (Williams 1984) cited 233 references at 
the end of the chapter on combustion instability. Each of these references are 
 
 23 
 
authoritative sources on various aspects of the instability problem. Oran and Gardner 
(1985) studied interactions between acoustics and chemistry in combustion systems. 
Laverdant et al. (1986) investigated the spatial structure of pressure oscillations in a 
combustion chamber.  Starting from the conservation equations for mass, momentum, 
energy and species, Laverdant et al. (1986) obtained an expression for the pressure 
perturbation in a combustion chamber with two source terms. Candel (1992) gave an 
elaborate review of various hydrodynamic processes that lead to pressure and heat 
release oscillations getting sufficiently in phase with each other so as to drive the 
instabilities.  Keller and Barr (1994) studied fluid dynamic stretch as a principle 
delay mechanism preceding ignition of a well stirred mixture of reactants and hot 
products. They showed that such a mechanism could explain experimental 
observations of the peak of energy release proceeding through a minimum during 
peak of reactant injection. Such a delay could influence the phase relation between 
energy release and resonant pressure waves and could thereby promote (or prevent) 
instability as per the Rayleigh?s criteria. Herding et al. (1996) studied flame 
stabilization mechanisms in cryogenic propellant combustion. The structure of the 
flame in the near field of a single element coaxial injector fed with liquid Oxygen 
(center jet) and gaseous Hydrogen (co-flow) was visualized and it was shown that the 
flame was initiated in the proximity of the injector exhaust plane. Kendrick et al. 
(1996) used a one dimensional acoustic model to predict resonant acoustic modes and 
corresponding resonant mode shapes for a laboratory dump combustor. A volumetric 
mass source introduced at a chosen frequency was used to represent the heat addition 
process. Pressure and velocity matching conditions in which velocity satisfied 
 
 24 
 
volumetric continuity at each segment boundary and pressure satisfied a continuity 
condition at the interfaces where one segment was connected to another were used to 
obtain mode shapes for different operating frequencies. A satisfactory analysis of the 
shift of resonant modes between cold-flow and reacting flow conditions was 
presented. B?chner and Leuckel (1996) studied the influence of fuel / air mixture 
oscillations on combustion instabilities in premixed combustors. Sreenivasan and 
Raghu (2000), extended Chu?s 1965 work by including the effect of species 
generation on combustion instability. They showed that under the following 
conditions perturbations inside a combustor are expected to decay in time  ?(a) a 
periodic mass addition antiphase with pressure fluctuations; (b) periodic body force 
antiphase with temperature fluctuations ; (c) periodic heat release rate antiphase with 
temperature fluctuations; (d) species generation antiphase with the appropriate 
chemical potential?. Since temperature and pressure fluctuations are in phase for a 
purely acoustic disturbance, (c) is equivalent to saying that perturbations inside a 
combustor should decay if heat is added antiphase with pressure fluctuations.  
2.2 Combustion Instability in Liquid Rocket Engines 
2.2.1 Introduction  
 Work on liquid rocket engine combustion instabilities began in the early 
1940s (Culick and Yang 1995). One of the most critical concepts in liquid rocket 
combustion instability, that of time lag (as a coordinating factor in influencing 
organized oscillations in liquid rocket combustion chambers) originated around this 
time in von K?rm?n?s group at the Jet Propulsion Laboratory around 1941 (cf. 
 
 25 
 
Summerfield 1951) shortly after oscillations were observed in early tests in liquid 
rocket engines in the United States. The essential idea was that there existed a finite 
time delay when an element of propellant entered the combustor and when heat was 
released from it. This delay controlled the phasing between heat release and pressure 
oscillations thereby making the system stable or unstable as per Rayleigh?s criteria. In 
the years that followed, this model was applied to various studies involving 
combustion instability in liquid rocket engines. Gunder and Friant (1950), Yachter 
(1951) and Summerfield (1951) analyzed low frequency chugging instability arising 
from the interaction between feed system and combustion process using a constant 
time lag model. Crocco (1951;1952) introduced the time varying combustion time lag 
and used it to analyze high frequency instability. Total time lag was separated into 
two parts : a constant (insensitive) time lag and a time varying (sensitive) time lag 
that responded to fluctuations in the chamber conditions and the idea of the 
?interaction index? was introduced. Crocco (1951) first applied the sensitive time lag 
theory to longitudinal oscillations. In the now well known monograph, Crocco and 
Cheng (1956) expanded and generalized the theory of longitudinal mode combustion 
instability. The aspect of linear instability was thoroughly considered but this work 
was published without any experimental verification. The application of the sensitive 
time lag theory to transverse mode instabilities was  first made by Scala (1957) who 
showed theoretically the destabilizing effect of increasing the nozzle entrance mach 
number. No experimental results were however shown. Crocco, Grey and Harrje 
(1960) through a series of experiments, later, showed the apparent validity of the time 
lag hypothesis.  
 
 26 
 
2.2.2 Representative Work in the Area 
 Starting from these early days of research,  a good volume of work has been 
conducted in the area of combustion instability in liquid rocket engines. In one of the 
early experimental works in the field of LRE combustion instability, Berman and 
Cheney (1953) used slit window photographic methods to study longitudinal modes 
of oscillations in rocket motors. They observed the development of small disturbances 
into high amplitude shock type waves with oscillation frequencies coming close to the 
acoustic frequencies of the combustor. Ellis et al. (1953) correlated pressure 
fluctuation measurements with the optical methods used by Berman and Cheney (cf. 
Berman and Cheney 1953). The optical studies were also used by Ellis to study 
transverse mode instabilities in liquid rockets (cf. Ellis 1960).  Very large particle 
velocities and spiral particle trajectories in planes normal to the chamber axis were 
observed. Bellman et al. (1953) used photographic method to investigate combustion 
instability in a 2 dimensional transparent rocket engine. Various injectors, parallel jets 
and impinging jets, were used to study various types of combustion. Male, Kerslake 
and Tischler (1954) at NASA Lewis Research Center conducted optical studies of 
screaming combustion in liquid rocket engines. They noted the  greatly increased heat 
transfer rates to the combustion chamber walls that is typically associated with 
transverse modes of instability in rocket engines. They also noted some interaction 
effects between longitudinal and transverse modes of oscillations. Male and Kerslake 
(1954) at NASA Lewis Research Center showed experimentally the effectiveness of 
longitudinal fins in attenuating transverse mode instabilities in rocket engines. They 
made the important observation that ?lateral oscillations appeared first at the injector 
 
 27 
 
end and then spread throughout the chamber?. Maslen and Moore (1956) theoretically 
studied the effects of viscous damping in a cylindrical combustion chamber without 
combustion. They showed that large amplitude non-shock type waves could exist in 
the spinning form of the tangential mode when viscosity was neglected. The standing 
form of the tangential mode was shown to be subject to damping proportional to the 
amplitude. The ?possible isentropy? of the strong transverse waves was  shown to 
further imply that if energy could be supplied to these waves by coupling with 
unsteady combustion, extremely violent waves may be more likely in transverse 
resonance than in the longitudinal resonance.  For low values of the chamber length 
to diameter ratio, the damping of the fundamental longitudinal mode was also shown 
to be greater than that of the first tangential mode. The authors showed that to a good 
degree of approximation, the shape and particularly the frequency of resonant 
transverse modes of oscillations could be described by linear acoustic theory. Baker 
and Steffen (1958) used high frequency response, water cooled, strain gauge type 
pressure transducers to study screaming tendency of the GH2/LOX propellant 
combination in a 200 lb thrust liquid rocket engine. Four injector classes, a total of 12 
different configurations, were tested with the chamber length varying between 3 to 24 
inches. Their results indicated that compared to all-liquid propellants, the gaseous 
Hydrogen liquid Oxygen propellant combination had considerably lower tendency 
towards screaming. In this work the effects of Hydrogen injection velocity was 
studied. Wieber et al. (1960) conducted a theoretical study of the effects of standing 
transverse acoustic oscillations on the vaporization of liquid fuel droplets and showed 
that in an acoustic field, a drop acquires an oscillating transverse velocity and a 
 
 28 
 
fluctuating rate of vaporization. Osborn and Bonnell (1960 a; 1960 b) used a gas 
rocket system to assess the effects of chamber geometry, chamber pressure and 
propellant chemistry on combustion instability. They noted important interaction 
effects between longitudinal and transverse modes. Working with a constant 
diameter, variable length motor, they observed (for some propellants) that when the 
chamber is length is increased to the point where longitudinal mode instability is 
possible, there is a sharp change in the stability behavior for transverse modes. They 
also noted widened instability region with propellants of higher heat release rates. 
Pickford et al. (1960) attempted to use an available energy concept to come out with a 
method for a priori calculation of stability behavior from the knowledge of the 
physical and chemical nature of the propellants, the injection process etc.  Reardon 
(1961) incorporated Crocco?s sensitive time lag hypothesis in his investigation of 
transverse mode combustion instability in liquid propellant rocket engines. The 
transverse modes of high frequency were studied both theoretically and 
experimentally. Reardon showed that the standing forms of the tangential modes were 
more stable than the spinning forms. Rupe and Jaivin (1964) made experimental 
investigations of the effects of resonant combustion and injection mass flux 
distribution on local heat transfer rates for a 20,000 lb thrust liquid rocket engine. 
Among various other results, variations in heat transfer due to resonant combustion 
for a particular chamber location, variations in transient temperature distributions due 
to resonant combustion and the effect of mixture ratio variation on local temperature 
were reported. For unstable cases, heat transfer rate to the chamber wall near the 
injector was reported to be an order of magnitude greater than those observed during 
 
 29 
 
steady combustion. Crocco (1965) reviewed early works on rocket engine combustion 
instability. Clayton and Rogero (1965) used a 20,000 lbs thrust, heavily instrumented 
laboratory scale liquid rocket engine to experimentally investigate high amplitude 
tangential mode rotating detonation like pressure waves excited during resonant 
combustion of the engine. Wanhainen et al. (1966) studied the effects of propellant 
injection area, propellant injection velocity, oxidant tube exit geometry and the effect 
of Oxygen tube recess on the overall stability of a 20,000 lbs Hydrogen-Oxygen 
rocket engine. Appearance of self triggering under Hydrogen injection temperature 
ramping was used to rate the stability of each of the injector designs. Reardon et al. 
(1967) studied velocity effects in transverse mode combustion instabilities in liquid 
rocket engines. Assuming fluctuations of the radial and tangential velocity 
components to influence the combustion process rates in a manner analogous to that 
proposed previously by Crocco for pressure perturbations, the authors showed that 
tangential velocity fluctuations could destabilize the spinning tangential modes of 
oscillations but will have no effect on the standing modes. Fluctuations in the radial 
velocity component were shown to have smaller yet significant effect. Both 
theoretical work and experimental verifications were performed. Crocco and 
Sirignano (1967) showed that axial oscillations in the rocket chamber (in the linear 
regime) could be damped substantially by increasing the length of the convergent 
section of the nozzle. For the transverse modes however (in both linear and nonlinear 
regimes) nozzles were almost ineffective in their ability to damp oscillations (cf. 
Crocco 1969).  Harrje et al. (1967) showed that the effectiveness of the acoustic 
cavities increased when the passages connecting the cavity with the chamber occurred 
 
 30 
 
at the pressure antinodes of a given mode. Their effectiveness also increased the 
closer they were placed to the injector. Wanhainen et al. (1967) studied Helmholtz 
type acoustic damping devices in suppressing high frequency combustion instability 
in Hydrogen-Oxygen rocket engines. Susceptibility to self triggering under varying 
Hydrogen injection temperatures was used as the criterion for assessing stability. 
Liner with lowest self triggering temperature was considered most stable. 
Interestingly, they showed that acoustic absorbing chamber walls could change 
stability limits and even frequencies of the instability. Sirignano et al. (1967) showed 
(for the acoustic cavity resonator which is derived from the Helmholtz resonator and 
is used to dampen oscillations in a combustor) that a jet is formed at the exit of the 
channel connecting the combustion chamber with the resonant cavity. The eventual 
dissipation of the kinetic energy of the jet provides a non-linear damping mechanism 
whose effectiveness improves with the oscillation amplitude. Barsotti et al. (1968) 
studied the full scale LOX/LH2 M1 engine thrust chamber and showed that its 
stability depended primarily on fuel oxidizer injection velocity ratio. Using the 
Hydrogen temperature ramping method they showed that higher velocity ratio and 
higher Hydrogen injection temperature, both improved engine stability. Crocco 
(1969) presented a detailed analytical framework for dealing with non-linear triggered 
instabilities in liquid rocket engines. Methods of solving for spinning waves in an 
annular chamber, application of the sensitive time lag model (cf. Crocco and Cheng 
1956) to non-linear instabilities and the use of a droplet evaporation model to find a 
solution to the non-linear instability problem were detailed. Crocco also observed that 
the largest oscillation amplitudes for the transverse modes were generally obtained 
 
 31 
 
close to the injector. P.D.McCormack, in his comments to Crocco?s paper on 
combustion instability, (cf. Crocco 1969) actually suggested that considerable 
experimental and theoretical work should be performed on processes occurring at the 
injector. This comment primarily came from McCormack?s observation that pressure 
transients in the injector resulted in ?rapidly spinning droplets, with greatly increased 
evaporation rate and change in trajectory?. Such a change could essentially change 
the nature of the applied perturbation (finite or infinitesimal) and in turn could change 
the resulting instability from one that could be treated through treatments of linear 
acoustics to one which would necessitate the use of non-linear theory. Zinn and 
Savell (1969) studied three dimensional linear combustion instability in liquid 
rockets. A concentrated combustion model (infinitesimally thin combustion zone 
adjacent to the injector faceplate) with Crocco?s time lag hypothesis was used to 
frame a boundary value problem in which the concentrated combustion zone 
boundary condition was satisfied at the injector end and nozzle admittance relation 
was satisfied at the nozzle entrance end. Effects of mach number of the mean flow, 
length of the combustion chamber and convergence of the nozzle on the linear 
stability of chamber modes were analyzed. Priem and Rice (1969) made a theoretical 
investigation of combustion instability in liquid rocket engines with finite axial gas 
velocities and assessed the effects of mach number, chamber length to radius ratio, 
nozzle flow response and acoustic liners on  the stability of the chamber modes. An 
irrotational wave formulation was used in conjunction with specific boundary 
conditions at the injector wall, nozzle entrance and the acoustic liners. Zinn and 
Powell (1971) studied non-linear combustion instability in liquid rockets. The authors 
 
 32 
 
predicted the existence of stable and unstable finite-amplitude limit cycles and 
showed that for moderate amplitudes of oscillations and a low mach number mean 
flow, combustion oscillations in the combustor could be described by a single non-
linear wave equation. A modified version of the classical Galerkin method was used 
to solve the non-linear wave equation. Harrje and Reardon (1972) compiled a 
comprehensive report dealing with the most significant developments, both 
theoretical and experimental, in the area of combustion instabilities in liquid rocket 
engines. Background information on the phenomena of instability, analytical models 
for low and high frequency instabilities, experimental aspects of the study of 
combustion instability and a section on the practical guide to designers focusing on 
the aspects of excitation and damping have been provided in this review. Culick 
(1975 a) developed a formal framework for analyzing the non-linear growth and 
limiting amplitude of acoustic waves in rocket engine combustion chambers. Two 
small parameters (one representing the mean flow field and the other representing the 
amplitude of oscillations) were used to expand the conservation equations resulting in 
a nonlinear inhomogeneous wave equation. The normal modes of the chamber with 
time varying amplitudes were used to synthesize the unsteady pressure and velocity 
fields. This study was essentially a development of a previous work (Culick 1971) 
and the methods used were similar to the ones used by Culick to study linear stability 
of the normal modes of a combustor (cf. Culick 1973; Culick 1975 b). Jahnke and 
Culick (1994) applied dynamical systems theory approach to model non-linear 
combustion instabilities. Mitchell (1994) reviewed progress in analytical modeling 
since 1970 and discussed contemporary developments in modeling the liquid rocket 
 
 33 
 
engine combustion instability problem. Both linear and non-linear approaches have 
been described in this work providing a good starting point for researchers trying to 
understand analytical aspects of the problem. Culick and Yang (1995) reviewed 
combustion instability in liquid rocket engines. Chronological development in the 
area was surveyed. Linear and non-linear behavior was described and examples of 
combustion instability in operational engines were summarized. How elementary 
processes associated with the injection system and the combustion chamber could act 
as mechanisms for exciting and sustaining combustion instabilities were discussed. 
Kim and Williams (1998) used a variational method to theoretically study the effects 
of non-homogeneities (arising, for instance, from density and sound speed variations) 
on the Eigenmodes of acoustic pressure oscillations in liquid rocket engine 
combustion chambers. Fischbach et al. (2007) theoretically examined acoustic 
streaming effects in liquid rocket engines with traveling transverse mode oscillations 
and showed that streaming could promote the development of large amplitude 
steepened wave fronts. 
2.2.3 Prior Research involving Shear-Coax Injector Element 
 The present study deals with flame acoustic interactions in the near field of 
the shear coaxial injector. This injector (also known as the multi tube concentric 
orifice injector) was developed during the late 1940s in the United States and 
eventually became the preferred injector for most flight engines. They were operated 
in the early programs without the indication of any combustion instability, a fact often 
attributed to high Hydrogen injection temperatures (161K) (Hulka and Hutt 1994). 
 
 34 
 
High frequency acoustic instability eventually showed up in exploratory tests in 
which Hydrogen injection temperature was maintained lower than what that these 
injectors were normally designed for.   
 From the early days of its inclusion, people recognized that the overall 
stability of the liquid rocket engine was somehow correlated with phenomena going 
on in the near field of the injector. Consequently, starting from the late 1950s, an 
extensive experimental work on correlating various parameters to engine stability was 
undertaken at NASA Lewis Research Center (LeRC) and NASA Marshall Space 
Flight Center (MSFC). Small changes in injector geometry, inclusion of a small 
recess, changes in fuel oxidizer injection temperature or velocity, changes in injection 
pressure drop - were all shown to affect the stability behavior of the engine 
significantly. Hulka and Hutt (1994) compiled an extensive review of such programs 
at Aerojet, Pratt and Whitney Aircraft, Rocketdyne, LeRC, MSFC and elsewhere 
since the 1940s that showed that the shear coaxial injector element indeed played a 
key role in influencing the overall stability of LOX/Hydrogen rocket engines. 
Oefelein and Yang (1997) conducted experimental investigations on coaxial jets 
simulating the injector and emphasized that parametric studies needed to be 
conducted to quantify the combined influence of key physical quantities like density 
ratio, velocity ratio and momentum ratio associated with the propellant streams to 
understand prevalent processes. Richecoeur et al. (2006) studied a three-element 
injector system under transverse-mode acoustic excitation. Experiments showed not 
only substantial modification in flame spread but also in-phase oscillations of heat 
release as evidenced by OH* emission at the excitation frequency. Non-reacting 
 
 35 
 
experiments (Chehroudi and Talley, 2002; Davis and Chehroudi, 2007)  conducted 
with simulated propellants at near supercritical conditions showed jet core length 
fluctuations associated with transverse forcing under certain conditions. 
2.3 Acoustically Driven Instabilities 
2.3.1 Introduction 
 Combustion instabilities arise due to complex feedback interactions between 
pressure and heat release oscillations. Acoustical oscillations in velocity and pressure 
can significantly influence all the critical processes involved in the operation of a 
liquid rocket engine ranging from atomization, vaporization, unsteady mixing to  
combustion and in turn help set up such complex feedback loops between pressure 
and heat release oscillations. When these oscillations are sufficiently in phase, a 
growth of the initial disturbance results often leading up to catastrophic proportions. 
In our studies, fuel and oxidizer are in gaseous phases and the effects of acoustics on 
combustion instability through its indirect influence on atomization and vaporization 
are not present. However, in order to give the reader a complete picture of why 
acoustical interactions are so important in the study of liquid rocket combustion 
instability, a broader review of relevant research is presented in this section. 
2.3.2 Unsteady Atomization under Acoustic Oscillations 
2.3.2.1 Cold Flow Experiments. 
 In order to understand the dynamic nature of coupling between acoustic 
oscillations and the atomization process, Miesse (1955) conducted cold flow 
 
 36 
 
experimental studies to show that considerable amounts of interactions can occur 
between low speed jets and large amplitude acoustic fields. Reba and Brosilow 
(1960)  studied the influence of longitudinal acoustic waves (created by a siren) on 
the behavior of liquid jets. In their cold flow experiments, strong interaction between 
liquid streams and acoustic fields was shown to occur for high acoustic amplitudes 
ranging from 5 to 30% of mean chamber pressure.  Morrell (1963) and Morrell and 
Povinelli (1963; 1964), in their cold flow experimental studies used high speed direct 
and streak photography to estimate the breakup time of  liquid jets impacted by shock 
waves. Buffum and Williams (1967) performed cold flow experimental and 
theoretical investigations on the interactions between a turbulent liquid jet and a 
standing planar acoustic wave with velocity vector transverse to the jet axis. By 
varying various parameters (injector orifice diameter, jet specific gravity, viscosity, 
injection velocity, sound frequency and amplitude) they showed definite velocity 
coupling between the jet and the acoustic field at amplitudes above 140 dB. Davis 
and Chehroudi (2007) recently studied the effects of transverse acoustics on coaxial 
jets under sub, near and supercritical conditions.  
2.3.2.2 Reacting Flow Experiments. 
 Heidmann (1965) studied acoustic field and jet interactions (LOX-GH2) in a 
two dimensional circular combustor operating under stable, chugging and spinning 
transverse instability regions under reacting conditions. Water cooled piezoelectric 
transducers were used to detect dynamic pressure conditions near the injectors and 
high speed photography was used to draw correlations between the acoustic field and 
 
 37 
 
the oscillatory jet breakup behavior. Progressive changes in the wave shape, 
frequency, and amplitude of the pressure oscillations were observed for both 
chugging and transverse mode instabilities. Heidmann and Feiler (1967), in a later 
year, filed a patent describing a dynamic method of controlling spinning or travelling 
transverse mode instabilities by correcting against oscillations as they started. The 
correction was achieved by injecting the propellant in a tangential way or by 
changing the vector direction of propellants. By sensing the direction of the travelling 
wave and by selectively providing a tangential velocity in the combustion chamber in 
opposition to the travelling wave an attenuation of the instability was aimed. Ingebo 
(1966), used a photomicrographic technique to experimentally study the atomization 
of liquid ethanol sprays under high frequency longitudinal acoustic forcing under 
reacting conditions. Improved atomization and reduced breakup lengths were 
observed under the oscillatory combustion environment. Resonant and non-resonant 
conditions were compared. Lecourt and Foucaud (1987) used the forcing method 
developed by Ingebo to study the stability behavior of several injectors under acoustic 
excitation. With injectors radially distributed along the midlength of the combustor, 
the spray and the combustion zones were submitted to acoustic velocity disturbances 
(velocity coupling) while with injectors distributed axially, the spray and combustion 
zones were submitted to acoustic pressure disturbances (pressure coupling). A 
comparison of the effects of pressure and velocity coupling on combustion instability 
was made and the influence of factors like injector type, chamber pressure and fuel 
were studied. By considering pressure and velocity couplings separately, the goal was 
to find which of the two modes of coupling (pressure or velocity) played a stronger 
 
 38 
 
role during spinning transverse mode instabilities in liquid rocket engines with head-
end injectors. Anderson et al (1998) studied the effects of transverse acoustics on 
periodic atomization in liquid-fuelled rockets and its effect on combustion instability. 
2.3.3 Unsteady Vaporization under Acoustic Oscillations  
 Strahle (Harrje and Reardon (1972)) identified five vaporization characteristic 
times : droplet lifetime, liquid thermal inertia, liquid thermal diffusion time, gas phase 
diffusion time for a locally stagnant gas field, and forced convection gas phase 
diffusion time. Pressure and velocity oscillations in the gas phase (acoustic 
perturbations) could influence the vaporization rate of liquid droplets if the period of 
oscillation corresponded to one of the above-mentioned vaporization characteristic 
times. Wieber and Mickelsen (1960) developed a theoretical model for the effect of a 
standing transverse acoustic field on the vaporization of liquid n-octane droplet. Their 
analysis indicated that a droplet assumed an oscillating transverse velocity and a 
fluctuating vaporization rate under the superimposed acoustic field. Heidmann and 
Wieber (1966) used a transfer function representation of the dynamics of vaporization 
process and developed a linear dynamic response model of a vaporizing droplet 
subjected to a travelling transverse acoustic excitation. When this analysis was 
applied to the vaporization of various fuels and oxidizers, a peak value in the dynamic 
response of the propellants was observed at a particular frequency. Crocco et al. 
(1967) developed a simplified droplet burning model based on a response function 
approach similar to that of Heidmann and Wieber and showed that under certain 
conditions the response function attained a maximum value in a certain frequency 
range. In their experiments, it was shown that vaporization increased significantly at 
 
 39 
 
locations where velocity or pressure was a maximum. Abramzon and Sirignano 
(1988) and Chiang, Raju and Sirignano (1989) included variable liquid properties into 
the classical vaporization model. The roles of convection and internal circulation 
were also considered in their model. 
2.3.4 Flame Response under Acoustic Oscillations 
 As has been already mentioned, acoustic coupling involves the interaction of 
the flame with standing and/or traveling pressure waves, and has been studied both 
experimentally (Crump et al. 1986; Yu et al. 1991; Broda et al. 1991, Cohen et al. 
2003; Lieuwen 2002) and theoretically (Marble and Candel 1978; Flandro et al. 2004; 
Lieuwen 2003; Subbaiah 1983; Lieuwen 2001; Zambon and Chelliah 2006). Acoustic 
waves can directly modulate heat release oscillations through its coupling with the 
flame (pressure coupling and velocity coupling) or can modulate heat release 
indirectly through an intermediate modulation of hydrodynamic instabilities (Candel, 
1992). Under such circumstances, coupling between flame and acoustics can take 
place due to periodic oscillations of equivalence ratio or mixture fractions (Clavin and 
Sun, 1991; Buckmaster and Clavin, 1992; Lieuwen et al. 1998), oscillations of flame 
surface area due to convective effects (Poinsot et al. 1987; Durox et al. 2002), 
oscillations of flame surface area due to acoustically driven accelerations (Putnam 
and Williams 1952; Markstein 1970; Searby and Rochwerger 1991; Pelc? and 
Rochwerger 1992) and also from the direct response of chemical reaction rate to 
pressure in its vicinity (Clavin et al. 1990; Ledder and Kapha 1991; McIntosh 1991; 
McIntosh 1993; McIntosh 1999, Wangher et al. 2008). Under favorable 
 
 40 
 
circumstances, small amplitude acoustic disturbances can cause large amplitude heat 
release oscillations. Self-sustaining oscillations can eventually be excited if the phase 
relation between the modulated burning rate variations and pressure oscillations is 
favorable, as per the Rayleigh?s criteria (Rayleigh, Lord, 1945; Sreenivasan and Ragu 
2000). When unsteady heat release couples sufficiently in phase with the acoustic 
oscillations, the corresponding eigen frequencies of the combustor may be excited as 
per Rayleigh?s criteria. If this energy gain exceeds that lost on reflection at the ends 
of the duct, linear acoustic waves grow in amplitude until limited by nonlinear effects 
(Dowling, 1997).  
 To mention some of the representative work in the area of flame acoustic 
interactions, Strahle (1965, 1967) studied the behavior of laminar jet flames subjected 
to transverse sound waves. McIntosh (1991) studied pressure disturbances of different 
length scales interacting with conventional flames. Candel (1992) reviewed 
combustion instabilities coupled by large scale fluid motions in the presence of 
pressure waves and discussed how hydrodynamic instabilities, vortex-rollup, vortex 
interactions, pulsations of flame or reacting jets , periodic extinctions and re-ignitions 
and flame acceleration could lead to oscillatory heat release. Selerland and 
Karagozian (1998) showed numerically that the response of gaseous diffusion flames 
to an oscillating strain rate (at the fuel oxidizer interface) is strongly dependent on the 
amplitude and frequency of oscillation. Ducruix et al. (2003), Schuller et al. (2003), 
Preetham and Lieuwen (2004), Preetham and Lieuwen (2005) studied the interaction 
between harmonic waves and premixed flames. Richecoeur et al. (2006) studied high-
frequency transverse acoustic coupling in a multiple-injector cryogenic combustor. 
 
 41 
 
Gutmark et al. (1989) used acoustic driver? upstream of the burner nozzle to study 
lean flammability limits of an unconfined premixed jet flame. Lang et al. (1987) and 
Gulati and Mani (1992) used acoustic driver mounted in a transverse direction to 
demonstrate the use of anti sound in controlling combustion instabilities. McQuay et 
al. (2000) experimentally studied the effect of acoustic fluctuations in a Rijke Tube 
on a propane (gaseous fuel) diffusion flame using an end mounted acoustic driver. 
They showed that the flame length decreased in regions with high amplitudes of 
acoustic velocity fluctuations. Enhanced mixing due to such fluctuations was 
hypothesized for the observed reduction in flame length. Farhat et al. (2005) 
experimentally studied the characteristics of a jet diffusion flame under loudspeaker 
induced standing waves. RMS amplitudes of pressure and velocity oscillations (along 
with static pressure amplitudes) were used to explain different kinds of flame acoustic 
interactions (blue flame, mushroom flame, stable flame etc).  However, no detailed 
mechanism was elucidated and the pressure and velocity measurements were 
conducted in corresponding cold flow tests. Also, flame interactions were conducted 
for longitudinal modes and not for transverse interactions. Dattarajan et al. (2006) 
experimentally studied the combustion characteristics (burning rate) of methanol 
droplets (liquid fuel) when placed at the pressure node (velocity antinode) and 
pressure antinode (velocity node) of a cylindrical acoustic chamber excited by an end 
mounted acoustic driver. Significantly greater levels of interaction were observed in 
microgravity environments. The authors reported a 80% variation in burning rate 
when the droplet was placed near a pressure antinode and a 100% variation in burning 
                                                 
? Annaswamy et al. (2000) have shown that the dynamics of the loudspeaker can be modified 
depending on the shape and size of the housing used. Helmholtz mode oscillations can arise from the 
volume enclosed by the loudspeaker housing.  
 
 42 
 
rate when placed at a pressure node. The aspect of an ?effective acoustic acceleration? 
was briefly considered in this work. While velocity straining effect leading to an 
increase in reactant consumption in the vicinity of the burning droplet (Selerland et 
al. 1998) was considered responsible for the observed increase in burning rates, a 
mechanism responsible for increased burning rates near a pressure antinode was not 
elucidated. Suzuki et al. (2007) used high speed imaging and shadowgraphy to 
experimentally study the structure and behavior of a Methane jet inside a diffusion 
flame under transverse acoustic forcing.  They showed that jet meandering behavior 
was synchronous to the external forcing and the meandering motion sometimes 
diverged into two branches under the influence of the transverse forcing. Baroclinic 
effects were not explored. Shanbhogue (2008) experimentally studied the role of 
acoustic forcing in exciting Kelvin-Helmholtz instability in the shear layer of a bluff 
body stabilized flame. The resulting periodic wrinkling of the flame sheet was shown 
to be associated with a consequential heat release oscillation. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 43 
 
Chapter 3: Review of Key Physical Mechanisms 
 Standing and travelling acoustic waves can modulate heat release oscillations 
directly, by coupling with the flame system within a combustor, or indirectly, by 
modulating hydrodynamic instabilities inside the combustor.  Such interactions can 
lead to heat release oscillations arising from periodic oscillations of equivalence ratio 
or mixture fractions, oscillations of flame surface area due to convective effects and 
oscillations of flame surface area due to acoustically driven accelerations. When the 
pressure oscillations are sufficiently in phase with the heat release oscillations, a 
growth in the pressure oscillations can result as per the Rayleigh?s criteria. 
 Since the combustion chamber of a rocket engine provides an acoustically 
charged environment to an otherwise density stratified flowfield, baroclinically driven 
hydrodynamic instabilities could be predominant. In the following sections, some of 
the hydrodynamic instabilities that could play key role during the onset of 
acoustically driven instabilities in amplifying small disturbances into large scale fluid 
motions are discussed.   
3.1 Baroclinic Vorticity Driven Instabilities 
 
 Baroclinic vorticity is generated when a pressure wave interacts with a flame 
front in such a way that the pressure gradient associated with the former is misaligned 
with the density gradient associated with the latter (Fig. 3.1). The strength of the 
rotational motion is given by the vorticity ? defined as the curl of the velocity field. 
The evolution of vorticity is given by the vorticity transport equation, Eq. 3.1, which 
is derived by taking the curl of the Momentum equation.  The first term on the right 
 
 44 
 
hand side of Eq. 3.1 is the baroclinic torque term which is produced from the 
interactions between misaligned density and pressure gradients and can be significant 
in shear-coaxial injector flowfields due to the presence of large density gradients 
across fuel-oxidizer interfaces and large amplitude pressure waves within the 
combustion chamber. 
                                                                   
( ) uuupDtD rrrrrr
r
22
2 )()( ???+?+?????+
???= ?????
?
??                      (3.1) 
 
It is clear that this term increases in proportion with (1) the strength of the density 
gradient, (2) the strength of the pressure gradient, (3) the sine of the angle between 
pressure and density gradient vectors and (4) the reciprocal of the square of the 
density (that is the effect is more pronounced at lower densities, usually associated 
with higher temperatures). The other four terms on the right-hand side of Eq. 3.1 
describe, respectively, the rate of change of vorticity ? due to stretching and tilting of 
the vortex lines, dilatation of the velocity field, viscous diffusion and vorticity 
production due to viscosity gradients.  For the present two dimensional flow, the 
contribution due to stretching is zero. Expansion of gases due to exothermic reactions 
cause velocity divergence to be positive and the dilatational term essentially 
represents an attenuation of any vorticity that may already be present in the reaction 
zone. The diffusion term causes a spreading of the vorticity in space and a reduction 
of the local vorticity (Ashurst and McMurtry, 1989). Since vorticity production from 
a viscosity gradient across a flame is negligible (Sinibaldi et al., 1998), the baroclinic 
torque term (?? x?p) / ?2 is the only dominant source of additional vorticity that 
 
 45 
 
could be created at the flame interface. In a combusting environment where the 
production of vorticity due to baroclinicity arising from misaligned density and 
pressure gradients is always accompanied by a decay of vortex strength because of 
gas expansion or dilatation (Sinibaldi et al., 1998), there will be a threshold such that 
flame perturbations arising from baroclinicity would occur only if vorticity generated 
through baroclinic interactions is greater than that attenuated due to thermal 
expansion. As illustrated in Fig. 3.1, the resulting rotational motion arising from 
baroclinic vorticity can lead to strong roll-up of the flame surface or its stabilization 
depending on the direction of the vorticity field that is established.  For instance, 
compression waves approaching the GH2/GO2 flame front from left could lead to 
either unstable interaction or stable interaction depending on the direction of the 
density gradient at the GH2/GO2 interface and the direction of the pressure gradient 
imposed on it. Across the flame, density gradient vector ?? is normal to the wrinkled 
flame surface and is directed from Hydrogen to Oxygen while the pressure gradient in 
the compression wave traveling from left to right is directed from right to left.  The 
new vorticity that is created from this baroclinic effect is essentially a vector cross 
product between the pressure and density gradients at the interface of the two fluids 
that generating counter-rotating vortex pairs. If the resulting fluid motions are as 
shown in Fig. 3.1a, it leads to an amplification of the initial wrinkling of the flame 
front whereas if the resulting fluid motions are as shown in Fig. 3.1b, it leads to a 
stabilization of the initial interfacial perturbations. When the pressure and density 
gradients are properly oriented, baroclinicity can thus amplify low amplitude acoustic 
fluctuations into large amplitude fluid motions. In a reacting environment, heat 
 
 46 
 
release oscillations can arise out of these large amplitude periodic motions of the fluid 
and in turn be coupled with pressure oscillations within the chamber. Favorable 
coupling between pressure oscillations and heat release oscillations can eventually 
lead to the onset and growth of large amplitude combustion instabilities. Baroclinic 
interactions occurring in premixed flames arising from pressure gradients acting 
across the flame surfaces separating dense unburnt reactants from lighter burnt 
products leading to similar folding events have been detailed in several papers 
(Sinibaldi et al., 1998; Batley et al., 1994; Batley et al., 1996).  An extension of these 
analyses and results to explain baroclinicity produced across a diffusion flame front, 
is, to a first approximation, pretty straight forward. 
3.2 RM and RT instability of acoustically accelerated interfaces 
 When an interface separating two fluids of different densities is accelerated 
such that the acceleration is directed from the denser fluid to the lighter fluid, the 
interface separating the two fluids become unstable with initial perturbations growing 
exponentially in time (Fig 3.2 and Fig 3.3). The same configuration with acceleration 
directed in the opposite direction is stable with interfacial perturbations remaining 
bounded in time. The Richtmyer-Meshkov instability, on the other hand, occurs when 
a density stratified interface is impulsively accelerated. Such a situation can occur due 
to the passage of a shock wave through a density stratified interface. (Fig. 3.4). It 
differs in two primary ways from the Rayleigh-Taylor instability. Firstly, RM 
instability does not depend on the direction of the acceleration and secondly, the 
initial interfacial perturbations grow linearly in time.  
 
 47 
 
 For the liquid rocket engine problem, a variant of the Richtmyer-Meshkov 
(RM) instability arising from the passage of finite amplitude steep fronted pressure 
waves through the density stratified interface and a variant of the classic RT 
instability arising from the acoustic acceleration of density stratified interfaces can be 
triggered (Taylor 1950; Richtmyer 1960; Meshkov 1969; Markstein and Squire 
1955). During such interactions, the flame simply acts as a density stratified interface 
between the fuel and the oxidizer, undergoing acceleration. Consequently the well-
known Rayleigh-Taylor instability can be excited, with the acceleration due to gravity 
in the classical RT equation replaced by that due to a fluctuating pressure gradient 
arising from acoustic interactions. The baroclinic roll-up of the interface is simply a 
more accentuated form of the Rayleigh-Taylor instability. Such instabilities in 
acoustically accelerated flames have been studied by Markstein and Squire (1955) 
and by Petchenko et al. (2006). The acoustic oscillations, in these experiments are 
seen to produce an effective acceleration field at the flame front leading to a strong 
Rayleigh-Taylor instability during every second half of the oscillation period. It has 
been further observed that under such instability, the flame front becomes strongly 
corrugated with elongated jets of heavy fuel mixture penetrating the burnt gas 
(Petchenko et al. 2006). The differences in density at different lateral locations 
encountered by the planar pressure wave with pressure gradient directed from the 
higher density fluid to the lower density fluid leads to differential induced velocities. 
This then causes a spike to develop such that a ?finger? of higher density fluid is 
pushed into the fluid with lower density. If the pressure gradient is in the other 
direction then the instability is suppressed (Liu et al. 1993; Sharp, 1984). 
 
 48 
 
 For the RT instability, the interface amplitude grows as  
02
2
=? ?? kgAdtd                                              ( 3.2)      
                          
where ? is the amplitude of the sinusoidal perturbation of the discontinuous interface 
between two incompressible fluids under acceleration g,  k is the wave number for the 
perturbation and A is the Atwood number across the interface defined 
as )/()( 1212 ???? +? . Here g is directed from 2?  to 1? . ( 2? > 1? ) Eq. 3.2 indicates that 
? grows exponentially with time if A > 0, showing that the interface is unstable, or 
oscillates if A < 0, showing stability. The growth rate for this classical instability, 
classicaln  is given as 
( ) 2/1gkAnclassical =                                         (3.3) 
 
Instead of the acceleration field being created due to gravity, in the present problem 
acceleration is due to passage of acoustic waves through the density stratified fuel-
oxidizer interface. If the complex form of the harmonic solution for the acoustic 
pressure of a plane wave is written as (Kinsler et al.,1982), 
                                
)()( kxtjkxtj BeAep +? += ??                                 (3.4) 
 
then the associated particle velocity ( +u  and ?u ) and acceleration due to acoustic 
forcing ( +a  and ?a  ) is, 
 
 
 49 
 
        )( cpu
o?
+
+ +=  And )( c
pu
o?
?
? ?=                                       (3.5) 
      )( cpja
o?
? +
+ +=     )( c
pja
o?
? ?
? ?=                                        (3.6) 
 
c is the speed of sound. Because of the frequency term (?), acceleration due to 
acoustics can be significant although the period through which such acceleration 
would act would decrease as the frequency is increased. Furthermore, viscosity would 
tend to stabilize the growth rate of the interface such that in real applications, there 
will be a wave number (k) for which the growth rate (n) will reach a maximum 
(Chandrasekhar,1961).  The growth rate vs. wave number  for a given dynamic 
viscosity for the two fluids can be obtained by letting y vary from 1 to ? in Eq. 3.7 
from Chandrasekhar (1961) and finding pairs of values for k (wave number) and n 
(growth rate) for every combination of Q(y) and y. Using a as the speed of sound,  
and ?  as kinematic viscosity, Q in this particular context is defined as  
                                                            23?kaQ =  
Qy( ) y 1?( )
?2 ?1?( )
??
?
??
?
y3 1 4?1? ?2?+( ) y2?+ 3 8?1? ?2??( ) y?+ 1 4?1? ?2??( )??? ???:=
       (3.7) 
kvy( ) a
?2
??
?
??
?
1
3 1
Qy( )
1
3
??
?
??
??
?
??
?:=
 
ny( ) a
2
?
??
?
??
?
1
3
y2 1?( )
Qy( )
2
3
??
?
??
??
?
??
?:=
 
 
 50 
 
 
22
2
1
OH
H
??
??
+=      22
2
2
OH
O
??
??
+=          2
22 HO ??? +=  
 
In this work, the possible presence of acoustically driven RT instability is shown 
experimentally and wave numbers for which high growth rates can be expected are 
evaluated. Through a linear analysis of the growth of a RT unstable interface and 
considering the effects of viscosity, it is shown that more than 200% growth in the 
amplitude of perturbations with the most unstable wavelength can be attained during 
half a period of the acoustic oscillation at certain frequencies. In reality, the interface 
between two fluids will have finite initial thickness. Since the baroclinic torque, being 
proportional to density gradient, is initially responsible for the RT growth, the initial 
growth of finite thickness interfaces, as in the present case, will be slower than that of 
discontinuous interfaces for the same density jump because the density gradient is 
smaller in the former. RT instability of interfaces having initial finite thickness has 
been studied by Lelevier et al. (1955) and Duff et al. (1962). Hsieh (1978) has 
formulated a general problem for interfacial Rayleigh?Taylor instability for fluids 
flow with heat and mass transfer.  
3.3 Jet Preferred Mode and Wake Mode Instabilities 
 Apart from instabilities arising from the acceleration of density stratified 
interfaces, the shear coaxial flowfield is also subjected to wake mode and jet 
preferred mode instabilities.  
 
 51 
 
 The jet preferred mode (Fig 3.5) is usually described as the mode with the 
largest growth rate of the shear layer formed between a jet and the surroundings. 
Defined in terms of the Strouhal number St = fD/U, the most dispersive modes 
correspond to frequencies which make the Strouhal Number fall somewhere between 
0.30 and 0.60. The precise value of the Strouhal number depends on the details of the 
jet, the injector and other associated parameters. 
 The wake mode (Fig 3.6) on the other hand is related to vortex shedding 
behind a bluff body and it generally corresponds to a Strouhal number of 0.20 in the 
turbulent regime.  This mode of instability leads to the shedding of vortices at some 
preferred frequency which might not correspond to the frequency of the most 
amplified KH mode. For high Reynolds number flows, a relation from Prasad and 
Williamson (1997) places the frequencies of the two instabilities as  
 
67.0Re0235.0
VKKH ff =  
 
The calculation of the wake mode frequency associated with the shear coaxial 
flow field relevant to this study needed a few special considerations. Firstly, the 
above criterion of Strouhal number = 0.21 has been experimentally verified for non 
reacting turbulent flows with Re in the range 102 < Re < 107 whereas the flow of 
interest is reacting and the shedding frequency could be influenced by buoyancy 
driven effects due to heat release. Secondly, dilatation due to heat release can lead to 
the stabilization of the VK mode behind a bluff body as has been suggested by recent 
numerical simulations due to Erickson et al. (2006). Although Erickson?s study has 
 
 52 
 
been for a bluff body stabilized premixed flame, a similar reasoning could be applied 
to diffusion flames established in the wake of a bluff body.  Thirdly, the flow around 
our bluff body (the splitter between fuel and oxidizer jets) has two different fluids 
(fuel and oxidizer) flowing around it at different velocities as shown in the schematic 
of Fig. 3.6 which makes the application of the St = fD/U, equation with S = 0.21 
slightly less straightforward. 
 Such instabilities of the shear layer between the fuel and the oxidizer, in the 
neighborhood of the injector can be amplified by certain modes of acoustic 
oscillations within the chamber. Sheridian et al. (1992) for instance showed that 
under the influence of harmonic excitation, the separated shear layer can roll up into 
vortices with a frequency commensurate with the forcing frequency. In a recent study, 
Shanbhogue et al. (2008) experimentally studied the role of acoustic forcing in 
exciting Kelvin-Helmholtz instability in the shear later of a bluff body stabilized 
flame and showed that the resulting periodic wrinkling of the flame sheet was 
associated with a consequential heat release oscillation.  
   
  
 
 
 
 
 
 
 
 53 
 
Chapter 4: Experimental Apparatus and Techniques 
4.1 Introduction 
 A model shear coaxial injector rig was designed to conduct flame acoustic 
interaction experiments relevant to the liquid rocket engine instability problem. A 
transversely mounted acoustic driver was used to simulate acoustic conditions 
occurring in the neighborhood of such injectors. As the acoustic output of the driver 
unit was limited, the model experiments were conducted at scaled-down conditions, 
ensuring relatively strong level of acoustic excitation compared to the level of natural 
turbulence fluctuation.  
 Fig. 4.1a shows a schematic of the near injector region for a liquid rocket 
engine with two shear coaxial injectors, each comprising of a center jet of liquid 
Oxygen (LOX) surrounded by co-flowing regions of high speed gaseous Hydrogen 
(GH2). Once injected into the combustor, the liquid jet of Oxygen is atomized, 
vaporized and a diffusion flame system is eventually formed between gaseous 
Hydrogen and vaporized Hydrogen.   
 The interactions between acoustics and the turbulent multiphase reacting flow 
field in the vicinity of the injector is very complex and involve processes associated 
with periodic atomization and vaporization of the liquid core, unsteady mixing 
between fuel and oxidizer and flame interactions with travelling and standing waves. 
As the goal of this study was to identify instability mechanisms associated in 
particular with interactions between flame and acoustics, a simpler physical model 
that considered the interactions between acoustic waves and GO2-GH2 diffusion 
 
 54 
 
flame fronts was accepted as a good starting point for design of apparatus .  This 
model, shown as an inset in Fig. 4.1a, appears physically meaningful because even in 
real rocket engines using LOX,  by the time the flame is produced downstream of the 
injector, it essentially sits between vaporized Oxygen and gaseous Hydrogen. A 
schematic of the resulting shear coaxial injector rig, based on this simplified model, is 
shown in  Fig. 4.1b with quartz glass windows, acoustic driver, parker skinner valves 
for  flow control and Setra pressure transducers for static pressure measurements 
upstream of choked orifices on the gas lines. The schematic in Fig 4.2 shows a more 
detailed view of the combustor along with the locations for pressure measurement 
taps. Fig. 4.3 shows a detailed view of the experimental rig setup for schlieren 
visualization.  
4.2 Description of Apparatus 
4.2.1 Combustor Geometry 
 The combustion chamber used in this study was of a rectangular waveguide 
geometry and had a dimension of 15?x 3.5?x 0.375?. As shown in Fig 4.2, it  was 
equipped with a 2D shear coaxial injector element at one end while the other end was 
open to the atmosphere. The two-dimensional injector had a center jet that was 0.75 
inch wide and two co-flow jets each 0.25 inch wide. Lip thickness between center jet 
and co-flow was 0.125 inch. The injector end of the combustor was also provided 
with 0.125? slots near the side walls for wall jet injection. Wall jets were only used 
for igniting the combustor and were turned OFF once the diffusion flame system 
between the center and the co-flowing jets was established. 1 inch thick quartz glass 
 
 55 
 
windows gave full access to the test section and allowed direct examination of the 
flame structure, schlieren and shadowgraph imaging and chemiluminescence 
measurements. For studies involving pressure measurements, one of the quartz glass 
sidewalls was replaced by a stainless steel sidewall with pressure taps that allowed 
the flush mounting of water cooled dynamic pressure transducers. Locations of the 
taps on the steel block corresponded to pressure tap locations shown in Fig 4.2b. 
4.2.2 Inlet Section 
 The inlet section, located upstream of the injector faceplate, connected the 
combustion chamber with the fuel and oxidizer lines. Inside the fuel and oxidizer 
lines stainless steel honeycomb sections were used to flatten inlet velocity profile, 
reduce turbulence level, and provide flashback protection. Fig. 4.4 shows an inside 
view of the inlet section with one of the side blocks intentionally removed for easy 
visual access. It shows injection points and flow paths for center, co-flow and wall 
jets along with flow straighteners for the center and the co-flow jets. In the backdrop, 
it also shows vibration dampers on the breadboard, one way check valves on the gas 
lines to prevent back flow of oxidizer or reactant gases and Setra pressure transducers 
to measure pressure on gas lines upstream of their choked orifices. Fig.4.5 and Fig 4.6 
show dimensional details of the injector plate. Fig. 4.7 shows inlet locations for 
center, co-flow and wall jet gases. Port 1 is injection location for the center jet gas, 2a 
and 2b for co-flowing gas and 3a and 3b for wall-jets. Open circles indicate the 
position of through holes used for bolting the side plates with the injector plate. All 
dimensions are in inches. 
 
 56 
 
4.2.3 Supply System for Fuel and Oxidizer 
 Pressurized tanks of Hydrogen and Oxygen supplied fuel and oxidizer to the 
chamber while Argon, Helium and Methane tanks served to dilute individual streams 
in modifying densities, velocities and chemical compositions of individual jets in 
specific experiments. Fuel, oxidizer and diluent gas lines were metered by choked 
orifices. Pressure transducers (Setra model - 206) were used to sense pressure 
upstream of each orifice and the pressure values were read off directly from Setra 
Datum 2000 metering units. Electrically operated, normally closed Parker Skinner 
valves with 0.25? orifices were used for switching purposes on the gas supply lines.  
4.2.4 Acoustic Driver 
 An acoustic driver of nominal impedance 16 ohms and a maximum power 
rating of 100 watts, mounted in a transverse fashion was used to produce controlled 
compression waves at various frequencies and amplitudes. A transition block 
connected the driver unit to the combustor side wall providing a smooth transition 
from a circular  section (driver end of effective diameter of 0.75?) to a 1? x 0.125? 
rectangular slit (combustor end). The acoustic driver had a range of optimal 
operability between 100Hz to 100,000 Hz. 
4.3 Instrumentation and Diagnostics 
4.3.1 Schlieren Imaging 
 The schlieren system (cf. Yang 2001) for the setup featured a typical Z 
configuration (Fig. 4.8). The light from an arc lamp of 10 W nominal power was 
 
 57 
 
collimated by a 60? focal length, 6? diameter spherical mirror. For extremely short 
exposure phase locked schlieren imaging, a 12 bit ICCD DiCam Pro camera was used 
with exposure times that could be controlled to go down to as low as 3ns. In our 
schlieren experiments, images with exposure times as low as 10?s were recorded. For 
phase locked imaging, synchronized pulses from the same wave generator were fed 
into an IDT Laser Timing Control board, which in conjunction with ProVision II 
software running on a Windows machine triggered a DicamPro 12 bit ICCD Camera 
at different phases of the acoustic forcing.  
4.3.2 Phase Sensitive OH*/CH* Chemiluminescence Visualizations  
 To improve our understanding of the instability driving mechanism it was 
necessary to collect some information on the heat release process. A simple technique 
that indicates the rate of combustion involves measuring chemiluminescent radiation 
from the free OH* radical. This radical appears almost exclusively in the reaction 
zone and their emitted light intensity can be directly related to the chemical reaction 
rate or, equivalently to the heat release rate. The relation maybe assumed linear 
(Poinsot et al. 1987; Langhorne 1988). A DiCam Pro ICCD camera with a UV lens 
and a 308 nm band pass filter was used to pick OH* Chemiluminescence from the 
oxy-Hydrogen  flame. For phase locked imaging, synchronized pulses from the same 
wave generator were fed into an IDT Laser Timing Control board, which in 
conjunction with a ProVision II software running on a Windows machine triggered a 
DicamPro 12 bit ICCD Camera at different phases of the acoustic forcing. Images 
with exposure times as low as 8?s were recorded. For instantaneous and ensemble 
averaged imaging, the light emitted by the diffusion flame system was imaged by an 
 
 58 
 
UV lens with a 308nm bandpass filter onto a S20 Multialkali photocathode for the 
OH* chemiluminescence. For the ensemble averaged images, the camera exposure 
was increased to the order of 500ms ? 750ms and a neutral density filter was used 
along with the bandpass filters to control the net amount of light falling on the CCD 
sensor. For CH* chemiluminescence (in cases where a blended fuel of H2 and CH4 
was used), a 430 nm band pass filter was used. 
4.3.3 Dynamic Pressure Measurements 
  To investigate the spectral content of pressure oscillations in the chamber, one 
of the quartz windows was replaced with a stainless steel plate with pressure taps onto 
which the dynamic pressure transducers along with their water cooled adapters could 
be flush mounted. The location of the taps are shown in Fig 4.9. 
  Kistler 211B5 voltage mode high bandwidth dynamic pressure transducers 
with measuring range of 0 to 250 psi were used for dynamic pressure measurements. 
Each Piezotron miniature pressure sensor, housed within a Kistler 228P water-cooled 
adapter was well suited for fast transient measurements under extreme environmental 
conditions. Sensor output was passed through a Kistler 5134A1 Piezotron coupler and 
then fed into a National Instruments Digital Acquisition Card which interfaced with a 
LabVIEW monitoring program. The Piezotron coupler allowed filtering and 
amplification of signal from the sensors. A filter of 10 kHz and a gain of 100 on the 
coupler were typically used. Data was sampled at a sampling rate of 20 kHz. The 
LabVIEW VI not only performed a runtime FFT on the sampled data but also saved 
the data in data files which were subsequently loaded into and analyzed with FFT 
codes in MATLAB. 
 
 59 
 
4.3.4 High Speed Cinematographic Imaging 
 A Photron Fastcam Ultima 1024 high speed camera was used for high speed 
imaging of flame front oscillations. In particular, it was used to observe the rollup of 
the diffusion flame front under transverse acoustic forcing and subsequent pairing and 
merging of vortices. A desktop PC running the Photron Fastcam software was used to 
capture and record images. The camera had an acquisition rate of 60-16000 frames 
per second (monochrome) and shutter speeds from 0.016 to 7.8E-6 s. For the 
requirements of the current investigation, the camera was operated at a framing rate 
of 1000 fps with an associated exposure of 1ms.  
4.3.5 Hotwire Measurements 
 The frequency of structures in the mixing layer between the center jet and the 
co-flow jets (for the non-reacting case) was measured using a conventional miniature 
hotwire probe (film sensor) and a constant temperature anemometer (TSI Model 
1750). The 1750 CTA provided trim control (to optimize the frequency response for a 
given cable length) and gain control that is set at the factory according to the type of 
sensor used (film or  wire).  A power source with an output of 25 volts DC was used 
to power the device.   
4.3.6 OH* / CH* Chemiluminescence Oscillation Measurements 
  A photomultiplier tube (PMT) using a HAMAMATSU R3788 High 
Sensitivity, Bi-Alkali Photocathode (8mm x 24mm) with good spectral response 
between 185nm ? 750 nm was used to measure frequencies at which flame front 
oscillated naturally or under the influence of external forcing. The PMT tube itself 
 
 60 
 
had a circular cross section with ID ~ 0.875? and OD~1.25?. For measuring the 
oscillations of the Oxy-Hydrogen diffusion flame, a 308nm circular bandpass filter 
was mounted inside the PMT tube in front of the photocathode sensor. A TENMATM 
Regulated DC Power Supply supplied the required 15 V DC for stable PMT operation 
while a potentiometer allowed amplification of the voltage signal from the PMT to a 
level suitable for data acquisition. For high frequency flame oscillations (forced at 
~1150Hz) LabVIEW based instrumentation acquired data at  a sampling rate of 
20kHz while a low pass filter filtered out signals above 10kHz. For low frequency 
flame oscillations (caused by eventual pairing and merging of flame front wrinkles) 
LabVIEW based instrumentation acquired data at a sampling rate of 3 kHz. The 
signal from the PMT was passed through a Dual Channel Filter and was band pass 
filtered between 1 Hz and 1.5 kHz. Since the oscillatory component of flame front 
oscillations was desired, AC coupling was used on the Dual Channel Filter to remove 
any DC bias in the signal from the PMT. The PMT was set up on a graduated 
mounting rail so that precise position of the sensor area with respect to the injector 
could be recorded.  
4.3.7 Other Lab Equipments 
4.3.7.1 Signal Generator and Amplifier 
 
 To be able to excite the chamber acoustically at various frequencies and 
amplitudes, a Wavetek 40MHz Universal Waveform generator was used. This signal 
generator provided various monotone and sweep signals which were amplified 
through a Bogen C-100 amplifier and fed into the 100 watts 16 ohm compression 
 
 61 
 
driver. For certain experiments where broadband signals and band limited white noise 
signals were required, LabVIEW based signal generators were also used. 
4.3.7.2 Oscilloscope and Filter 
 A Tektronix TDS 3014 four channel color digital phosphor oscilloscope was used 
for visualizing signals to and from sensors and actuators whereas a STANFORD 
RESEARCH SYSTEMS SR650 Dual Channel Filter was used for  filtering signal 
from sensors as and where applicable.  
4.3.7.3 LabVIEW Based VIs 
 For data acquisition, LabVIEW 8 based VIs running on a Pentium 4 Windows 
based PC was used. A BNC 2120 Data Acquisition Board connected to a PCI -6251 
Card was used to read data from sensors into the VIs. 
 
4.4 Flow Rate Calculations 
 The flow rates for fuel, oxidizer and diluents were established using choked 
orifices and Setra static pressure transducers mounted upstream of the orifices. 
Pressure and choked orifice area values were used to calculate mass flow rates by 
applying the well known equation for mass flow rate through a choked nozzle 
(orifice) 
)1/()1(*.
1
2)( ?+
???
?
???
?
+=
??
?
?
RT
Apm
o
o  
 
 62 
 
where symbols have their usual meanings. In some particular cases where mass flow 
requirement of diluent gases was too small, Bernoulli?s equation was used to 
calculate mass flow. While bottled gases from Airgas Inc. were used for fuel oxidizer 
and dilatants, air flow was established from the university?s compressed air supply 
system.  
4.5 Injection Arrangement 
 The oxidizer and the fuel lines were needed to be suitably adapted for 
performing various experiments reported in this thesis. In the reversal of density 
gradient experiments for instance, the switching of density gradient was achieved by 
interchanging the position of the denser oxidizer and the lighter fuel jets. In the 
configuration shown in Fig. 4.10a, denser gas (Oxygen) and lighter gas (Hydrogen) 
forms the center-jet and co-flow jets respectively whereas in the configuration shown 
in Fig. 4.10b, denser gas (Oxygen diluted with nitrogen) and lighter gas (Hydrogen) 
forms the co flow and center jets respectively. This interchange of position between 
the denser and the lighter gases while maintaining the same direction of acoustic 
forcing provided a convenient way of reversing the direction of the density gradient 
vector at the fuel-oxidizer interface with respect to the acoustic driver. One 
configuration then served as the baseline for the reversed configuration when the 
interface was acoustically accelerated from the same side. 
 For the density ratio tests performed as a part of this work, the center jet of 
Oxygen was diluted with Helium while the outer jet was diluted with Argon. This 
allowed changing the density ratio between oxidizer and fuel from 16:1 to 1:1 while 
keeping jet velocities and heat release relatively constant (Fig. 4.11a).  
 
 63 
 
 For the velocity ratio tests, the center jet was pure Oxygen while the outer jet 
was a mixture of Hydrogen, Argon and Helium. A mixture of 5.235% Argon and 
94.765% Hydrogen (by mole fractions) gave a mixture molecular weight of 4.002 
g/mole which was same as that of pure Helium. Addition of Helium to such a mixture 
of Argon and Hydrogen served to change the velocity of the outer jet while keeping 
its density unchanged (Fig. 4.11b).  
 For the effect of chemical composition tests, the center jet was a mixture of 
Oxygen and Argon while the outer jet was a mixture of Hydrogen, Helium and 
Methane (Fig. 4.11c). For the momentum effect tests, data collected as part of the 
density effect tests and the velocity effect tests were used. 
4.6 Firing sequence for reacting flow experiments 
4.6.1 Ignition  
 Particular attention was given to prevent ignition of a pre-mixed charge of fuel 
and oxidizer that could form near the injector region of the combustor under certain 
conditions. This was achieved by first allowing air to flow into the combustion 
chamber through the wall jets lines of the combustors. Once airflow was established, 
a butane igniter was lit and placed near the exit of the combustor. Pilot Hydrogen gas 
was then switched ON and a air-Hydrogen flame was established. The initial flow of 
air ensured that Hydrogen did not accumulate near the injector before ignition and 
that the oxidizer was always present in abundance compared to the amount of fuel. 
Once the initial flame was established, Oxygen was switched ON. At this time air was 
switched OFF and the flow rate of Hydrogen was increased until H2 and O2 were in 
 
 64 
 
stoichiometric or near stoichiometric? proportions. Given the particular type of test, 
other gases like Argon, Helium and / or Methane were introduced at this stage and the 
diffusion flame system was acoustically forced at the desired frequency and 
amplitude and related measurements were made. The steps for igniting the combustor 
are reiterated for convenience of reading. 
1. Air ON 
2. Butane Igniter Flame ON. 
3. Hydrogen pilot ON.  
4. Oxygen ON. 
5. Air OFF. 
6. Hydrogen mains ON.  
8. Inert gases and /or secondary fuels ON. (if applicable) 
7. Acoustic excitation ON. 
4.6.2 Extinction 
 The steps for extinguishing the flame in the combustor  on the other hand 
followed the following sequence. Once again, the primary goal was to prevent too 
much fuel from being surrounded by too little oxidizer.  
1. Air ON 
2. Hydrogen mains and secondary fuels (If applicable) OFF 
                                                 
? Near stoichiometric for cases where Methane was also used. In such cases, the entire Methane-
Hydrogen-Oxygen combination would be stoichiometric once Methane was introduced. 
 
 65 
 
3. Oxygen OFF 
4. Inert gases OFF.(If applicable) 
5. Air OFF when combustor is sufficiently cooled 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 66 
 
Chapter 5 :  Experimental and Analytical Characterization 
of Chamber Acoustics using Broad-Band Forcing 
 Since interactions between acoustic waves and density stratified reacting and 
non-reacting flowfields inside a combustion chamber with a given geometry was key 
to this investigation, it was important to characterize the acoustic modes of the 
chamber so that interactions at different frequencies and amplitudes could be better 
interpreted. However, the analytical derivation of modal frequencies for a combustor 
with a non-homogenous flow field is usually complicated  by the presence of non-
homogeneity in density and temperature, and hence in the speed of sound. Such  
heterogeneity affects the eigen frequencies and the eigen modes of the chamber (Kim 
and Williams 1998) and makes it necessary to use both the geometry of the 
combustor and the distribution of acoustic media within that geometry to obtain the 
dominant modes.  
 A more straightforward approach is to find the dominant frequencies of the 
combustor experimentally by exciting it acoustically with white noise forcing.  
Resulting pressure spectra inside the combustor, measured using wall mounted 
pressure transducers could then be used to understand the resonance behavior of the 
experimental setup with local maxima and minima in pressure spectral intensity 
indicative of standing wave behavior due to acoustic resonance.   
 
 
 
 67 
 
5.1 Preliminary Experiments 
 With this consideration in mind, non-reacting flow tests were conducted at 
four different flow conditions as shown in Table 5.2.  Band-limited (< 5000 Hz) 
white noise forcing (at a speaker power rating of ~ 9 watts) using LabVIEW based 
instrumentation was used to acoustically excite the chamber. Dynamic pressure 
response of the combustor to the externally imposed white noise excitation was 
measured using wall mounted Kistler 211B5 piezoelectric transducers. Tap locations 
for the measurement ports are shown in  Fig.4.9. The time trace of the pressure signal 
was converted to frequency domain spectra using a standard FFT code written in 
Matlab. About 400 spectra were averaged to obtain the results, which showed distinct 
spectral peaks corresponding to various acoustic modes of the chamber. Data 
acquisition was carried out at a sampling frequency of 20 kHz using a Pentium IV PC 
equipped with a National Instruments PCI-6251 Multifunction DAQ card.  
 Fig. 5.1 shows the resulting pressure spectra at Taps #1 through  #4 under no-
flow conditions (quiescent air). Fig. 5.2 shows pressure spectrum from Tap #4 
redrawn from previous figure with some of the characteristic frequencies labeled and 
tabulated for easy visual reference. Table 5.1 compares some of these experimentally 
obtained characteristic frequencies with calculated values. Fig. 5.3 through Fig. 5.5 
represent pressure spectra corresponding to the first three flow conditions in Table 5.2 
without reaction. For these tests, the combustor was excited at a speaker power rating 
of ~ 9 watts.  For each density ratio condition,  pressure spectra corresponding to the 
first four tap locations at y=0.5-in are presented.  In general, there were up to three 
distinctive spectral peaks worth noting that have been denoted as f1, f2, and f3 in the 
 
 68 
 
ascending order of frequency in the figures. From a comparison of the peak 
frequencies between the different taps and the three different flow conditions (cf. 
Table 5.3) the following observations?  could be made : 
1. The frequency f1 was relatively unaffected by tap locations and flow 
conditions.  This indicated that it was possibly related to the oxidizer 
condition which was held constant throughout the various tests. 
2. The frequency  f2 changed substantially among different flow conditions 
but relatively little between the tap locations.  This indicated that it was 
possibly a longitudinal mode of the chamber that was related to the product 
conditions. 
3. The frequency f3 also changed substantially among different flow 
conditions but practically remained constant across the tap locations.  This 
indicated that it was possibly a transverse mode of the chamber and related to 
the product conditions as well. 
5.2 Model Development 
 To be able to interpret and understand modal behavior for both non-reacting 
and reacting flows, a simple model was developed in which the average speed of 
sound was used to calculate modal frequencies. Since experimental data relating to 
species concentration was not available, it was necessary to model the distribution of 
fuel, oxidizer and fuel-oxidizer mixture in various regions of the combustor in a 
physically meaningful way such that the average speed of sound could be calculated 
                                                 
? The pressure spectra corresponding to the last flow conditions were omitted because they were less 
interesting.  Both the density ratio and velocity ratio were small in this case, and the resulting spectra 
resembled those of the no-flow condition with numerous spectral peaks. 
 
 69 
 
from its speed in individual media. For example, for the non-reacting flow situation 
shown in Fig. 5.6, the products could simply be assumed to be a stoichiometric 
mixture of fuel and oxidizer as dictated by initial flow rates? and the first quarter-
wave mode in the transverse direction could be calculated using the simple 
expression: 
 
?
?
?
?
?
?
?
?
???
?
???
? ??+
???
?
???
?+
???
?
???
?
=
p
fo
f
f
o
o
a
WWW
a
W
a
W
f
224
1
4/?                             (5.1) 
 
where ao, af, and aP  denote seed of sound as it travels through oxidizer, fuel and 
products respectively, while W, Wo  and Wf  denote chamber width, width of oxidizer 
jet and width of individual fuel jets respectively.   
 In Eqn. 5.1, one finds that the frequency of the transverse mode depends on 
the assumption one uses to arrive at the product composition. Along with using a 
stoichiometric mixture of fuel and oxidizer as dictated by the initial inflow rates to 
estimate product composition, two more approaches were considered that 
incorporated the known phenomenon of jet mixing length and a new experimental 
result of preferential excitation under transverse acoustic forcing to estimate the 
product composition. The essential idea was to model the product composition in the 
product dominated regions (1 and 3 in Fig. 5.7 ) and to use the corresponding speed 
of sound in the product ap in calculating the frequency of transverse modes  and 
                                                 
? It will be shown in the model development section that the fully mixed model is based on the 
assumption of a stoichiometric mixture. Corrections due to mixing length and acoustically driven 
entrainment are considered in the other two models. 
 
 70 
 
longitudinal modes associated with the product column. For isothermal experiments 
where flow temperatures were known, calculated Eigen frequencies from these 
models were in good agreement with measured frequencies. The following section 
introduces each of these model in some detail. The models essentially differ in the 
way they control the value of the parameter  ?  in the standard equations 5.2 - 5.5 
applied to the reaction between a blended fuel of Hydrogen and Methane with 
Oxygen 
(cf. Table 5.2). ?O2 , ?CH4, ?H2 represent the number of moles involved in a 
stoichiometric reaction between the gases. 
 
2
242
2
4
242
4
2
242
2
422
)()()(
),,,(
O
OCHH
O
CH
OCHH
CH
H
OCHH
H
CHOHmix
MWMWMW
MW
????
??
????
?
????
?
????
++++++++
=        (5.2) 
 
2
242
2
4
242
4
2
242
2
422
)()()(
),,,(
O
OCHH
O
CH
OCHH
CH
H
OCHH
H
CHOHmix
????? ??????? ?????? ?
?????
++++++++
=
         (5.3) 
 
),,,(),,,( 422422 CHOHmix
univ
CHOHmix MW
RR
???????? =                                 (5.4) 
 
TRa CHOHmixCHOHmixCHOHmix ),,,(),,,(),,,( 422422422 ????????????? =
 
(5.5) 
 
 71 
 
5.2.1 Full Mixing Model / Well Stirred Reactor Model  
 According to this model, average speed of sound is calculated using a fully 
premixed mixture of fuel and oxidizer in the product regions. Molar concentrations 
based on volumetric flow rate of fuel and oxidizer jets (isothermal case) are used.  In 
our tests, since the volumetric flow rates were chosen to maintain stoichiometric 
mixture of fuel and oxidizer, this model essentially gave us a stoichiometric mixture 
of fuel and oxidizer. In the reacting flow scenario, this model would imply using 
equilibrium products of reaction to calculate the speed of sound in the product 
regions. 
? =1 
 
),,,( 422 CHOHanga ???? = ),,,( 422 CHOHmixa ????  
 
The frequency of the three quarter longitudinal mode of the combustor, for example 
could then be calculated as 
 
)34(
),,,(),,,(
'
422
422 L
af CHOHang
CHOH
???????? =  
Where, ?
?
??
?
?+=
26.0'
DLL   (End correction) 
 
 
 72 
 
5.2.2 Jet Mixing Length Model 
 This was a velocity ratio and potential core length based mixing model. It was 
argued that between the injector face plate and the distance from the injector where 
the potential core of the center jet ceases to exist, the velocity ratio between center 
and co-flow jets will bias the mixture towards the slow moving jet in the product 
region . Because of greater residence time, the slower jet will contribute more to the 
mixture fraction than if the two jets were at the same velocity. A correction factor was 
used to account for this increase in molar concentration of the slower jet using the 
velocity ratio of the two jets. This correction was applied only in a small region near 
the injector 0 < y < 6D.  Beyond y > 6D, a full mixing model was assumed. 
According to this model, for an isothermal stoichiometric flow of GH2 and GCH4 as 
fuel and GO2 as oxidizer, with velocity ratio ?  = (VH2 / CH4 / VO2) the frequency of 
the three quarter mode in the longitudinal direction associated with the product 
column would be calculated as below :  
2
4/2
O
CHH
V
V=?  
 
??
?
??
? ?+
??
?
??
?=
),,,1(
6'
),,,(6
'),,,(
422422
422
CHOHmixCHOHmix
CHOHang
a
DL
a
D
La
???????
????  
 
)3'4(
),,,(),,,( 422
422 L
af CHOHang
CHOH
???????? =  
 
 73 
 
5.2.3 Acoustically Driven Entrainment Model 
 Entrainment (?), of the center jet fluid into the co-flow, is affected by the ratio 
between transverse jet momentum (due to the acoustic driver) and momentum of 
main flow. If the acoustic amplitude is kept  fixed ( which in turn implies that the 
transverse jet momentum is kept fixed), the entrainment of the center jet fluid into the 
co-flow would be dependant on the momentum of the main flow. According to this 
model, fuel oxidizer mole fractions in the mixture is corrected using entrainment of 
Oxygen (or the center jet fluid) into the co-flow regions and this correction is applied 
along the entire length of the combustor 0 < y < L. It should be noted that while more 
of the center jet is entrained into the driver side co-flow (Region 1 in Fig. 5.7 ), there 
is a decrease in the amount of the center jet fluid available to be entrained into the 
wall-side co-flow (Region 3 in Fig. 5.7 ). This difference in the composition of the 
two co-flows arising from this discrepancy in entrainment of center jet fluid into the 
driver side co-flow and wall side co-flow possibly accounts for the difference in 
frequency of the three quarter mode (longitudinal) of the chamber as observed in the 
experimentally obtained pressure spectra. 
 For an isothermal stoichiometric flow of a GH2/GCH4 fuel (co-flow with a 
flow momentum given by JH2/CH4) and GO2 oxidizer (center jet with a flow 
momentum given by J O2) , the frequency of the three quarter mode in the longitudinal 
direction can be calculated using  Eq. 5.2 - 5.5, in which, ? , under the assumptions of 
this model, would represent a measure of the entrainment of the center jet Oxygen 
into the co-flow regions. This factor will depend on the ratio between the acoustically 
 
 74 
 
driven transverse jet momentum (JA) and the total momentum of the main flow 
(Jtotal=JO2+2JH2/CH4).  
 On the driver side, entrainment of center jet fluid will increase when total jet 
momentum is decreased (while the transverse jet momentum is kept fixed).As fluid 
from the center jet is entrained into the co-flow on the driver side, a decrease in the 
amount of center jet fluid available to be entrained into the co-flow region away from 
the driver side would result. The value of the control parameter ?  could then be 
expressed as 
)(1 1
total
reference
J
J?? +=
     Driver side  
)(1 2
total
reference
J
J?? ?=
     Wall side 
 
Constants Jreference, ?1 and ?2 are obtained from experimental results. 
 
),,,( 422 CHOHanga ???? = ),,,( 422 CHOHmixa ????  
 
)3'4(
),,,(),,,( 422
422 L
af CHOHang
CHOH
???????? =  
 
 It can be seen that as the total jet momentum (Jtotal ) becomes arbitrarily large, 
correction due to entrainment factor approaches 1 on both wall side and driver side. 
This would then lead to the frequency of the three quarter longitudinal mode of the 
 
 75 
 
chamber measured in the product column to be less dissimilar in value between the 
driver side and the wall side. Including the effects of entrainment on both driver side 
and wall side frequencies, the predicted frequencies of the three quarter mode 
improve significantly as is shown in the next section. 
5.3 Comparison of Isothermal Case Data with Model 
 Fig. 5.8 compares values obtained from experiments and from the various 
models for the isothermal flow conditions. Comparing experimental data from 
isothermal case with values predicted by the model, the following general 
observations could be made. 
1. Resonance at the lowest frequency (f1), shown to be the one quarter 
longitudinal mode of the oxidizer post was well predicted. 
2. Resonance at the second lowest frequency (f2), shown to be the three 
quarter longitudinal mode of the chamber, was adequately predicted by 
various models. The jet mixing length model biased the result towards the 
lower frequencies; full mixing model biased it towards the higher frequencies 
while the acoustically driven entrainment showed good agreement with modal 
frequencies on both driver side and wall side.  
3. Resonance at the third lowest frequency (f3), shown to be the first quarter 
transverse mode of the chamber was under-predicted by complete reaction 
model. This implied that the fuel content was actually higher than the 
equilibrium approximation used to calculate the frequency. 
 
 76 
 
5.4 Extension to Density Stratified Reacting Flows 
 In a similar manner as in the previous section, reacting flow experiments were 
conducted with band-limited white noise excitation. Test conditions were similar to 
the non-reacting flow conditions as detailed in Table 5.2, only this time the fuel-
oxidizer system was ignited. Again, the first three flow conditions resulted in well-
defined spectral peaks as shown in Fig. 5.9 through Fig.5.11.  In these experiments, 
only two spectral peaks were worth noting, marked as f1 and f2.  Values for 
frequencies  f1 and f2 from the reacting flow tests are summarized in Table 5.4. 
Although the actual frequencies were different from those in the isothermal 
experiments, the nature of the two dominant modes appeared to be similar to the f1 
and f2 mode for their non-reacting counterparts.  More precisely, the frequency f1 
appeared to be related to the quarter-wave mode of the Oxygen post and the 
frequency f2 appeared to be the three-quarter-wave mode of the combustion chamber. 
Since temperature measurements were not available at the time these tests were 
performed, the validity of the model for the reacting flow conditions could not be 
tested. However, a reverse approach in which the models were used to back calculate 
temperature of products given the experimentally obtained value for frequency gave 
product temperatures within reasonable ranges. Further experiments involving the 
measurement of product temperature are needed for accurate assessment. 
  
 
 
 
 
 77 
 
Chapter 6:  Acoustic Excitation of Density Stratified Non-
Reacting Flow Fields 
 Since reacting flow tests do not offer the convenience of extensive exploratory 
investigations, simultaneous studies were conducted involving the acoustic excitation 
of a density stratified He / Air flow configuration. Phase locked Schlieren and 
Shadowgraphic imaging techniques were used to visualize flow structures under 
acoustic excitation; Dynamic pressure sensors were used to measure resonant 
characteristics under white noise excitation. Hotwire probes, placed in the shear layer 
between the center jet and the co-flowing jet were used to measure dominant 
frequencies that could be associated with wake mode and jet mode instabilities.  
 It is natural to expect that acoustic forcing at frequencies close to the acoustic 
modes of the chamber (for a given flow-field configuration) would undergo resonant 
amplification and cause greater flow field activity with the flow responding to the 
standing waves set up in the chamber. Forcing at frequencies that are removed from 
the resonant modes of the chamber would on the other hand lead to flow field 
interacting with travelling waves. Acoustic forcing at frequencies close to the 
hydrodynamic modes would cause greater flow field activity leading to organized 
large scale motions of the fluid system.  It is the purpose of this chapter to investigate 
such phenomena in greater detail so as to form a ?feel? for the way acoustic waves 
might be expected to interact with flame system in the reacting flow cases. It should 
however be noted that the absence of heat release in the cold flow studies prevents 
any chance of amplification of pressure oscillations through favorable coupling with 
heat release oscillations (Thermoacoustic Coupling). Consequently, interactions in the 
 
 78 
 
reacting flow studies can be expected to be significantly different from their cold flow 
counterparts when such amplifications become operative. 
6.1 Acoustic Modes 
6.1.1 Characteristic Acoustic Frequencies 
 Fig 6.1 shows the flow arrangement for the cold flow tests with a center jet of 
air at 6m/s and co-flow jets of Helium at 18 m/s. Velocity ratio between the fuel-
oxidizer simulants was maintained at 3 because this was the default velocity ratio 
between fuel and oxidizer in the reacting flow tests.  Fig. 6.2 shows acoustic spectra 
for the chamber (with the given flow field) acoustically excited by a band limited 
(100Hz ? 10KHz) white noise excitation at a speaker power rating of ~ 10 W (RMS) 
from the left. About 400 spectra were averaged to obtain these results, which show 
distinctive spectral peaks corresponding to various acoustic resonance modes.   
6.1.2 Acoustic Excitation at Characteristic Frequencies 
 The pressure spectrum from Tap #4 is redrawn in Fig. 6.3 showing spectrum 
in the frequency range of interest. Using the pressure trace from Tap # 4 as 
representative of the chamber modes for the combustor, the flow configuration shown 
in Fig. 6.1 was excited at some of the characteristic frequencies from left and the 
nature of the interaction between flow and acoustics was investigated using phase 
locked schlieren imaging at 90o phase intervals.  Fig. 6.4 shows a series of such 
images of flow field excited acoustically from the left. Since the exposure times in the 
images is very short (10?s - 30?s) turbulent structures can be seen along with the 
 
 79 
 
dominant fluid modes. While forcing at frequencies close to f1,   f2 and f4  (cf. Fig. 6.3) 
showed flow interactions with longitudinal waves close to resonance, forcing at 
frequencies close to f3  showed flow interactions with non-resonant travelling waves 
from the acoustic driver.  The frequencies f1 , f2 , f4  and f6  could, to a good level of 
confidence, be recognized as the first quarter mode (longitudinal) of the chamber, 
first quarter mode (longitudinal) associated with the oxidizer post, three quarter mode 
(longitudinal) of the chamber and first quarter mode (transverse) of the chamber, 
respectively. 
 A few observations can be made from the visualizations shown in Fig 6.4. 
Compared to the unexcited baseline case (Fig.6.4a) it can be seen that near the 
longitudinal resonant frequencies f1 and f2 (cf. Fig 6.4b, 6.4c, and 6.4d ) flow 
responds strongly to the external forcing and exhibits well defined phase-locked 
varicose mode oscillations. It is apparent from the rather symmetric nature of the 
disturbance that the flow lacks immediate knowledge of the exact location of the 
source of disturbance (i.e. the location of the acoustic driver) and responds, rather, to 
the resonant oscillations setup in the chamber under the agency of such external 
forcing.  
  Forcing at frequencies between f2 and f4 (cf. Fig.6.4e, 6.4f, 6.4g, 6.4h) causes 
the main flow to curve away from the driver, an interaction that indicates that 
acoustic waves originating from the driver (at off-resonant frequencies) are 
compression strong and rarefaction weak, such that, on the average, the main flow is 
subjected to a cross flow originating from the acoustic driver. Compared to flow 
response under longitudinal response where seemingly the flow has no apparent 
 
 80 
 
knowledge of the exact location of the source of disturbance, flow here knows where 
the source of disturbance is and in some sense curves away from it under acoustic 
excitation. The interaction can be looked upon as a main flow interacting with a 
transversely oriented synthetic jet. The compression pulses of the transversely 
oriented synthetic jet originating from the driver mounted on the left penetrate deep 
into the flow field and interact with the main flow causing a strong push effect. The 
rarefaction pulses, on the other hand, do not penetrate deep into the flowfield to cause 
any significant pull effect. In fact, during the rarefaction cycle of the driver, fluid is 
drawn in from the immediate neighborhood of the driver exit and the rarefaction 
pulses are neutralized in the vicinity of the driver mount itself. The synthetic jet 
behavior of acoustic waves generated by the driver in the non-resonant band of 
frequencies is important to understand because it forms the basis of the baroclinic 
vorticity generation argument that will be presented in the reacting flow experiments. 
Because of this behavior, acoustic waves from the driver (in this frequency band) 
have a preferred direction for the pressure gradient vector they carry along. It will be 
shown in the reacting flow experiments that when this pressure gradient is allowed to 
interact with the density gradient (across the density stratified fuel-oxidizer interface), 
a plausible baroclinic interaction is generated causing significant flame-acoustic 
interactions leading to violent flame front oscillations.  
 It is to be noted that because of a center jet of air flowing between co-flowing 
jets of Helium, acoustic boundaries created by air-Helium interfaces essentially 
divide the 3.5? span of the combustor into 3 acoustic regions (columns) as shown in 
Fig.6.5. Tap #1 and Tap #4 then measure acoustic signatures in the driver side 
 
 81 
 
column and wall side column respectively. It is interesting to note that when the 
pressure spectrum from Tap #1 and Tap #4 are considered together, there is an 
observable difference in the frequency of the three quarter mode of the chamber 
(longitudinal) measured on either sides of the center jet (Fig. 6.6). This difference in 
frequency between the driver side and wall side product columns could arise due to 
source effects (the acoustic driver being near Tap #1) or due to differential 
entrainment of the center jet fluid into the co-flow as already discussed in section 
5.2.3? . Forcing at frequencies close to f4 (cf. Fig. 6.3), where such asymmetry in 
longitudinal resonance occurs between driver side and wall side product columns 
results in partly asymmetric interaction  (Fig. 6.4i, 6.4j, 6.4k, 6.4l ) with the driver 
side interface showing more interfacial activity than the wall side interface. In fact, it 
becomes a matter of apparent conjecture as to if the difference in resonance frequency 
between the driver side and wall side product columns is a cause for this asymmetric 
interaction or is a product thereof. 
 Forcing at frequencies beyond f4 (cf. Fig. 6.3), leads to the flow ?straightening 
up? (Fig. 6.4m, 6.4n, 6.4o) with no significant interactions in this range of frequencies 
for the range of forcing amplitudes that were tested. 
 In summary, a frequency of interest (denoted by  f3  in Fig. 6.3) was found that 
could be used to generate a transversely directed travelling acoustic wave with the 
characteristics of a synthetic jet. It corresponded to the frequency associated with the 
trough between the first quarter mode of the oxidizer post and three quarter mode of 
the product column in the acoustic spectrum at Tap #4 (wall side). Although the 
                                                 
? cf. Acoustically driven Entrainment Model, section 5.2.3 
 
 82 
 
precise value of this frequency would depend on the particular fuel oxidizer 
combination used and would differ between reacting and non-reacting flows, it would 
still be possible to locate it from its position in the pressure spectrum calculated using 
pressure data from the wall side sensor.  For the reacting flow case using GO2 and 
GH2, such a mode was obtained at 1150 Hz. Interactions between travelling acoustic 
waves and density stratified GO2-GH2 flame fronts revealed interesting insight into 
mechanisms of flame acoustic coupling. Details of such interactions are discussed in 
Chapter 7. 
6.2 Hydrodynamic Modes 
 To study any potential amplification of fluid motions due to acoustic coupling 
with hydrodynamic modes, the wake mode and the jet preferred mode frequencies 
associated with the flow field were calculated and shear layer response to acoustic 
excitation at those hydrodynamic mode frequencies experimentally tested through 
hotwire anemometry. Since the splitter plate between fuel and oxidizer had two 
different fluids flowing on either sides of it, a slightly modified approach was taken to 
calculate the wake mode frequency. The thickness of the splitter plate was divided 
into two parts x and y (Fig. 6.7) such that frequencies of shedding on either side of 
the splitter matched each other and the following conditions were satisfied. 
 
wakeTyx =+  
21.0=tS  
???
?
???
?=
???
?
???
?=
y
US
x
USf Htot
22  
 
 83 
 
???
?
???
?=
???
?
???
?
H
o
U
U
y
x  
 
The calculated value of the wake mode frequency f for this case was 794 Hz.  Based 
on a flow speed of 6m/s (speed of center jet of air) across a bluff body of width Twake  
this frequency would be 397 Hz while based on a flow speed of 18m/s (speed of co-
flowing Helium) across a bluff body of the same width, the wake mode frequency 
would be  1191 Hz.  The jet preferred mode frequency?, based on the velocity of the 
center jet (VO2 ~ 6m/s) ranged from  ~ 80 Hz ? 200 Hz (based on width of the center 
jet) and ~ 118 Hz ? 283 Hz (based on hydraulic diameter of center jet). 
6.2.1 Characteristic Hydrodynamic Frequencies  
 Fig. 6.8a shows a schematic of the flow arrangement with a center jet of air at 
6m/s and co-flowing jets of gaseous Helium flowing at 18 m/s used for the hot wire 
tests. Fig. 6.8b shows location of the hot wire probe with respect to the shear layer 
between center and co-flow jets. The exact location of the probe was 1.375 inches 
away from the driver side wall and 0.819 inches away from the injector plate. Signal 
from the probe was filtered using a low pass filter (5 KHz cut-off) with an input gain 
of 10dB and the input was AC coupled. Sampling was done at 20,000 samples per 
second and 32 seconds of data was collected and processed. Forcing was from left, 
the side closer to the sensor.  
Fig. 6.9 shows preliminary frequency response characteristics of velocity 
fluctuations in the shear layer between the center and the co-flowing jets. For baseline 
                                                 
? Calculated based on St ~ 0.25 ? 0.60. 
 
 84 
 
case, the frequency domain representation of the signal from the hotwire showed a 
series of low quality peaks in the spectrum with peaks centered at 429.7 Hz and two 
of its higher harmonics. It should be noted that the second harmonic at ~ 860 Hz falls 
close to the calculated value of 794 Hz of the wake mode. Although one of the 
acoustic modes from the density stratified cold flow case (the one associated with the 
quarter mode of the oxidizer post) also came close to this frequency, the broad band 
nature of this particular signal was indicative of its hydrodynamic origin.  
 It seems probable that for the given combustor geometry and the operating 
conditions under which data was collected, both the quarter mode frequency of the 
oxidizer post and the wake mode frequency (for the given velocities and splitter plate 
thickness) occurred in close proximity. It might be noted here that unlike 
hydrodynamic modes, acoustic modes of chambers are typically have higher qualities. 
Interestingly, it was observed that when the Helium-Air flow field was excited at 
frequencies of 351.6 Hz, 429.7 Hz, 500 Hz and 600 Hz respectively (with the forcing 
amplitudes kept constant at 2 Vpp) the amount of amplification of each of these 
modes closely followed the amplitude of the un-forced jet frequency response (Fig. 
6.9). The plot shown in Fig. 6.9 is a good example demonstrating that acoustic 
forcing at preferred modes (either acoustic or hydrodynamic) would cause greater 
flow field activity compared to excitation at non-preferred modes. Since various 
competing mechanisms would be operative in the flame acoustic interaction process, 
the identification of various frequencies at which such amplified interactions occur 
are important to the investigation because it provides a systematic way of including or 
 
 85 
 
eliminating physical mechanisms that could be operative in the flame acoustic 
interaction process. 
 When the flow field was excited with a broadband source of sound (100Hz to 
1500Hz with frequency spacing of 2Hz) a response curve as shown in Fig. 6.10 was 
obtained. Broadband forcing at low amplitudes showed a trend similar to the unforced 
response but with an increase in the amplitude of forcing, a shift of the response 
curves to lower frequencies was observed. For large amplitude broadband excitation, 
significant departure of the response curve from the unforced response was observed. 
This change could possibly be attributed to either a decrease in velocity in the 
neighborhood of the wire due to an increase in local pressure, a decrease in velocity 
due to an increase in cross-flow or due to the shear layer now starting to move away 
from the jurisdiction of the sensor filament.  
6.2.2 Acoustic Excitation at Characteristic Hydrodynamic Frequencies 
 Fig. 6.11 shows a series of phase locked schlieren images (imaged at 90o 
phase intervals) of the flow arrangement shown in Fig. 6.8a interacting with acoustic 
waves at the experimentally determined predominant roll-up frequency of 429.7 Hz. 
Interaction for a range of forcing amplitudes is shown. Large, persistent, two-
dimensional rollers are observed as the shear layer is excited at the natural rollup 
frequency at increasing levels of acoustic forcing amplitudes.  
 In summary, this chapter detailed experimental studies on cold flows excited 
acoustically at preferred mode frequencies. The preferred modes included both 
acoustic and hydrodynamic modes. While forcing at characteristic frequencies that 
corresponded to the acoustic modes of the chamber showed flow interactions with 
 
 86 
 
standing and travelling waves, forcing at near the hydrodynamic mode frequency 
showed the excitation of wake mode instability. Since the frequency of the preferred 
hydrodynamic mode, 429.7 Hz corresponded close to an acoustic mode of the 
chamber a possible hydrodynamic-acoustic coupled interaction was noted in Fig. 
6.11. Such interactions (where the external forcing couples simultaneously with both 
acoustic and hydrodynamic modes) could be stronger than when the external forcing 
just couples exclusively with either acoustic mode or some preferred hydrodynamic 
mode of the combustor. 
 
 
 
 
 
 
 
 
 87 
 
Chapter 7: Acoustic Excitation of Chemically Reacting Flow 
Fields 
The present chapter details results from the acoustic excitation of chemically 
reacting flow fields and constitutes the most important chapter of this thesis. While 
the previous chapters mostly serve the purpose of ?preparation?, it is this chapter that 
systematically examines the acoustic excitation of model shear-coaxial diffusion 
flames formed between gaseous Hydrogen (GH2) and gaseous Oxygen (GO2)? to 
characterize flame-acoustic interactions that could typically occur in liquid rocket 
engines during the onset of combustion instability. In this chapter, characteristic 
interactions between flame and acoustics at various frequencies are presented,  
important parameters in flame acoustic coupling are identified and the first known 
experimental evidence that suggests baroclinic vorticity as a potential mechanism in 
triggering flame-acoustic interactions associated with LRE shear coaxial injectors is 
reported. 
7.1 Characteristic Flame Acoustic Interactions  
 Preliminary reacting flow tests involved transverse acoustic excitation of a 
diffusion flame system formed between a center jet of gaseous Oxygen and co-
flowing jets of gaseous Hydrogen through a broad range of frequencies (200 Hz-2000 
Hz)  and amplitudes. Fig. 7.1 shows the flow field arrangement and the location of the 
compression driver with respect to the flowfield. Velocity of the center jet of Oxygen 
                                                 
? Depending on the goal of particular tests, individual jets of fuel and oxidizer were mixed with other 
gases like Helium, Argon and Methane. 
 
 88 
 
(VO2) was 6m/s while that of co-flowing Hydrogen (VH2) was 18 m/s. The velocity 
ratio of 3 used in the current experiment is well within the range of velocity ratios 
studied by others (cf. Foust et al. 1996, Tucker et al. 1997) 1. Reynolds number of the 
center jet based on hydraulic diameter was ~ 4900 while that based on the width of 
the center jet was ~ 7300. In the range of Reynolds numbers considered, the flowfield 
could be regarded as sufficiently turbulent.  
 Since acoustic excitations at various frequencies could be further amplified or 
suppressed by the resonant characteristics of the system, the amplitudes at which 
acoustic waves interacted with the flame fronts would not only be functions of 
forcing frequencies and input voltages but would also be functions of the system 
geometry. Fig. 7.3 shows spectral content in pressure response from Tap #4 obtained 
using band-limited (100Hz-10kHz) white noise excitation of the combustor with the 
turbulent reacting flowfield inside at a speaker power rating of ~ 9 watts. Resonant 
modes were observed around  f1 ~ 300Hz,  f2 ~ 500 Hz and  f4 ~ 1500 Hz while a 
suppressed mode was observed around  f3  ~ 1150 Hz.   
Table 7.1 lists flow parameters and forcing conditions for the baseline case 
and two other cases where characteristic flame acoustic interactions were observed. 
Fig. 7.2 shows an instantaneous OH* chemiluminescence image of the unforced  
GH2 / GO2 / GH2 flame exhibiting small amplitude spontaneous oscillations and 
provides a baseline case to compare flame response to externally imposed acoustic 
excitations. Fig. 7.4  shows phase locked instantaneous OH* chemiluminescence 
images (imaged at 90o phase intervals) of the reacting flow field forced at 300Hz 
                                                 
1 For a detailed list of injector parameters used in more realistic rocket engine cf. Santoro (1997) and 
Conley (2007). 
 
 
 89 
 
from the transverse direction. An almost symmetric varicose mode oscillation of the 
flame fronts is observed that indicates possible coupling of acoustic waves at this 
frequency with a longitudinal mode of the chamber. It is apparent from the rather 
symmetric nature of the disturbance that the flow lacks knowledge of the exact 
location of the source of disturbance (i.e. the location of the acoustic driver) and 
responds, rather, to the resonant oscillations setup in the chamber under the agency of 
the external forcing. Figure 7.5 shows phase locked instantaneous OH* 
chemiluminescence images (imaged at 90o phase intervals) of the flame system 
forced at f3 ~ 1150 Hz.  This frequency corresponds to a suppressed mode between 
the two resonant modes f2 and f4 in the pressure spectrum  obtained from Tap #4 (cf. 
Fig. 7.3) .Under this condition of forcing, the flame front located closer to the 
acoustic driver interacted strongly with the acoustic waves resulting in violent flame 
front oscillations. Flame front located away from the driver showed almost no 
interaction in the neighborhood of the injector. The stable side was eventually 
affected when the forcing amplitude was increased substantially over the threshold at 
which the interactions on the driver side showed up. Significant feedback from the 
flames to the acoustic driver was also noted under this condition when the amplitude 
of forcing was arbitrarily increased.  
7.2 Baroclinic Vorticity as a Potential Mechanism 
 Among various mechanisms that could explain the asymmetric wrinkling of 
flame fronts observed at around the 1150 Hz forcing?, one that seemed physically 
                                                 
? This frequency was much lower than the first transverse cut-off frequency of the chamber thereby 
indicating that the observed interaction was not due to a standing wave in the transverse direction. 
 
 90 
 
plausible was that due to baroclinicity. It was hypothesized that favorable baroclinic 
torque generated at the flame front located closer to the acoustic driver caused by 
misalignment of density gradient at the fuel-oxidizer interface and pressure gradient 
in acoustic waves generated by the acoustic driver could be responsible for the 
observed asymmetric interactions. The mechanism for baroclinicity has already been 
introduced in a general sense in section 3.1. To argue that this mechanism plays key 
role in the particular case of the asymmetric interaction observed at 1150 Hz, a few 
preliminary considerations are needed. It should be noted from a comparison of the 
pressure spectrum plots of Fig. 6.3 and Fig. 7.3, that the suppressed mode f3 for the 
reacting flow field configuration (cf. Fig. 7.3) corresponds to the suppressed mode  f3 
for the non-reacting flow field configuration (cf. Fig. 6.3). Acoustic forcing of the 
non-reacting density stratified flow field at frequencies close to f3 ~ 750 Hz (cf. Fig. 
6.3) resulted in a ?curving away? of the main flow from the acoustic driver (cf. Fig. 
6.4f, 6.4g, 6.4h). It was argued that this effect was due to the main flow interacting 
with a transversely directed travelling acoustic wave (cf. Section 6.1.2). The 
characteristic deflection of the main flow indicated that the incident waves were 
?compression strong? which created the apparent ?push effect? causing the main flow 
to bend away from the source of the disturbance (compression driver in this case). 
Although the exact value of the frequency for the f3 mode for the reacting flow 
configuration differed from the frequency of the f3 mode for the non-reacting flow 
configuration, a qualitative similarity in the nature of acoustic waves generated at 
these frequencies between reacting and non-reacting flow field configurations could 
still be expected. Acoustic forcing at 1150 Hz for the chemically reacting flow could 
 
 91 
 
then be considered to generate a transversely directed synthetic jet  travelling from 
left to right away from the acoustic driver. Sufficiently removed from the source of 
disturbance, such waves could be stronger on the compression pulse but weaker on 
the rarefaction. This could lead to wave fronts travelling from left to right with 
pressure gradients that are directed from right to left (cf. Fig. 3.1). Although density 
gradient is present at both the reacting interfaces separating denser Oxygen from 
lighter Hydrogen, the particular direction of the pressure gradient in the travelling 
wave determines on which interface favorable baroclinic torque would be generated. 
For instance, when the pressure wave passes through the flame front located close to 
the acoustic driver, it travels from lighter Hydrogen to denser Oxygen. Given the 
direction of the pressure gradient across the acoustic wave and density gradient across 
the interface, this leads to an unstable baroclinic interaction leading to the 
amplification of interfacial perturbations as described in Fig. 3.1a. Violent flame front 
folding occurs as a result of this interaction. On the other hand, when this pressure 
wave travels from denser Oxygen to lighter Hydrogen, a stable baroclinic interaction 
as shown in Fig. 3.1b occurs. This leads to the suppression of any perturbations 
already present in the flame front located away from acoustic driver leading to its 
apparent stability.  
The remainder of this section  discusses, through various validation tests, if 
baroclinic vorticity could be regarded as a plausible mechanism in the onset of 
combustion instability in liquid rocket engines. The aspect of baroclinicity becomes 
intuitive in the rocket engine instability problem when one recognizes that a rocket 
engine combustor essentially houses a highly density stratified reacting flowfield 
 
 92 
 
inside an acoustically charged environment. Although experimental confirmation of 
the possible role of baroclinic vorticity in driving such instabilities is presented, more 
work needs to be done before this theory can be proved or disproved with a sufficient 
level of confidence.  
7.2.1 Pressure Amplitude Change Experiment 
 Since baroclinic torque is given by the cross product between density gradient 
and pressure gradient, (?? x?p) / ?2 , a change in the magnitude or the direction of 
the density gradient vector at the fuel-oxidizer interface would affect the nature and 
intensity of the interaction for a given pressure gradient passing through the interface. 
Also for a given density gradient across the fuel oxidizer interface, the intensity of the 
interaction will depend on the strength of the pressure gradient imposed on the 
interface.  
Fig. 7.6 shows ensemble averaged OH* chemiluminescence images (contour 
plot) of the oscillating flame (exposure time ~ 750 ms) with the intensity of acoustic 
forcing increased in steps from 0 to 12.5 watts. For these tests, velocity of center jet 
Oxygen (VO2) was 4.5 m/s, velocity of co-flowing Hydrogen jet (VH2) was 13.5m/s 
and Reynolds number based on the center jet hydraulic diameter (ReO2) was 3700.  An 
increase in the acoustic forcing amplitude was seen to cause greater perturbation of 
the flame front located close to the acoustic driver where the acoustic waves travelled 
from lighter Hydrogen to denser Oxygen. Flame front away from the driver did not 
show any appreciable increase in interaction where the waves travelled from denser 
Oxygen to lighter Hydrogen. Although in keeping with the baroclinic vorticity 
 
 93 
 
mechanism, no strong conclusion in favor of the mechanism could be drawn from this 
observation because the gradual increase in the level of interactions could be 
attributed to an increase in the transverse acoustic velocity imposed directly on the 
flame front located closer to the acoustic driver without any intermediate 
baroclinicity.  
7.2.2 Density Ratio Change Experiment  
 Following the previous test, the acoustic forcing level was fixed at 12.5 watts 
(40 Vpp) and the density ratio between fuel and oxidizer was systematically varied by 
adding small amounts of noble gases (Helium to Oxygen and Argon to Hydrogen), 
while holding other flow field characteristics relatively constant. For a fixed level of 
acoustic forcing, it is reasonable to expect, that an increase in the magnitude of 
density gradient across the fuel-oxidizer interface would lead to increase in the 
amount of flame acoustic interaction as per the baroclinic vorticity mechanism. Use 
of noble gases to dilute fuel and oxidizer streams allowed an exponential change in 
density ratio between fuel and oxidizer while keeping velocities of individual jets to 
remain unchanged. Although a small change in heat release was introduced across the 
span of density ratios tested, from practical considerations this approach was ideal for 
isolating and testing the effect of density on the baroclinic vorticity production term 
in the vorticity transport equation. Table 7.2 summarizes density ratio (?o/?f), velocity 
ratio (uf /uo), and mole fraction (Y) for the 16 cases considered as a part of the density 
ratio change experiments. Fuel and oxidizer were introduced in stoichiometric 
proportions. With  eqi-molar dilution  ranging from 0 to 45% , density ratios from 
16:1 to 1:1 between center and co flow jets were systematically created and the 
 
 94 
 
interaction with pressure waves generated by an acoustic driver of nominal 
impedance 16? driven at a fixed frequency of 1150Hz at a forcing amplitude of 12.5 
watts from the left was quantified through flame oscillation measurements.  
 Fig. 7.7a shows instantaneous flame wrinkling images (OH* 
chemiluminescence) with the  density ratio between oxidizer and fuel decreased  from 
15.9 to 5.0 while Fig. 7.7b shows contour plots corresponding to ensemble averaged 
OH* chemiluminescence images for the same cases. Acoustic forcing was kept 
constant in amplitude and was applied from the same location in all the tests. Both the 
instantaneous and ensemble averaged images showed a monotonic decay of 
oscillations as density ratio between fuel and oxidizer was decreased from 15.9 to 5. 
Since the level of acoustic forcing and most other physical parameters were kept 
unchanged, this test highlighted the importance of the magnitude of density gradient 
between fuel and oxidizer in controlling the level of interaction between flame and 
acoustics. The extent of flame-acoustic interaction was quantified by measuring the 
thickness of perturbed flames from ensemble averaged images. The thickness of the 
acoustically perturbed flame-front  at a given streamwise location (y) was defined as  
?flame(y)=| ro - ri |, such that the intensity I(y,x) satisfied  
 
Imax(y)-I(y,xo)=Imax(y)-I(y,xi)=0.9[Imax(y)-Ibackground(y)] 
 
In other words, flame wrinkling amplitude, ?flame, was defined as the thickness 
beyond which the flame intensity fell below 10% of its maximum intensity and was 
measured from the ensemble averaged images through image processing routines 
 
 95 
 
developed in Matlab. Fig. 7.8 shows flame thickness at a non-dimensionalized 
streamwise location (y/D) = 4.7 for several different density ratios.  Fig.7.9 shows flame 
width vs. density ratio for three different streamwise locations from the injector 
faceplate. A strong correlation between flame perturbation thickness (?flame) and fuel-
oxidizer density ratio is observed with the level of interaction increasing significantly 
as density ratio between oxidizer and fuel is increased from 3 to 15.9.  Fig. 7.10 shows 
the effect when the amplitude of excitation and the density ratio between fuel and 
oxidizer were both varied. Flames with higher fuel oxidizer density ratios, not only 
responded to acoustic waves at lower amplitudes of forcing  but also showed steeper 
response as the forcing was gradually increased. Consequently, the strong dependence 
of flame-acoustic interaction on the density ratio between fuel and oxidizer was in 
agreement with the hypothesis that periodic baroclinic vorticity strengthened by large 
density gradient in shear-coaxial injector element could be a potential mechanism 
influencing the degree of interaction between flame and acoustics.  
7.2.3 Density Gradient Reversal Experiment  
 Since baroclinic torque is a cross product between pressure gradient and 
density gradient, a change in the direction of one of the vectors while keeping the 
direction of the other unchanged would reverse the direction of the torque produced. 
To test the effect of changing the direction of the density gradient vector at the fuel 
oxidizer interface, a nearly opposite injector configuration was considered with 
central Hydrogen jet and surrounding oxidizer flow. Test conditions are summarized 
in Table 7.3 and compared with test conditions for Oxygen-in-the-center case. 
 
 96 
 
Although the Hydrogen-in-the-center jet configuration was not a practical one, it 
provided an opportunity to reverse the direction of the density gradient at the fuel-
oxidizer interfaces. Flame front closer to the acoustic driver now had density gradient 
directed from right to left while flame front away from the acoustic driver had density 
gradient directed from left to right. Acoustic waves generated by the acoustic driver 
travelled away from the driver from left to right through the two interfaces with 
pressure gradients directed from right to left as in all the previous cases. Fig. 7.11 
shows an instantaneous UV filtered image of an unforced GO2-GN2/GH2/GO2-GN2 
turbulent flame exhibiting spontaneous flame front oscillations. Velocity of the 
central Hydrogen jet (VH2) was 5 m/s and velocity of the co-flowing jet of air (VO2 / 
N2) was 17.8 m/s. Reynolds number of the center jet based on the hydraulic diameter 
(ReH2 ) was 600 while that based on the co-flowing Oxygen jet based on the hydraulic 
diameter (ReO2/N2) was 8800. The flow arrangement is schematically shown in Fig. 
4.10b. When excited acoustically at 300 Hz, the Hydrogen-in-the-center flame 
responded to the acoustic forcing in a discernable sinuous mode oscillations with both 
flame fronts participating in the interaction. Fig. 7.12a shows UV filtered phase 
locked images (imaged at 90o phase intervals) of flame fronts undergoing such 
interactions. Asymmetric interaction eventually showed up when the flame system 
was excited acoustically at a frequency of 580 Hz. Fig. 7.12b shows UV filtered 
phase locked images (imaged at 90o phase intervals) of flame fronts undergoing such 
interactions. Large amplitude flame front wrinkles were observed on the flame front 
located away from the acoustic driver while the flame front located closer to the 
driver showed comparatively little interaction. The elongated spikes of denser 
 
 97 
 
oxidizer pushing into lighter Hydrogen and ?tongues? of lighter center jet protruding 
into the denser co-flow seen in Fig. 7.12b on the flame front located away from the 
driver resemble structures commonly encountered in the Rayleigh-Taylor (RT) 
instability in the linear and early non-linear stages. 
 It is interesting to note that the simple reversal of the density gradient vector at 
the fuel oxidizer interface changed the flame-front which underwent selective flame-
front oscillation under transverse acoustic forcing. For this configuration where the 
lighter gas formed the center jet, unstable baroclinic interaction as shown in Fig. 3.1a 
occurred at the flame front located away from the acoustic driver with pressure waves 
traveling from lighter to denser medium. The interaction of pressure waves with the 
flame front closer to the acoustic driver on the other hand caused a stabilizing 
interaction as shown in Fig. 3.1b. 
 To investigate if the asymmetric oscillations of the flame fronts under 
transverse forcing could be attributed to differences in dynamic pressure fluctuations 
near the flames instead of a baroclinic interaction, pressure oscillation amplitudes 
across the combustor span were measured using wall-mounted pressure transducers. 
Locations of the transducers are shown in Fig. 4.9 and RMS values of dynamic 
pressure fluctuations for asymmetric interactions for both the Oxygen-in-the-center 
case and Hydrogen-in-the-center case are shown in Fig 7.13. Preliminary pressure 
data indicated that flame oscillations could not be attributed solely to the RMS value 
of local pressure oscillations. Pressure amplitude at Tap #2 for the Oxygen-in-the-
center case showed large increase in dynamic pressure fluctuations that correlated to 
large flame front oscillation in its neighborhood. However, pressure amplitude at Tap 
 
 98 
 
#2 for the Hydrogen-in-the-center case didn?t show any significant difference from 
that at Tap #3, yet flame front in the neighborhood of Tap #3 showed large amplitude 
flame front oscillations. This anomaly suggested that the amplitude of local pressure 
fluctuations was not solely responsible for the asymmetric interactions observed in 
the experiments and that some other mechanism was operative. 
7.2.4 Further Considerations for the Density Ratio Variation Tests 
7.2.4.1 Effect of Heat Release Variation 
 Although equimolar dilution of individual fuel oxidizer jets (cf. Table 7.2) 
allowed the injection velocities of fuel and oxidizer remain unchanged, there was a 
gradual decrease in the overall heat release as more and more Argon replaced 
Hydrogen (cf. Fig. 7.14). To ascertain that the change in the amplitude of flame 
wrinkling at different molar dilutions of Oxygen and Hydrogen with Helium and 
Argon respectively as reported in section 7.2.2, was not solely due to heat release 
changes,   an experiment was performed with test conditions given in Table 7.4. From 
Fig. 7.14, in which two plots for density ratio variation are shown, density change is 
achieved either by adding Argon to Hydrogen and Helium to Oxygen (the way 
density of fuel and oxidizer jets were tailored in the density ratio variation 
experiments) or by adding Argon to Oxygen and Helium to Hydrogen. The latter 
allows a gradual change in density ratio as compared to the exponential change 
facilitated by the former. Also, for a given percentage dilution, although the two 
approaches can produce very different density ratios, both of them will produce the 
same heat release. 
 
 99 
 
  Fig. 7.15a shows OH* chemiluminescence image (contour plot) of the 
baseline case with 6% molar dilution but no acoustic forcing. In the arrangement 
shown in Fig. 7.15b, 6% dilution by mole is achieved by adding Argon to Hydrogen 
and Helium to Oxygen whereas in Fig. 7.15c, 6% dilution by mole is achieved by 
adding Helium to Hydrogen and Argon to Oxygen. So while the molar dilution and 
the heat release is maintained same between the cases shown in Fig. 7.15b and Fig. 
7.15c, the density ratio between oxidizer and fuel is 7 for the case shown in Fig. 7.15b 
and 15.2 for the case shown in Fig. 7.15c. It is seen that although associated with the 
same heat release, the configuration in Fig. 7.15c with higher density ratio between 
fuel and oxidizer undergoes greater acoustic perturbation when subjected to the same 
amplitude of forcing as the configuration in Fig. 7.15b. Fig. 7.16 shows the growth 
rate of flame perturbations as a function of streamwise locations for the different 
cases mentioned above. From Fig. 7.15 and Fig. 7.16, acoustic forcing is seen to 
cause greater flame wrinkling for the higher density ratio case although most other 
factors, including heat release, were maintained same between the configurations.  
7.2.4.2 Effect of Total Jet Momentum Variation                
 
Although equimolar dilution of individual jets allowed injection velocities of 
fuel and oxidizer to be kept unchanged, the addition of Argon to Hydrogen at a given 
injection velocity increased the outer jet momentum significantly. While the addition 
of Helium to Oxygen decreased center jet momentum, the total momentum of the jets 
was progressively increased as more and more Argon replaced Hydrogen (Fig. 7.17). 
To ascertain that the sharp decrease in the amplitude of flame wrinkling with the 
 
 100 
 
decrease of density ratio between fuel and oxidizer did not arise exclusively from a 
fixed amount of acoustic forcing (transverse flow) interacting with a main flow with 
progressively increasing total jet momentums, a simple validation test was performed. 
Table 7.5 shows test conditions for the two cases. Fig. 7.18a and Fig. 7.18b show 
instantaneous and time averaged OH* chemiluminescence images of a GH2+He / 
GO2 / GH2+He diffusion flame with an outer jet momentum of 0.0055 kg.m/s2 and 
an inner jet momentum of 0.0047 kg.m/s2 undergoing transverse acoustic excitation at 
1150 Hz at a power rating of 15.8 watts.  Fig. 7.19a and Fig. 7.19b on the other hand 
show instantaneous and time averaged OH* chemiluminescence images of a GH2+Ar 
/ GO2+He / GH2+Ar diffusion flame with an outer jet momentum of 0.0055 kg.m/s2 
and an inner jet momentum of 0.0036 kg.m/s2 undergoing transverse acoustic 
excitation at the same frequency and amplitude. Although the outer jet momentums 
were same and the center jet momentum for the case shown in Fig. 7.18 was greater 
than the center jet momentum for the case shown in Fig. 7.19, greater flame acoustic 
interaction was noted for the flame shown in Fig. 7.18.  It might be noted that 
although the momentums of the individual jets for the arrangement shown in Fig. 
7.19 were less than or equal to the momentums of individual jets for the arrangement 
shown in Fig. 7.18, the density ratio between fuel and oxidizer for the configuration 
shown in Fig. 7.19 was around 2 while for the other arrangement it was 8. Even with 
higher momentums of individual jets, the flame with greater fuel to oxidizer density 
ratio showed greater flame acoustic interaction highlighting the role of density 
gradient in such interactions. 
 
 101 
 
 
7.2.4.3 Effect of Change in Acoustic Mode Shape 
Although equimolar dilution of individual jets allowed injection velocities of 
fuel and oxidizer to be kept unchanged, it changed various critical acoustic 
parameters of the system including densities of individual fuel and oxidizer jets, total 
heat release, acoustic impedance at the fuel-oxidizer interfaces etc. It was necessary 
then to check if the pressure spectrum (resonance characteristics) had shifted 
significantly during the course of the density ratio change experiments resulting from 
density tailoring using inert gases. Such a change in resonance characteristics could 
change the amplification of a mode at a given frequency and could cause a change in 
the level of flame acoustic interaction. Although this would still emphasize the role of 
fuel and oxidizer densities in affecting flame acoustic interactions, it would decrease 
confidence in considering baroclinicity as a potential mechanism. A change in flame 
acoustic interaction could then be attributed to a change in local amplitude of pressure 
oscillations inside the combustor making it difficult to justify the intermediate 
mechanism of baroclinicity, even though it might still be operative.  
To address this issue, resonance characteristics of the chamber for some of the 
density ratios tested were considered. Pressure spectrum collected from Tap #1 and 
Tap #4 for three different density ratios (16, 10 and 6) under reacting flow conditions 
and subjected to band limited white noise excitation are shown in Fig. 7.20a and 
7.20b respectively. Fig. 7.20a, represents modal characteristics on the driver side (Tap 
#1) and show similar spectral signatures around the forcing frequency of interest 
(1150 Hz). Since flame oscillations in the neighborhood of Tap #1 have been 
 
 102 
 
compared in the density ratio variation test, it is reasonable to assume that the sharp 
change in flame acoustic interaction with the change in density ratio between fuel and 
oxidizer is not totally due to changes in resonance characteristics of the chamber. 
Care should however be exercised to ascertain how much of the interaction is due to 
density gradient and how much is due to acoustic amplitude. There could be cases 
where a higher density ratio flame could  undergo lower flame acoustic interaction as 
compared to a lower density ratio flame if the modal characteristics are such that a 
resonant peak for the lower density ratio case falls very near the forcing frequency 
while it is far removed for the higher density ratio flame. Acoustic signature from Tap 
#4 also showed slight variations in the pressure spectrum with the crest between the 
first two dominant modes shifting to lower frequencies as density ratio was decreased 
from 16 to 6. It is not very clear how much such shifts in pressure spectrum around 
Tap #4 would actually influence the flame acoustic interaction process near Tap #2. 
The fact that local amplitudes of pressure fluctuations do not entirely correlate with 
the amount of flame acoustic interaction in its neighborhood has already been shown 
(cf. Section 7.2.3) and will be considered again in Section 7.2.5. Furthermore, it 
should also be appreciated that acoustic forcing of the flowfield can in itself affect the 
f4 mode of the chamber (cf. Fig 7.20) through redistribution of acoustic media in the 
volume of interest by causing perturbation and folding of interfaces and through 
acoustically driven entrainments (cf. Section 5.2.3). Unlike pressure spectra obtained 
from volumes with a fixed distribution of acoustic media using white noise excitation, 
in this particular configuration, the imposed forcing in itself changes the distribution 
of acoustic media and in effect changes the spectral characteristics of the chamber 
 
 103 
 
depending on factors like amplitude of forcing, density ratio between fuel and 
oxidizer etc. Consequently, near the forcing frequency of 1150 Hz where such effects 
can be present, care should be exercised in using the spectral characteristics as 
indicative of wave amplification due to chamber resonance. 
7.2.5 Simultaneous Measurement of Pressure and Heat Release Oscillations 
Simultaneous measurement of pressure and heat release oscillations were 
conducted to be able to show that for the same level of pressure perturbations 
imposed on an interface, a larger density ratio interface would typically lead to 
greater flame acoustic interactions. For this, a Photomultiplier Tube with a  308nm 
band pass filter was used for the OH* chemiluminescence oscillation measurements 
while a Kistler Dynamic Pressure sensor was used for local pressure oscillation 
measurements. Two cases (as shown in Table 7.6) of density ratios 14.5 and 3.0 
(using a blended GH2/GCH4 fuel mixture) were acoustically excited at a forcing 
frequency of 1150 Hz (40 Vpp) and simultaneous measurement of pressure and OH* 
chemiluminescence oscillations (plausibly representative of heat release oscillations) 
were conducted at 6 different locations as shown in Fig. 7.21. In Fig. 7.21, an 
ensemble averaged OH* chemiluminescence image (contour plot) for DR 14.5 case 
under acoustic excitation at 1150 Hz, ~ 40 Vpp is used as backdrop to show sensor 
location with respect to the excited flames.  
When the DR 14.5 case was forced at 1150 Hz, which corresponded to a 
suppressed mode in the pressure spectrum at Tap#4 (cf. Fig. 5.9 ) it was seen that 
although the amplitude of pressure oscillations were similar at both the flame fronts, 
 
 104 
 
flame front closer to the acoustic driver where acoustic waves travelled from lighter 
to denser fluid showed greater heat release oscillations (Fig. 7.22). While the same 
trend was observed for the lower density ratio case, the amount of heat release 
oscillation for the same amount of pressure perturbation was significantly decreased 
(Fig. 7.23).  This observation was particularly true for measurement locations D1, 
W1, D2 and W2. This test indicated that both the direction and the magnitude of 
density gradient at the fuel oxidizer interface are critical in influencing flame 
interactions under imposed acoustic excitations. 
7.3 Estimation of Growth Rates for the Flame Perturbations 
As observed by Markstein and Squire (1954) and Petchenko et al. (2006), 
acoustic waves can give rise to acoustic acceleration driven RT instability in flames 
(cf. Section 3.2). Because of the frequency term, acceleration due to acoustics can be 
significant at high frequencies although the period through which such acceleration 
would act would decrease as the frequency is increased. Consequently, one has to 
check if the instability has sufficient time to develop. For that purpose characteristic 
growth rate of the RT instability for an acoustically accelerated Hydrogen-Oxygen 
interface at 580 Hz excitation and peak pressure amplitude of 0.03 psi is evaluated. 
This frequency and pressure amplitude correspond to the situation near the flame 
front located away from the acoustic driver (cf. Fig. 7.12b) for the Hydrogen-in-the-
center flame under 580 Hz acoustic excitation showing significant flame front 
oscillations. 
A GO2/GH2 interface has an Atwood number of 0.88. A 580 Hz acoustic 
signal with peak pressure of 0.03 psi generates a peak acceleration of 1100 m/s2. 
 
 105 
 
Using these values and performing a linear RT stability analysis using a viscous 
interface, first the most unstable wavelength for the instability was obtained. The rate 
of growth of this most unstable wavelength was then plotted as a function of the 
acoustic period within which it could develop. Fig. 7.24 shows growth rates that 
could be expected under a forcing frequency of 580Hz with different pressure 
fluctuation amplitudes for the physical case shown in Fig. 7.12b at the flame front 
located away from the acoustic driver. Since higher frequency and higher pressure 
means higher acoustic acceleration, the maximum value for the growth rate increases 
with frequency and pressure fluctuation amplitudes. For a gas-gas interface, viscosity 
plays a stabilizing role. Hence there is always a critical wave number where 
maximum growth occurs beyond which the growth rate falls off. In Fig. 7.25, the 
amplification of the growth rate for the most preferred wavelength corresponding to 
the 580Hz, 0.03psi RMS case, as a function of the fraction of the acoustic cycle is 
shown. Even though acceleration is intermittent, it is sufficiently large so to cause 
significant amplification of perturbations in the time scale over which it acts. Up to 
200% amplification for the most preferred wavelengths is observed in less than half a 
cycle of acoustic forcing. 
7.4 Parametric Studies 
7.4.1 Dimensional Analysis 
Flames interacting with transverse acoustics undergo violent flame front 
wrinkling that essentially leads to an increase in the excited flame brush thickness. 
One can thus measure the average flame brush thickness (?) and use it as a measure 
 
 106 
 
of flame wrinkling or flame-acoustic interaction. It is easy to see that acoustically-
excited flame brush thickness will depend on many parameters including fuel and 
oxidizer properties as well as acoustic amplitude.  When the surrounding conditions 
such as acoustic amplitude and temperatures are held constant, one can express this 
relationship in the following general form: 
 
,...),...,,,,,( 1 nfofo YYuuyf ??? =  
 
The mole  fractions Y1, ? Yn can be further simplified by introducing a characteristic 
chemistry time scale chem?  to denote the propensity of the fuel-oxidizer combination 
for rapid reaction.  The above equation can then be simplified as 
 
),,,,,( chemfofo uuyf ???? =  
 
There are 7 dimensional variables in this equation while the number of primary 
dimensions is only 3, namely dimensions for mass, length, and time.  Thus, according 
to the Buckingham Pi theorem, there will be 4 dimensionless variables.  Using such a 
dimensional analysis, one can reduce this problem into: 
 
)/,,(
o
chem
o
f
f
o
uyu
uf
y
?
?
?? =  
 
 
 107 
 
Since the distance y is continually varying, it may be easier to take into the 
consideration a scaling aspect by using the center post diameter D.  Then, one can 
measure ?/D at a fixed y.  Also, instead of using the Damkohler number for chemistry 
time scale, it may be possible to use the fuel mole fraction if more than one fuel is 
used.  So, the problem is slightly modified to investigate (?/D) at fixed y, fixed 
temperature conditions, and fixed forcing conditions.  Thus, 
 
?
D = f(
?o
?f ,
uf
uo,
YCH4
YCH4 +YH2) 
 
By quantitatively obtaining partial derivative functions, one can assess how 
sensitively flame-acoustic interaction will be affected by each of these non-
dimensional variables.  In other words, the propensity of shear-coaxial injector flames 
to couple with acoustic forcing can be obtained as partial sensitivity of acoustically-
excited flame brush thickness to each of these variables.  The following will be 
measured in the experiments while holding all other conditions as constant as 
possible: 
 
? ?/D( )
? ?o/?f( ), 
? ?/D( )
? uf /uo( ), 
? ?/D( )
? YCH4/(YCH4 +YH2)( ) 
 
Also, by normalizing the variables, they can be written in the following equivalent 
forms: 
 
 108 
 
?
D = f(
?o ? ?f
?o + ?f ,
uf ?uo
uf +uo,
YCH4
YCH4 +YH2) 
 
? ?/D( )
? (?o ? ?f)/(?o + ?f)( ), 
( )( )
)/()(
/
ofof uuuu
D
+??
?? , ? ?/D( )
? YCH4/(YCH4 +YH2)( ) 
 
Apart from density ratio, velocity ratio and fuel mixture fraction, the effect of 
momentum ratio will also be tested. Since momentum of the jets could be changed by 
changing either jet velocity or jet density,  two different measures of  partial 
sensitivity will be obtained for the effect of momentum ratio of the jets. In one case, 
the momentum of the outer jet will be varied by varying the velocity of the outer jet 
while keeping its density constant while for the other case, momentum of the outer jet 
will be varied by varying the density of the outer jet while keeping its velocity 
constant.  
7.4.2 Effect of Density Ratio. 
Using flame brush thickness data obtained as a part of the density ratio 
variation experiments (cf. Section 7.2.2), the following exponential curve fit provided 
a good correlation between perturbed flame thickness and normalized density 
difference at given axial locations 4.7 < y/D < 6.1 as shown in Fig. 7.26: 
 
???
?
???
?
+=??
??
?
? ?
fo
fo
u
CCD ?? ??? .exp 21    Where 1C~ 0.02 and 2C ~ 5.1 
 
 
 109 
 
The results can be explained using periodic baroclinic torque generated by misaligned 
density gradient and pressure gradient. The direction of pressure waves is such that 
the resulting baroclinic torque amplifies the disturbances on the left side flames while 
it stabilizes the disturbances on the right side. The strength of baroclinic torque 
increases with the increase in density across the fuel-oxidizer interface as expected. 
7.4.3 Effect of Velocity Ratio. 
A series of tests were conducted to study the effect of velocity ratio on flame 
acoustic coupling. A mixture of 5.235% Argon and 94.765% Hydrogen (by mole 
fractions) gave a mixture molecular weight of 4.002 g/mole which was same as that 
of pure Helium. Further addition of Helium to this mixture of Hydrogen and Argon 
then gave a convenient way of changing (increasing) the velocity of the outer jet 
while keeping its density unchanged. Hence, while the velocity of the outer jet was 
increased from 13.5m/s to 23.57m/s by adding different amounts of Helium to the 
outer jet, its density could be kept constant at 0.163 kg/m3. The center jet was of pure 
Oxygen flowing at 4.47m/s. The flow rates were adjusted in such a way so that fuel 
and oxidizer were in stoichiometric proportions.  Test conditions are summarized in 
Table 7.7. Instantaneous and ensemble averaged OH* chemiluminescence images are 
shown in Fig. 7.27 and Fig 7.28 respectively. For each velocity ratio, instantaneous 
images were captured with an exposure time of 15?s whereas average images were 
captured with an exposure time of 750 ms. In all the images, shown in Fig. 7.27 and 
Fig. 7.28, acoustic excitation was applied from the left at a power rating of 15.82 
watts (45volt peak to peak at an impedance of 16 ohms). Fig. 7.29 shows average 
 
 110 
 
linear regression fit obtained for the empirical trend in the range of axial locations 4.7 
< y/D < 6.1. The dependence on velocity change could be expressed in linear form as: 
43 Cuu
uuC
D of
of +
???
?
???
?
+
?=?
?
??
?
?
?
?    where 
3C ~ -3.5 and 4C ~ 3.6 
 
 While flame perturbation had an exponential dependence on non-
dimensionalized density difference, its dependence on non-dimensionalized velocity 
difference was linear. A possible cause for this slight reduction in flame-acoustic 
interaction with increase in outer jet velocity appeared to be the decrease in 
volumetric heat release because of the addition of an inert gas to the outer jet in 
successively higher amounts. The increase in the total momentum of the main flow 
for a fixed acoustically driven cross flow momentum could also be responsible.  
7.4.4 Effect of Momentum Ratio 
 
 Since momentum of a flow could be changed either by changing velocity or 
density or both, two sets of flame acoustic interaction tests were conducted. In one, 
jet momentum was varied by varying velocity while holding density constant while in 
the other, jet momentum was varied by varying density while holding velocity 
constant. Table 7.8 shows test conditions for experiments in which jet momentum 
was varied by varying the density of the jets while their velocities were kept 
unchanged. Table 7.9 shows test conditions where outer jet momentum was varied by 
varying the velocity of the outer jet while keeping the densities of the individual jets 
 
 111 
 
as well as the velocity of the center jet constant. It is to be noted that the outer jet 
momentums in Table 7.8 and Table 7.9 are exactly matched.  
 When excited acoustically at a power rating of 15.82 watts (45volt peak to 
peak at an impedance of 16ohms) from the left, flames under conditions shown in 
Table 7.8 showed steeper flame-acoustic response as compared to cases shown in 
Table 7.9. Fig. 7.30 shows instantaneous and ensemble averaged OH* 
chemiluminescence images of flame acoustic interactions for test conditions given in 
Table 7.8 while Fig. 7.31 shows instantaneous and ensemble averaged OH* 
chemiluminescence images of flame acoustic interactions for test conditions given in 
Table 7.9.  
 As the outer jet momentum was progressively increased, there was a decrease 
in flame response amplitude. A linear regression fit yielded the following dependence 
on non-dimensionalized momentum difference when the outer-jet momentum was 
increased by increasing the outer jet velocity while keeping individual densities of the 
center and co-flow jets unchanged as shown in Fig. 7.32a. In the range of axial 
locations 4.7 <y/D < 6.1 
 
87 CJJ
JJC
D of
of +
???
?
???
?
+
?=?
?
??
?
?
?
?    Where 
7C ~ -1.24 and 8C ~ 1.25 
 
 The dependence of flame perturbation on non-dimensionalized momentum 
difference was found to follow an exponential curve when the outer-jet momentum 
was increased by increasing the outer jet density while keeping individual velocities 
 
 112 
 
of the center and co-flow jets unchanged as shown in Fig. 7.32b. In the range of axial 
locations 4.7 <y/D < 6.1 
 
???
?
???
?
+
?=?
?
??
?
?
of
of
u JJ
JJCC
D .exp 109
?    Where 
9C ~ 0.29 and 10C ~ -2.85 
 
This observation reiterated the importance of density ratio in flame acoustic coupling. 
The decrease in flame brush thickness for an increase in jet momentum could be 
attributed to a fixed cross flow momentum interacting with an increasing main flow 
momentum. For the decrease in momentum that was accompanied by a decrease in 
density ratio between fuel and oxidizer (cf. Table 7.8) additional damping of flame 
oscillations could have resulted from a decrease in density gradient across the flame 
front from 6.0 to 2.0. 
7.4.5 Effect of Chemical Composition of Fuel. 
 Effect of fuel composition on flame-acoustic interaction was studied by 
adding Methane to the Hydrogen fuel line. The configuration is shown in Fig. 4.11c. 
Methane was included in the study of the effect of chemical composition of fuel for 
two primary reasons. First, a Methane Hydrogen mixture may be considered for space 
exploration mission if Methane can be harvested from Mars in the future. 
Furthermore, because Methane is substantially denser than Hydrogen, it can also be 
used to control fuel-oxidizer density ratio that sensitively affects the flame-acoustic 
interaction process. Thus, a blended fuel could be considered for instability control 
purpose as well. In this experiment, Methane-Hydrogen mixture was used for the fuel 
 
 113 
 
line and the mole fraction was varied by 10% increment. The fuel and oxidizer 
streams were appropriately diluted with inert gases to maintain the fuel-oxidizer 
density ratio and velocity ratio constant. The resulting test conditions are shown in 
Table 7.10. The flames were subjected to a fixed-amplitude acoustic excitation as 
before, and the resulting flame acoustic interaction was measured using OH* and 
CH* chemiluminescence measurements.  
 When only Methane was used, however, it resulted in lifted flame structure 
quite different from others (cf. Fig. 7.33). In all cases containing 10% or more 
Hydrogen, the general flame structure was very similar to the Hydrogen only flame 
case (cf. Fig. 7.34). 
Fig. 7.35 shows the processed results obtained when the flame system was 
excited from the left at a power rating of ~ 19.5W. As the Methane mole fraction was 
increased, there was a slight decrease in flame response amplitude. A linear 
regression fit yielded the following dependence on Methane mole fraction when 
density ratio and velocity ratio were held constant in the range of axial locations 4.1 < 
y/D < 5.2: 
 
65
, 24
4 C
YY
YC
D HCH
CH
u
+??
?
?
???
?
+=??
??
?
?
?
?    Where 
5C ~ -0.87 and 6C ~ 2.3 
 
 Since the density ratio and velocity ratio were held constant, the effect was 
mainly due to the change in mole fraction. The main cause for this slight reduction in 
flame-acoustic interaction with Methane mole fraction appeared to be the decrease in 
thermal output. As more and more Methane replaced Hydrogen when the amount of 
 
 114 
 
Oxygen available was fixed, the total heat release output was reduced as seen in 
Table 7.10. This meant that the amplification due to heat release was reduced at 
higher Methane mole fraction. When the fuel was exclusively Methane, the flame was 
lifted because the ignition time of Methane is longer than that of Hydrogen. Thus for 
the same fuel and oxidizer velocities, the location of ignition of pure Methane was 
farther from the injector than Hydrogen. Although a dependency on Methane mole 
fraction was obtained, it is difficult to say if the correlation is indicative of flame 
acoustic interaction under varying chemistry time scales. The presence of hydrogen in 
the mixture (even in small quantities) seems to drive the chemistry time scale of the 
mixture towards that of Hydrogen and makes an unbiased study of the effect of 
chemistry time scale on flame acoustic coupling, by varying methane and hydrogen 
mole fractions, possibly inappropriate. 
7.5 Spectral Measurements and High Speed Imaging 
7.5.1 High Speed Imaging Results 
 To gain further insight into physical processes occurring in flame acoustic 
interactions for the shear co-flow injector, spectral measurements and high speed 
imaging of flames under transverse excitation were conducted. Tests indicated that 
downstream of the injector plate, difference in velocities between center jet and the 
co-flow jets caused stretching and merging of vortex structures initially excited by the 
baroclinic interactions between flame and acoustics.  For all these tests, the Oxygen-
in-the-center GO2/GH2 diffusion flame was excited by the transversely mounted 
acoustic driver at a frequency of 1150 Hz and at an amplitude of 40 Vpp from left. 
 
 115 
 
Velocity of center jet Oxygen was 4.5 m/s while velocity of co-flowing Hydrogen 
was 13.5 m/s. 
7.5.1.1 Vortex Pairing and excitation of secondary modes 
 A series of high-speed images of the flame front oscillations captured at 1000 
fps revealed distinct vortex pairing events leading to the apparent decrease in flame 
front oscillation frequencies. In Fig. 7.36, a clear vortex pairing event is circled in the 
images taken from t=0ms to t=25ms.  
7.5.2 PMT tube OH* Chemiluminescence oscillation results 
 A photo multiplier tube with a 308nm filter was used at various streamwise 
and span wise locations to measure the OH* chemiluminescence oscillations at the 
flame fronts subjected to acoustic excitation at 1150 Hz. Scoping locations and the 
corresponding flame front oscillation frequencies are reported in Fig. 7.37, Fig. 7.38, 
Fig. 7.39 and Fig. 7.40. In all the flame front oscillation measurement experiments 
using PMT as reported in this section, an Oxygen-in-the-center GO2/GH2 diffusion 
flame was acoustically forced at 1150 Hz at an amplitude of 40 Vpp from the left. 
7.5.2.1 Near and far field frequencies 
 Fast Fourier Transform of OH* chemiluminescence oscillations collected 
from various streamwise locations using a Photo Multiplier Tube with a 308nm band 
pass filter showed that near the injector plate, the flame oscillated at the frequency at 
which it was driven. Beyond around y/D ~ 3.5, spectral measurements revealed non-
linear nature of the interaction process in which that flame system forced at 1150 Hz 
 
 116 
 
gave rise not only to 1150 Hz oscillations but also triggered flame oscillations 
occurring at substantially lower frequencies. Large amplitude flame front folding 
events developed in this region that continued downstream. It is important to 
recognize that such a scenario could allow other modes of the combustor (typically 
the low frequency bulk modes) to be excited by coupling with heat release 
fluctuations associated with these low frequency but large amplitude flame front 
oscillations. 
 Although structures at the forcing frequency were not apparent on these large 
scale wrinkles, FFT of PMT signal revealed that the high frequency structures were 
still present embedded in the low frequency large amplitude convolutions (Fig. 7.41). 
An apparent preference for the selection of flame sections where these high frequency 
oscillations selectively appeared was noted. The possibility of a RT driven instability 
arising from acoustic acceleration of a density stratified interface or a baroclinic 
interaction between pressure waves from the driver passing through the density 
stratified interface could be responsible for such an interaction and is considered in 
the next section.  
            
7.5.2.2 Secondary Evidence of Acoustically Driven RT Instability 
 Downstream of the injector, the convolutions on the flame front merged and 
paired (cf. Fig. 7.36) and gave rise to oscillations at considerably lower frequencies 
than the frequency at which the flame was forced. OH* chemiluminescence 
oscillation results as showed in Fig. 7.41b and Fig. 7.41c obtained through PMT 
measurements at locations marked A and B respectively of the oscillating flame front 
 
 117 
 
(cf. Fig. 7.41a), indicated two interesting features. Firstly, although low frequency 
flame oscillations showed up downstream beyond y/D ~ 3.5, the high frequency 
component was still present embedded within the low frequency large scale wrinkles. 
Secondly, and more interestingly, the high frequency oscillations had a preference as 
to which side of the low frequency large amplitude convolution they would typically 
occur. 
 As shown in Fig. 7.41a, at a PMT probing location marked A, the passage of a 
large amplitude low frequency flame structure essentially involves the passage of two 
flame fronts - one with Hydrogen on the top and Oxygen on the bottom and the other 
with Oxygen on the top and Hydrogen on the bottom. As the structures convect 
downstream across the PMT sensor at location A, OH*chemiluminescence 
oscillations are recorded by the sensor located there. As shown in Fig 7.41b, OH* 
chemiluminescence oscillation measurements from this sensor at location A show 
1150 Hz high frequency oscillations (associated with the forcing frequency) riding on 
the ?falling? slope of the low frequency OH* chemiluminescence oscillation trace 
(associated with the low frequency resulting from pairing and merging of vortices). 
 A closer look at the OH* chemiluminescence oscillation plot (Fig 7.41b) 
reveals that the flame front where the 1150 Hz oscillations predominantly show up 
correspond to the interface that separates GH2 and GO2 such that as acoustic waves 
from the driver travel from GH2 to GO2 across this it. As per our earlier discussion, 
this interface is RT unstable (heavier fluid GO2 on top of lighter fluid GH2 with 
respect to the pressure gradient due to acoustic wave) and hence leads to an 
amplification of structures at the forcing frequency.  
 
 118 
 
  Similarly, a closer look at the OH* chemiluminescence oscillation plot (Fig 
7.41c) reveals that the flame front where the 1150 Hz oscillations predominantly 
show up correspond to the interface that separates GH2 and GO2 such that as acoustic 
waves from the driver travel from GH2 to GO2 across this it. Consequently, 1150 Hz 
oscillations appear on the ?rising? slope of the underlying low frequency OH* 
chemiluminescence oscillation trace. 
 
 
 
 
           
           
   
 
 
 
 
                                     
           
  
 
 
 119 
 
Chapter 8: Summary and Conclusions 
 An experimental investigation was conducted to study physical mechanisms 
related to the onset of acoustically coupled combustion instabilities that predominate 
in liquid rocket engines (LREs) particularly in the vicinity of the injector. Flame 
acoustic interactions of this kind play critical role in many types of combustion 
instabilities, because they can amplify small amplitude acoustic disturbances during 
the onset of combustion instability leading to very large amplitude self-sustaining 
combustion oscillations that are detrimental to the operability and survivability of the 
engine. The following sections will summarize key tasks and important findings 
related to this work. 
8.1 Summary of key tasks 
 1. An experimental setup was designed to simulate the near field of a shear-
coaxial injector typically used in liquid rocket engines and a transversely mounted 
acoustic driver was used to simulate acoustic conditions occurring in the 
neighborhood of such injectors. Since the acoustic output of the driver unit was 
limited, the model experiments were conducted at scaled-down conditions, ensuring 
relatively strong level of acoustic excitation compared to the level of natural 
turbulence fluctuation.  
 2. Acoustic modes of the chamber under no-flow, isothermal-flow and 
reacting-flow conditions were experimentally identified and a set of analytical models 
to interpret acoustic modes of a combustor with a density stratified flow field was 
developed. For these tests, a mixture of gaseous H2 and CH4 was used as fuel and O2 
 
 120 
 
was used as oxidizer. The combustor was acoustically excited using band limited 
white noise excitation. A Fast Fourier Transform (FFT) was applied to pressure data 
collected using wall mounted high bandwidth dynamic pressure transducers to obtain 
Eigen frequencies of the chamber.  
 3. Carefully controlled flame experiments were conducted, in which, a 
turbulent GH2-GO2 diffusion flame created between co-flowing jets of Oxygen and 
Hydrogen and confined between two parallel plates was acoustically forced by the 
transversely mounted driver unit. Forcing parameters and flow parameters were 
varied and the interaction between flame and acoustics qualitatively and 
quantitatively studied.   
 
Forcing parameters that were varied included: 
? Frequency of forcing 
? Amplitude of forcing 
 
Flow Parameters that were varied included: 
? Relative orientation of fuel and oxidizer jets? 
? Fuel -oxidizer Density ratio 
? Fuel-oxidizer Velocity ratio 
? Fuel-oxidizer Momentum ratio 
? Chemical composition of fuel (GCH4-GH2 blended fuel used) 
 
                                                 
? Change in the orientation of fuel and oxidizer jets with respect to the acoustic driver was used to 
change the direction of the density gradient vector at the fuel-oxidizer interface. 
 
 121 
 
 4. Resulting flame-acoustic interactions were visualized using phase-locked 
schlieren, shadowgraphy and OH* / CH* chemiluminescence imaging. Direct flame 
front visualizations were made using high speed cinematographic imaging. Pressure 
data from the combustor was captured using high bandwidth dynamic pressure 
transducers. OH* / CH* oscillations (associated with oscillations of the flame fronts) 
were captured using Photo-Multiplier-Tube (PMT) measurements. LabVIEW based 
instrumentation was used to generate and log data while Matlab based routines were 
used to process collected data. 
8.2 Summary of important findings 
 The specific findings, both experimental and analytical, obtained as a part of 
this thesis work are summarized in the next few sections.  
8.2.1 Qualitative characterization of flame-acoustic interactions  
 When excited acoustically by the driver unit mounted in a transverse 
direction, the diffusion flame system showed characteristic flame acoustic 
interactions. Flame oscillations were affected by excitation frequency, excitation 
amplitude, and the configuration of the Oxygen-Hydrogen interface.  
 1. Low-frequency asymmetric forcing that excited longitudinal acoustic 
modes of the chamber (and oxidizer post) resulted in symmetric flame front 
oscillations.  This happened both for Oxygen-in the-center and Hydrogen-in-the-
center cases. The Oxygen-in-the-center case produced varicose-mode flame front 
oscillations. The Hydrogen-in-the-center case produced sinuous-mode oscillations. 
Pressure sensors near the flames recorded almost similar RMS pressure amplitudes 
 
 122 
 
and flame structures showed almost equal amplitudes of oscillations. This indicated 
that for low frequency forcing, with wave motion dominant in the longitudinal 
direction, wrinkling on flame fronts was directly correlated to the amplitude of RMS 
pressure fluctuation near the flame fronts. 
 2. In the neighborhood of certain frequencies?, asymmetric acoustic forcing of 
the GO2-GH2 flame system resulted in asymmetric flame front oscillations.  For the 
Oxygen-in-the-center case, large asymmetric flame front wrinkles were observed on 
the flame front that was located close to the acoustic driver while for the Hydrogen-
in-the-center case large amplitude asymmetric wrinkles were observed on the flame 
front that was located away from the acoustic driver. This observation indicated that 
the direction of the density gradient at the fuel oxidizer interface influenced the way 
acoustic waves (at certain frequencies) interacted with the fuel-oxidizer interface. 
 3. For the case resulting in asymmetric flame front oscillations, while there 
was a slight correlation between flame wrinkling and the RMS amplitude of local 
pressure fluctuations for Oxygen-in-the-center case, there was no correlation between 
local RMS amplitude of local pressure fluctuations and flame wrinkling for the 
Hydrogen-in-the-center case. For this case, the flame front, which was further away 
from the acoustic driver, wrinkled more severely, even though the RMS pressure 
amplitudes appeared to be similar near both the flame fronts.  This indicated the 
presence of other physical mechanisms that potentially affected flame front wrinkling 
as observed in the experiments. 
                                                 
? 1150 Hz for Oxygen-in-the-center case and 580 Hz for Hydrogen-in-the-center case. Combustor 
dimension was 15?x3.5?x 0.375?  
 
 123 
 
 4. For asymmetric flame-acoustic interactions observed in the Oxygen-in-the-
center case, evidence of the influence of the direction of density gradient at the fuel-
oxidizer interface was also observed downstream of the injector face plate where the 
initial small amplitude wrinkles (driven at the frequency of the external forcing) 
paired and merged into flame front oscillations that were significantly larger in size 
and lower in frequency. A selective manifestation of high frequency wrinkles (driven 
at the frequency of forcing) was noted on flame fronts allowing the passage of 
acoustic waves from lighter to denser media while they were absent on flame fronts 
allowing the passage of acoustic waves from denser to lighter media.  
8.2.2 Identification of new physical mechanism  
 1. A Baroclinic Vorticity based mechanism, in which the pressure gradient in  
a transversely directed acoustic wave interacted with a misaligned density gradient at 
the fuel-oxidizer interface generating baroclinicity was proposed for the first time as a 
driving mechanism for combustion instability in Liquid Rocket Engines. This 
mechanism was theoretically conjectured, experimentally verified (to a good level of 
confidence) and successfully adapted to explain the strong asymmetric flame-acoustic 
interactions observed in our experiments.  
 Since a baroclinic interaction would depend strongly on the direction and 
magnitude of the density gradient at the fuel-oxidizer interface, three tests were 
conducted to verify baroclinicity as a potential instability mechanism in flame 
acoustic interactions.  
 
 
 124 
 
? In the first test, the direction of the density gradient at the fuel oxidizer 
interface was reversed and the resulting flame system was subjected to 
acoustic excitation from the same direction. Flame front oscillations were 
observed to occur selectively on the interface where acoustic waves travelled 
from lighter to denser media. For the Oxygen-in-the-center case, asymmetric 
interactions were observed on flame front closer to the acoustic driver 
whereas for Hydrogen-in-the-center case, similar oscillations were noted on 
flame front located away from the acoustic driver. 
? In the second test, the magnitude of the density gradient at the fuel-oxidizer 
interface was systematically changed by the addition of noble gases and the 
degree of interaction between flame and acoustics was quantified for a fixed 
level of acoustic forcing. Forcing at a fixed amplitude from the same direction 
was noted to cause lesser and lesser flame-acoustic interaction as the 
magnitude of the density gradient at the fuel-oxidizer interface was gradually 
decreased. An exponential dependency was noted. 
? In the third test, a diffusion flame system using a Hydrogen Methane (GH2 / 
GCH4) blended fuel mixture was acoustically forced and simultaneous 
measurements of OH* Chemiluminescence oscillations and pressure 
oscillations were made at various locations inside the combustor. For all valid 
measurement locations, although the amplitude of pressure oscillations were 
similar, the flame front closer to the acoustic driver where acoustic waves 
travelled from lighter to denser fluid showed greater heat release oscillations. 
 
 
 125 
 
 Results from all the tests showed that there was a preferred orientation of 
pressure and density gradients under which flames responded strongly to acoustic 
forcing, sometimes folding up into violent flame front oscillations. It supported the 
notion that periodic baroclinic vorticity strengthened by large density gradient in 
shear-coaxial injector flow-field could be a problem, making the affected 
configuration susceptible to combustion instability. Such physical mechanism 
involving intermittent baroclinic torque has never been considered in rocket motor 
combustion instabilities.  
 2.  The possible role of an acoustically accelerated Rayleigh-Taylor Instability 
in driving the flame acoustic coupling process was  also explored. Quantification of 
the possible growth rates of the interfacial perturbations using a time dependent 
acoustically driven acceleration field indicated that more than 200% growth of 
perturbation amplitudes is possible in less than half a cycle of acoustic forcing at 
certain frequencies.  
8.2.3 Sensitivity analysis and measurements  
 Sensitivity analysis and measurements of flame-acoustic coupling to other 
flowfield parameters were conducted. 
 1. Using dimensional analysis and an intuitive argument to replace Damkohler 
number with fuel mixture fraction, three non-dimensional groups were identified as 
important in flame acoustic interaction problems. These included non-
dimensionalized density difference, velocity difference and a measure of chemistry. 
Measure of chemistry was represented by the Methane mole fraction in a Hydrogen -
Methane blended fuel.        
 
 126 
 
 
),,(
24
4
HCH
CH
of
of
fo
fo
YY
Y
uu
uuf
D ++
?
+
?=
??
???  
 
Partial sensitivities of flame acoustic coupling to each of these non-dimensional 
variables were described in terms of first order partial derivative functions : 
 
? ?/D( )
? (?o ? ?f)/(?o + ?f)( ), 
( )( )
)/()(
/
ofof uuuu
D
+??
?? , ? ?/D( )
? YCH4/(YCH4 +YH2)( ) 
 
 2. While the parameter under investigation was gradually varied, other 
parameters were kept almost unchanged in these tests. The resulting flame system 
was perturbed by fixed-amplitude acoustic forcing and the extent of flame 
perturbation was quantified by measuring the flame brush thickness through OH* and 
CH* chemiluminescence imaging. Throughout these tests, the temperature and the 
total pressure were held unchanged.  In the ranges tested, the amount of flame-
acoustic interaction was most sensitive to changes in density ratio. Changes in 
velocity ratio and fuel mixture ratio produced relatively small effects.  
 
Results from the tests are summarized below: 
? In the first parametric test, the density ratio between oxidizer and fuel was 
varied between 16 and 5, while the velocity ratio and the fuel composition 
were held constant. Density ratio possibly affected flame-acoustic interaction 
 
 127 
 
by changing the amplitude of periodically applied baroclinic torque on the 
mixture interface. The observed dependence on density ratio was exponential. 
 
???
?
???
?
+=??
??
?
? ?
fo
fo
u
CCD ?? ??? .exp 21    Where 1C~ 0.02 and 2C ~ 5.1 
 
? In the second test, the velocity ratio was varied between 3.0 and 5.3, while the 
density ratio and the fuel composition were held constant. Increasing the outer 
jet velocity reduced the amount of interaction almost linearly. This effect was 
attributed to the decrease in acoustic energy per mass flow rate. The observed 
dependence on non-dimensionalized velocity difference was found to be : 
 
43 Cuu
uuC
D of
of +
???
?
???
?
+
?=?
?
??
?
?
?
?    Where 
3C ~ -3.5 and 4C ~ 3.6 
 
? In the third test, a Hydrogen-Methane mixture fuel was tested by varying the 
mixture fraction while both the density ratio and the velocity ratio were held 
constant.  Increasing the Methane mole fraction also reduced the amount of 
interaction linearly. This effect was attributed to the reduction in total heat 
release rate which affected the amplification mechanism. The observed 
dependence on Methane mole fraction was found to be : 
 
 
 128 
 
65
, 24
4 C
YY
YC
D HCH
CH
u
+??
?
?
???
?
+=??
??
?
?
?
?    Where 
5C ~ -0.87 and 6C ~ 2.3 
 
? Using data collected as  apart of the velocity ratio test and the density ratio 
test, the effect of momentum ratio on flame acoustic coupling was also 
studied. Increase in outer jet momentum for a fixed level of acoustic forcing 
also caused a reduction in the amount of interaction. For cases where outer jet 
momentum was increased by increasing outer jet velocity while keeping outer 
jet density constant (density ratio between outer and inner jet remained 
constant in the process) flame brush thickness decreased linearly as outer jet 
momentum was increased. The observed dependence on momentum ratio was 
found to be : 
 
87 CJJ
JJC
D of
of +
???
?
???
?
+
?=?
?
??
?
?
?
?    Where 
7C ~ -1.24 and 8C ~ 1.25 
 
? For cases where outer jet momentum was increased by increasing outer jet 
density while keeping outer jet velocity constant (density ratio between outer 
and inner jet decreased in the process) the flame brush thickness decreased 
exponentially as the outer jet momentum was increased indicating the stronger 
role played by fuel-oxidizer density ratio in controlling flame-acoustic 
interaction. The observed dependence on momentum ratio was found to be : 
 
 
 
 129 
 
???
?
???
?
+
?=?
?
??
?
?
of
of
u JJ
JJCC
D .exp 109
?    Where 
9C ~ 0.29 and 10C ~ -2.85 
 
8.2.4 Non-linear response in flame-acoustic interaction 
 1. High speed imaging and spectral measurements of the flame system under 
transverse acoustic forcing showed that downstream of the injector face plate, the 
initial small amplitude wrinkles (driven at the frequency of the external forcing) 
paired and merged into flame front oscillations that were significantly larger in 
amplitude and lower in frequency as compared to the initial interaction zone near the 
injector face plate.  Various time scales showed up in the flame oscillations 
downstream of the injector with high frequency small amplitude oscillations at the 
forced frequency riding over large amplitude low frequency ones.  
 2. This showed that large amplitude heat release oscillations could essentially 
occur at frequencies that were significantly different from the frequency of forcing. 
As a result of this, other modes of the combustor whose Eigen frequencies do not 
correspond to the forcing frequency could also be excited leading to the excitation of 
lower frequency modes of the combustor.  
8.2.5 Model development.  
 Three different analytical models were developed to interpret and explain 
experimentally observed acoustic modes of the chamber under density stratified 
isothermal and reacting flow conditions. The experimental results showed good 
quantitative agreements with the model computation. Interestingly enough, the 
 
 130 
 
acoustically driven entrainment model was even able to account for the discrepancy 
of the frequency of the 3?/4-mode of the chamber length (closed-open boundaries) 
measured on either sides of the central flame zone.  
 
The three models were based on (1) well-stirred reactor , (2) jet mixing length, and 
(3) acoustically driven entrainment models. The models differed in the way the 
average molecular weight and gamma of the medium inside the combustor was 
calculated. It essentially involved using a correction factor ? to correct the average 
molecular weight and the average ratio of specific heat equations used by each of 
them. 
 
2
242
2
4
242
4
2
242
2
422
)()()(
),,,(
O
OCHH
O
CH
OCHH
CH
H
OCHH
H
CHOHmix
MWMWMW
MW
????
??
????
?
????
?
????
++++++++
=
 
 
 
2
242
2
4
242
4
2
242
2
422
)()()(
),,,(
O
OCHH
O
CH
OCHH
CH
H
OCHH
H
CHOHmix
????? ??????? ?????? ?
?????
++++++++
=
 
 
? In the Well Stirred Reactor based model, the average molecular weight and 
gamma of the mixture were calculated assuming a fully premixed mixture of 
fuel and oxidizer, in  stoichiometric proportions( ? = 1) 
 
 131 
 
? In the Jet Mixing Length based Model, two separate length scales were used. 
To a distance equivalent to the potential core length of the center jet from the 
injector faceplate, the average molecular weight and gamma of the mixture 
was calculated assuming a fully premixed mixture of fuel and oxidizer, mixed 
in their stoichiometric proportions but corrected using the velocity ratio 
between fuel and oxidizer. Beyond this region, a fully premixed 
stoichiometric mixture was used. 
 
            
2o
fuel
V
V=? , for Dy 60 ??  
? = 1 for Dy 6? . 
 
  
? In the acoustically driven entrainment based model, two separate values of ? 
were used near the driver and away from the driver regions because an excess 
entrainment of the center jet into the co-flow on the driver side would lead to 
a decrease in the amount of the center jet fluid entrained by co-flow on the far 
side of the driver. Values for 1? and 2?  were experimentally determined 
 
)(1 1
total
reference
J
J?? +=   Driver side 
)(1 2
total
reference
J
J?? ?=    Wall side  
 
 132 
 
8.3 Concluding remark 
 This work highlighted the role of the density gradient between fuel and 
oxidizer as a facilitator for initiating combustion instability. Reducing the density 
gradient between fuel and oxidizer was shown to increase the resistance of flames to 
acoustic coupling providing a greater margin of stability. In fully unstable combustion 
inside a rocket thrust chamber, the amplitude of pressure oscillations becomes rather 
large, making flame-acoustic coupling inevitable. However, during the onset of 
combustion instability the pressure oscillation amplitude would be small, but could be 
just large enough to cause further amplification through coupled heat release. The 
present results show that baroclinic interactions could amplify heat release coupling. 
Experimental confirmation of the possible role of density gradient in promoting heat 
release oscillations is presented, but more work needs to be done before this theory 
can be proved or disproved with a sufficient level of confidence. Nonetheless, this is a 
useful finding because it suggests reducing the density gradient between fuel and 
oxidizer as a possible control mechanism. Reducing the density gradient between fuel 
and oxidizer would lead to greater resistance to flame-acoustic coupling, thus 
providing a greater margin of stability.  Needless to say, such extrapolation of the 
present results must be taken with caution because a change in chemical kinetics 
could have even more sensitive effect on flame stability. 
 
 
 
 
 
 
 
 
 133 
 
Appendices 
Appendix A: Images 
 
Figure 1.1. Schematic showing typical flow field in the neighborhood of a 
LOX- GH2 shear coaxial injector. 
 
 
 
 
 
Figure 3.1. Baroclinic interactions between pressure gradient and density 
gradient at a density stratified interface. (a) Destabilizing interaction. (b) 
Stabilizing interaction. 
 
 
 134 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.2. RT unstable configurations. (a) Single-mode case. (b) Multi-
mode case ( After Kumar, 2003). 
 
 
 
 
Figure 3.3. RT instability, single wavelength initial perturbation (After 
Youngs 1984). 
 
 
 
 
 
 
 
                 
 
 135 
 
                             
 
 
 
 
 
 
 
 
 
                         
 
                  
 
                             
 
 
Figure 3.4. Richtmyer-Meshkov instability (After Sunhara et al.,1996). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 136 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.5. Jet preferred mode instability. 
 
 
 
 
            
 
 
Figure 3.6. Wake mode instability.  
 
 
 
 
 137 
 
 
 
 
 
 
Figure 4.1. (a) Physical model. (b) Schematic of the shear-coax injector 
rig. All dimensions are in inches. 
 
 
 
 
 
 
 138 
 
 
 
 
Tap#1 
(0.5?,-1.625?)
Tap#4 
(0.5?,1.625?)
Tap#2 
(0.5?,-0.5?)
Tap#3 
(0.5?,0.5?)
Oxydizer FuelFuel
Acoustic 
Driver
 
    (a)                                                                         (b)          
 
Figure  4.2. Schematic view of shear coax combustor. (a) Overall setup. 
(b) Near injector region showing pressure tap locations. All dimensions 
are in inches. 
 
 139 
 
       
 
Figure 4.3. Physical setup. 
 
 
Figure 4.4. Physical model of inlet to combustor. 
 
 140 
 
 
 
 
 
 
Figure 4.5. Schematic showing dimensions for inlet to combustor. All 
dimensions are in inches. 
 
 
 
 
 141 
 
 
 
 
 
Figure 4.6. Schematic showing position and size of through holes for bolts 
for fixing the side plates between which the center piece is sandwiched. 
All dimensions are in inches. 
 
 
 
 142 
 
 
 
 
 
 
 
 
Figure 4.7. Schematic showing side plate with injection location for gases. 
All dimensions are in inches. 
 
 
 
 
 143 
 
 
 
 
 
Figure 4.8. Schlieren setup. (a) Laboratory arrangement. (b) Schematic. 
                
 
 144 
 
 
 
              
              
Tap#1 
(0.5?,-1.625?)
Tap#4 
(0.5?,1.625?)
Tap#2 
(0.5?,-0.5?)
Tap#3 
(0.5?,0.5?)
Oxydizer FuelFuel
Acoustic 
Driver
 
Figure 4.9. Kistler dynamic pressure sensor locations. cf. Table 3.1. for 
location of pressure taps. All dimensions are in inches. 
 
 
 
 
 
 
 
 
Figure 4.10. Injection arrangement for reversal of density gradient test. (a) 
Normal configuration. (b) Reversed configuration. 
 
 
 
 
 
 145 
 
 
 
 
 
 
 
 
 
           (a) 
 
 
 
              (b) 
 
 
 
            (c) 
 
 
Figure 4.11. Injection arrangement for the different tests. (a) Effect of 
density ratio. (b) Effect of velocity ratio. (c) Effect of chemical 
composition of fuel. 
 
 
 
 
 
 
 
 
 146 
 
 
(a)                                                              (b) 
 
(c)                                                                 (d) 
 
 
 
Fig. 5.1.  Pressure Spectrum at (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) 
Tap#4 . No-Flow Conditions. Chamber is excited with band limited white 
noise forcing. 
 
 
 
 
 
 147 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.2.  Pressure spectrum of no flow quiescent air excited with 
white noise redrawn from previous figure. Tap #4.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Symbol Frequency 
(Hz) 
  
f1 136 
f2 392 
f3 600 
f4 1024 
f5 1920 
 
 148 
 
 
 
 
 
 
                                         (a)                                          (b) 
  
                                        (c)                                          (d) 
  
 
 
Figure 5.3.  Pressure spectrum of isothermal case excited with white noise.  Density 
ratio = 14.5.  (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4 
 
 
 149 
 
 
 
 
                                          (a)                                         (b) 
  
                                         (c)                                         (d) 
  
 
 
 
Figure 5.4.  Pressure spectrum of isothermal case excited with white noise.  Density ratio = 11.   
(a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4 
 
 150 
 
 
 
 
 
                                        (a)                                        (b) 
  
                                         (c)                                         (d) 
  
 
 
 
Figure 5.5.  Pressure spectrum of isothermal case excited with white noise.  Density 
ratio = 7. (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4 
 
 151 
 
 
 
 
Figure 5.6. Schematic showing distribution of acoustic media in a 
combustor.  
 
 
 
              
 
Figure 5.7.  Schlieren visualization showing three different acoustic 
regions of the combustor. Regions 1 and 3 are product dominated and can 
have different resonant behaviors in the longitudinal direction because 
they are bounded from each other by interfaces with sudden density 
changes. 
 
 152 
 
 
 
 
 
 
 
 
         
 Figure 5.8. Comparison of experimental and predicted values of resonant 
frequencies for isothermal case. 
 
 
 
 
 
 153 
 
 
 
 
 
                                 (a)                                       (b) 
 
 
                                        (c)                                       (d) 
 
 
 
Figure 5.9.  Pressure spectrum of reacting flow case excited with white noise.  
Density ratio = 14.5. (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4 
 
 
 154 
 
 
 
 
                              (a)                                         (b) 
 
 
                                           (c)                                        (d) 
 
 
 
Figure 5.10.  Pressure spectrum of reacting flow case excited with white noise.  
Density ratio = 11.  (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4. 
 
 
 155 
 
 
 
 
 
 
                                     (a)                                       (b) 
 
 
                                             (c)                                      (d) 
 
 
 
Figure 5.11.  Pressure spectrum of reacting flow case excited with white noise.  
Density ratio = 7.  (a) Tap #1, (b) Tap #2, (c) Tap #3, (d) Tap #4. 
 
 
 156 
 
 
 
 
 
 
 
 
 
 
Figure 6.1.  Flow arrangement. Band limited (100Hz ? 10KHz) white 
noise forcing is applied from the left. Center jet of air is at 6m/s and 
co-flowing Helium jets are at 18m/s. 
 
 
 
 
 
 
 
 
 
 
 157 
 
 
 
                                  (a)                                                             (b) 
   
                                   (c)                                                               (d)  
 
 
Figure 6.2.  Pressure spectrum of isothermal case excited with white 
noise.  He-18m/s-Air-6m/s-He-18m/s. (a) Tap #1 , (b) Tap #2, (c) Tap 
#3, (d) Tap#4. 
 
 
 
 
 
 
 158 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 6.3.  Pressure spectrum of isothermal case 
excited with white noise redrawn from previous figure (Tap #4). He-
18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 
 
 
Symbol Frequency 
(Hz) 
  
f1 234 
f2 458 
f3 750 
f4 1016 
f5 1433 
f6 1608 
f7 2100 
f8 2466 
 
 159 
 
 
 
 
      
      
Figure 6.4(a). Baseline case, no forcing, exposure ? 30?s. He-18m/s-Air-
6m/s-He-18m/s.  
 
 
 
 
 160 
 
 
 
 
     
     
Figure 6.4(b). Flow response to forcing from left at 200 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 161 
 
 
 
 
     
     
Figure 6.4(c). Flow response to forcing from left at 234.4 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 162 
 
 
 
 
     
     
Figure 6.4(d). Flow response to forcing from left at 400.4 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 163 
 
 
 
 
     
     
Figure 6.4(e). Flow response to forcing from left at 500 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 164 
 
 
 
 
     
     
Figure 6.4(f). Flow response to forcing from left at 625 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 165 
 
 
 
 
    
    
Figure 6.4(g). Flow response to forcing from left at 771.5 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 166 
 
 
 
 
     
     
Figure 6.4(h). Flow response to forcing from left at 820.3 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 167 
 
 
 
 
     
     
Figure 6.4(i). Flow response to forcing from left at 947.3 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 168 
 
 
 
 
     
     
Figure 6.4(j). Flow response to forcing from left at 1016 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 169 
 
 
 
 
     
     
Figure 6.4(k). Flow response to forcing from left at 1094 Hz, 40Vpp, 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 170 
 
 
 
 
     
     
 
Figure 6.4(l). Flow response to forcing from left at 1094 Hz, 50 Vpp 
exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 171 
 
 
 
 
     
     
Figure 6.4(m). Flow response to forcing from left at 1250 Hz, 50Vpp, 
exposure ? 10?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 172 
 
 
 
 
     
     
Figure 6.4(n). Flow response to forcing from left at 1850 Hz, 50Vpp, 
exposure ? 10?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 173 
 
 
 
 
     
     
Figure 6.4(o). Flow response to forcing from left at 2676 Hz, 50Vpp, 
exposure ? 10?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 
 174 
 
 
Figure 6.5.  Acoustic regions of the combustor. Tap #1 measures acoustic 
signature in Region 1 while Tap #4 measures acoustic signature in Region 
3. 
 
 
 
 
Figure 6.6. Comparison of pressure spectrum between Tap #1 and Tap #4 
of isothermal case excited with white noise. He-18m/s-Air-6m/s-He-
18m/s.  
 
 
Symbol Frequency 
(Hz) 
  
g1 611 
g2 750 
g3 889 
g4 1016 
g5 1094 
  
 
 175 
 
            
 
Figure 6.7. Schematic for wake mode instability calculation.  
 
 
 
         
 
Figure 6.8 (a) Injection arrangement (b) Hotwire probe location 
 
 
 
 
 
 
 176 
 
 
Figure 6.9. Frequency response of velocity in unforced and forced cases 
(monotone excitation). 
 
 
   
 
Figure 6.10. Frequency response of velocity in unforced and forced cases 
(broadband excitation). 
 
 
 177 
 
 
 
 
 
     
     
Figure 6.11(a). Baseline, no forcing, exposure ? 30?s, He-18m/s-Air-
6m/s-He-18m/s.  
 
 
 
 178 
 
 
 
 
     
     
Figure 6.11(b). Flow response to forcing from left at 429.7 Hz, 4 Vpp. 
Exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 179 
 
 
 
 
     
     
Figure 6.11(c). Flow response to forcing from left at 429.7 Hz, 12 Vpp. 
Exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 180 
 
 
 
 
     
     
Figure 6.11(d). Flow response to forcing from left at 429.7 Hz, 16 Vpp. 
Exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 181 
 
 
 
 
     
     
Figure 6.11(e). Flow response to forcing from left at 429.7 Hz, 20 Vpp. 
Exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 182 
 
 
 
 
     
     
Figure 6.11(f). Flow response to forcing from left at 429.7 Hz, 30 Vpp. 
Exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 183 
 
 
 
 
     
     
Figure 6.11(g). Flow response to forcing from left at 429.7 Hz, 40 Vpp. 
Exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 184 
 
 
 
 
     
      
Figure 6.11(h). Flow response to forcing from left at 429.7 Hz, 50 Vpp. 
Exposure ? 30?s, He-18m/s-Air-6m/s-He-18m/s.  
 
 
 
 
 
 185 
 
 
 
 
Figure 7.1. Flow arrangement for the GH2 / GO2 / GH2 turbulent 
diffusion flame system. VO2 = 6 m/s, VH2 = 18 m/s, ReO2 = 4900. Acoustic 
forcing is from the left. 
 
 
 
 
 
 
Figure 7.2. OH* chemiluminescence showing natural instabilities in an 
unforced GH2 / GO2 / GH2 turbulent flame. VO2 = 6 m/s, VH2 = 18 m/s, 
ReO2 = 4900. 
 
 
 
 
 186 
 
   
 
 
 
 
 
 
 
Figure 7.3. Pressure spectrum from Tap #4 under band limited (100Hz-
10kHz) white noise excitation (9 watts).  
 
 
 
 
 
 
 
 
 
 
 
 
 187 
 
 
 
 
 
 
    
   
 
Figure 7.4. OH* chemiluminescence at various phases of oscillation (00, 
900, 1800 and 2700) of a GH2 / GO2 / GH2 turbulent flame forced at 300 
Hz from the left. VO2 = 6 m/s, VH2 = 18 m/s, ReO2 = 4900. D is the width 
of the center jet = 0.75 inch. 
 
 
 
 
 188 
 
 
 
 
 
 
    
   
 
Figure 7.5. OH* chemiluminescence at various phases of oscillation (00, 
900, 1800 and 2700)  of a GH2 / GO2 / GH2 turbulent flame forced at 1150 
Hz from the left. VO2 = 6 m/s, VH2 = 18 m/s, ReO2 = 4900. D is the width 
of the center jet = 0.75 inch 
 
 
 
 189 
 
 
 
 
 
 
 
 
   
 
 
Figure 7.6.  Contour plots showing flame response to an increasing set 
of acoustic forcing amplitude. VO2 = 4.5 m/s, VH2 = 13.5 m/s, ReO2 = 
3700. Forcing is increasing from left to right and top to bottom, 0 
watts, 4.5 watts, 5.3 watts, 7 watts, 9.6 watts and 12.5 watts.                  
 
 
 
 
 
 190 
 
 
 
 
Figure 7.7(a). Instantaneous OH* chemiluminescence images showing a 
monotonic decay of oscillations as density ratio between fuel and oxidizer 
is decreased from 15.9 to 5. VO2 = 4.5 m/s, VH2 = 13.5 m/s, ReO2 = 3700. 
 
 
 191 
 
  
   
  
Figure 7.7(b). Contour plots of ensemble averaged OH* chemiluminescence 
images showing a monotonic decay of oscillations as density ratio between 
fuel and oxidizer is decreased from 15.9 to 5. VO2 = 4.5 m/s, VH2 = 13.5 m/s, 
ReO2 = 3700. 
 
 
 192 
 
 
Figure 7.8.  Normalized intensity for flame across the width of the 
combustion chamber for different oxidizer-fuel density ratios at an 
axial location y/D=4.7. At a given axial location, width of flame, ?(y) 
=| ro- ri |, where the horizontal line corresponds to an intensity of 10% 
of the maximum. 
 
 
Figure 7.9.  Measured flame brush thickness at various density ratios 
and axial locations 
 
 193 
 
 
           
Figure 7.10.  Flame brush thickness as a function of density ratio and 
acoustic forcing amplitude. 
 
 
 
 
 
Figure 7.11. UV filtered flame image showing natural instabilities in an 
unforced Hydrogen-in-the-center turbulent diffusion flame. VO2/N2 = 
17.8m/s m/s, VH2 = 5 m/s, ReH2 ~ 600, ReO2/N2 ~ 8800.  
 
 
 
 
 194 
 
 
 
 
 
  
 
 
 
 
 
Figure 7.12(a). UV filtered images at various phases of oscillation (00, 900, 
1800 and 2700) of a Hydrogen-in-the-center turbulent diffusion flame 
forced at 300 Hz (at 30 Vpp) from the left. VO2/N2 = 17.8m/s m/s, VH2 = 5 
m/s, ReH2 ~ 600, ReO2/N2 ~ 8800.  
 
 
 
 
 
 195 
 
 
 
 
 
 
Figure 7.12(b). UV filtered images at various phases of oscillation (00, 900, 
1800 and 2700) of a Hydrogen-in-the-center turbulent diffusion flame 
forced at 580 Hz (55 Vpp) from the left. VO2/N2 = 17.8m/s m/s, VH2 = 5 
m/s, ReH2 ~ 600, ReO2/N2 ~ 8800.  
 
 
 196 
 
                     
Figure 7.13. Dynamic pressure distribution across the flames. Pressure 
Tap # 1 is closest to the speaker. 
 
 
 
 
Figure 7.14. Variation of density ratio and heat release rate with molar 
dilution. 
 
 
 
 197 
 
 
 
                  (a)                               (b)                               (c) 
Figure 7.15. Comparison of flame-acoustic interaction under similar 
forcing and heat release conditions (15 kW) but different density 
ratios. OH* chemiluminescence images. Density ratios from left to 
right are as 7.0 or 15.2, 7.0 and 15.2 respectively. 
 
 
 
      
Figure 7.16. Growth rate of flame perturbation thickness as a function 
of streamwise location. 
 
 
 198 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 7.17. Variation of density ratio and jet momentums with molar 
dilution. Momentum, Total = Momentum, center Jet + 2x Momentum, 
Co-Flow Jet. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 199 
 
 
  
      (a)                               (b) 
Figure 7.18. Outer jet momentum = 0.0055 kg.m/s2, center jet momentum 
= 0.0047 kg.m/s2. Density ratio between oxidizer and fuel is ~ 8. Acoustic 
forcing is from the left and is held fixed at 15.8 Watts.   
 
 
 
 
 
 (a)                                (b) 
Figure 7.19. Outer jet momentum = 0.0055 kg.m/s2, center jet momentum 
= 0.0036 kg.m/s2. Density ratio between oxidizer and fuel is ~ 2. Acoustic 
forcing is from the left and is held fixed at 15.8 Watts. 
 
 
 200 
 
 
               (a) 
 
                (b) 
Figure 7.20. Pressure spectrum at Tap #1 (a) and at Tap #4 (b) for reacting 
flow-fields under white noise excitation for density rations 16, 10 and 6. 
 
 
 
 201 
 
 
 
 
 
 
 
Tap# D3 W3 D2 W2 D1 W1 
x (in) -0.500 0.500 -0.500 0.500 -0.500 0.500 
y (in) 0.750 0.750 2.250 2.250 3.750 3.750 
 
 
 
Figure 7.21. Location of pressure measurement and OH* 
chemiluminescence oscillation measurement ports. 
 
 
 
 
 202 
 
 
 
Fig. 7.22. Comparison of local OH* chemiluminescence fluctuations 
responding to pressure oscillation at density ratio=14.5.  The sensors 
are located horizontally at x=-0.67D (left column) and x=0.67D (right 
column), and vertically at (a) y=5D, (b) y=3D, (c) y=1D 
 
 
 
 203 
 
 
 
Figure 7.23. Comparison of local OH* chemiluminescence 
fluctuations responding to pressure oscillation at density ratio=3.  The 
sensors are located horizontally at x=-0.67D (left column) and 
x=0.67D (right column), and vertically at (a) y=5D, (b) y=3D, (c) 
y=1D. 
 
 
 204 
 
 
Figure 7.24. Classical RT mode instability analysis yields wavelength-
dependent growth rate. 
 
 
Figure 7.25. Amplification in growth rates as function of acoustic cycle. 
 
 
 
 205 
 
 
 
 
 
 
 
 
Figure 7.26. Measured flame brush thickness at various density ratios and 
streamwise locations. 
 
 
 
 
 
 
 
 
 206 
 
 
 
 
 
 
 
Figure 7.27. Instantaneous OH* chemiluminescence images showing 
flame perturbations affected by fuel-oxidizer velocity ratio. Fuel 
oxidizer velocity ratios are in increasing order from left to right and 
from top to bottom. Velocity ratios are as  uf / uo=3.02, uf / uo=3.36, uf / 
uo=3.64, uf / uo=4.01, uf / uo=4.51, uf / uo=5.03 and uf / uo=5.27. 
 
 
 
 
 207 
 
 
 
 
 
 
 
Figure 7.28. Time averaged OH* chemiluminescence images showing 
flame perturbations affected by fuel-oxidizer velocity ratio. Fuel oxidizer 
velocity ratios are in increasing order from left to right and from top to 
bottom. Velocity ratios are as  uf / uo=3.02, uf / uo=3.36, uf / uo=3.64, uf / 
uo=4.01, uf / uo=4.51, uf / uo=5.03 and uf / uo=5.27. 
 
 
 
 
 
 
 
 208 
 
 
 
 
 
 
 
 
 
Figure 7.29. Measured flame brush thickness at various velocity ratios and 
streamwise locations. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 209 
 
 
 
 
 
 
 
 
 
Figure 7.30. Flame perturbations affected by fuel-oxidizer momentum 
ratio involving no change in velocity ratio. uf / uo =  3, ?o / ?f = 6, ?o / ?f = 
5,?o / ?f = 4, ?o / ?f = 3, ?o / ?f = 2, Jo/Jf =1.99, Jo/Jf =1.67, Jo/Jf =1.33, Jo/Jf 
=1.00, Jo/Jf =0.67. 
 
 
 
 
 
 
 
 210 
 
 
 
 
 
 
 
 
Figure 7.31. Flame perturbations affected by fuel-oxidizer momentum 
ratio involving no change in density ratio. ?o / ?f = 7.99, uf / uo=3.36, uf / 
uo=3.64, uf / uo=4.01, uf / uo=4.51, uf / uo=5.27, Jo/Jf =2.12, Jo/Jf =1.80, Jo/Jf 
=1.49, Jo/Jf =1.18, Jo/Jf =0.86. 
 
 
 
 
 
 211 
 
 
                                                                (a) 
 
(b) 
 
Figure 7.32.  Flame perturbations affected by non-dimensionalized fuel-
oxidizer momentum difference.  (a) Momentum change through velocity 
change. (b) Momentum change through density change. 
 
 212 
 
 
 
 
        (a)                                 (b) 
 
    (c)                                 (d) 
 
Figure 7.33. Lifted flame using 100% CH4. No acoustic excitation. (a) 
Instantaneous CH* chemiluminescence image (b) Instantaneous OH* 
chemiluminescence image (c) Average CH* chemiluminescence 
image (d) Average OH* chemiluminescence image.  
 
 
 
 213 
 
 
 
 
     (a)                               (b) 
 
       (c)                              (d) 
 
Figure 7.34.  50% CH4, 50% H2 fueled flame acoustically excited from 
left at 1150 Hz. (a) Instantaneous CH* chemiluminescence image. (b) 
Instantaneous OH* chemiluminescence image. (c) Average CH* 
chemiluminescence image. (d) Average OH* chemiluminescence 
image.  
 
 
 
 
 
 214 
 
 
 
 
 
 
 
 
 
 
 
Figure 7.35. Measured flame brush thickness at various fuel 
compositions and axial locations. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 215 
 
 
 
 
 
Figure 7.36. High-speed imaging showing a typical vortex pairing 
event when the GO2 / GH2 turbulent flame is forced at 1150 Hz. VO2 = 
4.5 m/s, VH2 = 13.5 m/s., Center jet width, D = 0.75 inch. 
 
 
 
 
 216 
 
 
 
 
 
  
(1 time unit=0.05 msec) 
 
 
 
 
Figure 7.37. Time domain and frequency domain measurement of 
OH* chemiluminescence oscillations using PMT. Probe location (x, y) 
= (-0.375?, 0.375?) is shown by the circle on the flame image. VO2 = 
4.5 m/s, VH2 = 13.5 m/s., Center jet width, D = 0.75 inch. Forcing is 
from left at 1150 Hz. 
 
 
 
 
 
 
y 
 y 
x 
 
 217 
 
 
 
 
 
 
                                           (1 time unit=0.05 msec) 
 
 
 
 
Figure 7.38. Time domain and frequency domain measurement of 
OH* chemiluminescence oscillations using PMT. Probe location (x, y) 
= (-0.375?, 2.25?) is shown by the circle on the flame image. VO2 = 4.5 
m/s, VH2 = 13.5 m/s., Center jet width, D = 0.75 inch. Forcing is from 
left at 1150 Hz. 
 
 
 
 
 
 
y 
 y 
x 
 
 218 
 
 
 
 
 
 
(1 time unit=0.05 msec) 
 
 
 
Figure 7.39. Time domain and frequency domain measurement of 
OH* chemiluminescence oscillations using PMT. Probe location (x, y) 
= (-0.375?, 3.75?) is shown by the circle on the flame image. VO2 = 4.5 
m/s, VH2 = 13.5 m/s., Center jet width, D = 0.75 inch. Forcing is from 
left at 1150 Hz. 
 
 
 
 
 
 
 
y 
 y 
x 
 
 219 
 
 
 
 
 
 
  (1 time unit=0.05 msec) 
 
 
 
Figure 7.40. Time domain and frequency domain measurement of 
OH* chemiluminescence oscillations using PMT. Probe location (x, y) 
= (-1.375?, 3.75?) is shown by the circle on the flame image. VO2 = 4.5 
m/s, VH2 = 13.5 m/s., Center jet width, D = 0.75 inch. Forcing is from 
left at 1150 Hz. 
 
 
 
 
 
 
 
 
 
 
 
y 
 y 
x 
 
 220 
 
           (a) 
 
          (b)            
 
         (c) 
    
 
Figure 7.41. Instantaneous OH* chemiluminescence image for a 
GH2/GO2/GH2 flame forced at 1150 Hz from left (a) and OH* oscillation as 
picked up by PMT sensor at location marked ?A? (b) and ?B? (c). OH* 
oscillations are large when acoustic waves from driver are passing from 
lighter H2 to denser O2. 
 
B 
A 
A 
B 
 
 221 
 
Appendix B: Tables 
 
Tap # 1 2 3 4 
x(in) -1.625 -0.500 0.500 1.625 
y(in) 0.500 0.500 0.500 0.500 
 
Table 3.1. Location of pressure taps. y-axis is streamwise, x-axis is 
transverse. 
 
 
Tap Mode No Flow (Quiescent Air) 
  #  
Measured 
(Hz) 
Calculated 
(Hz) 
4 f1 136?10 141a 
 f2 392 399 b 
 f3 600 639 c 
 f4 1024 976d 
 f5 1920 1952e 
 
 
a ? Quarter-wave mode longitudinal in the combustor with oxidizer post. 
b ? Quarter-wave mode longitudinal in oxidizer post. 
c ? Three-quarter-wave mode longitudinal in the combustion chamber. 
d ? Quarter-wave mode (Transverse) across the chamber width.   
e ? Half-wave mode (Transverse) across the chamber width.   
 
 
Table 5.1. Comparison of measured spectral peak frequencies and 
calculated resonance frequencies for no-flow with quiescent air. 
 
 
 
 
 
 
 222 
 
 
 
 
 
 
 
 
 
Flow Conditions A B C D 
Density Ratio (?o/??f) 14.5 11 7 3 
O2 flow rate (g/s) 1.06 1.06 1.06 1.06 
Velocity (m/s) 4.5 4.5 4.5 4.5 
Oxygen 
Reynolds number 5500 5500 5500 5500 
H2 flowrate (g/s) 0.125 0.104 0.070 0.018 
CH4 flowrate (g/s) 0.015 0.058 0.126 0.231 
H2 mole fraction 99% 94% 82% 37% 
CH4 mole fraction 1% 6% 18% 63% 
 
 
Fuel 
Velocity (m/s) 13.0 11.3 8.7 4.6 
Velocity Ratio (uf/uo) 2.9 2.5 1.9 1.0 
Rate of Heat Release (kW) 15.9 15.5 14.9 13.8 
 
Table 5.2. Flow conditions for the different test runs for model development. 
 
 
 
 
 
 
 
 
 223 
 
 
 
 
 
Location Mode Density Ratio = 14.5 Density Ratio = 11.0 Density Ratio = 7.0 
Measured Calculated Measured Calculated Measured Calculated 
  (Hz) (Hz) (Hz) (Hz) (Hz) (Hz) 
Tap #1 f1 434?10 430 423?10 430  423?10 430  
 
f2 900 
980a 
912b 
900c 
868 
928 a 
877b 
859c 
752 
843 a 
817b 
791c 
  f3 1508 1430 1453 1370 1270 1269 
Tap #2 f1 434 430 434 430 423 430 
 f2 933 980 868 928 770 843 
  f3 1508 1430 1453 1370 1269 1269 
Tap #3 f1 433 430 434 430 423 430 
 f2 1017 980 889 928 791 / 900 843 
  f3 1580 1430 1518 1370 1400 1269 
Tap #4 f1 438 430 434 430 423 430 
 
f2 1011 
980a 
912b 
1011c 
911 
928 a 
877b 
955c 
781 / 900 
843 a 
817b 
864c 
  f3 1528 1430 1453 1370 1399 1269 
 
a ? Frequency calculated using full mixing model.  
b ? Frequency calculated using jet mixing length model. 
c ? Frequency calculated using acoustically driven entrainment model. 
When method is not indicated for a calculated frequency, a full mixing model 
is used by default. 
 
Table 5.3. Comparison of measured spectral peak frequencies and calculated 
resonance frequencies for isothermal flow conditions 
 
 
 
 
 
 
 224 
 
 
 
 
Table 5.4.  Comparison of measured spectral peak frequencies under 
reacting flow conditions. 
 
 
 
 
Table 7.1. Test conditions for flame response to acoustic forcing at 
characteristic frequencies. 
 
 
 
 
 
 
Location Mode Density Ratio = 14.5 Density Ratio = 11.0 Density Ratio = 7.0 
Tap #1 f1 477 Hz ? 10Hz 466 Hz ? 10Hz 434 Hz ? 10Hz 
 f2 1323 1270 1171 
Tap #2 f1 477 455 445 
 f2 1345 1312 1117 
Tap #3 f1 520 474 445 
 f2 1410 1331 1204 
Tap #4 f1 520 465 434 
 f2 1410 1331 1204 
?o / ?f uf / uo uf uo Heat Release  Forcing frequency Flame-Acoustic Interaction ReO2 
  (m/s) (m/s) (kW) (Hz)   
16 3 18 6 22.1 None Low 3700, 4900, 7300 
16 3 18 6 22.1 300 Hz High-Symmetric 3700, 4900, 7300 
16 3 18 6 22.1 1150 Hz High-Asymmetric 3700, 4900, 7300 
 
 225 
 
 
 
 
 
?o / ?f uf / uo Oxidizer Fuel 
  YO2 YHe YH2 YAr 
16 3 1 0 1 0 
15 3 0.997 0.003 0.997 0.003 
14 3 0.993 0.007 0.993 0.007 
13 3 0.988 0.012 0.988 0.012 
12 3 0.983 0.017 0.983 0.017 
11 3 0.978 0.022 0.978 0.022 
10 3 0.971 0.029 0.971 0.029 
9 3 0.962 0.038 0.962 0.038 
8 3 0.952 0.048 0.952 0.048 
7 3 0.939 0.061 0.939 0.061 
6 3 0.922 0.078 0.922 0.078 
5 3 0.899 0.101 0.899 0.101 
4 3 0.867 0.134 0.867 0.134 
3 3 0.817 0.183 0.817 0.183 
2 3 0.731 0.27 0.731 0.27 
1 3 0.545 0.455 0.545 0.455 
 
 
Table 7.2.  Test conditions for the density ratio variation experiments. 
 
 
 
 
 
 
 
 
 
 
 
 226 
 
 
 
Table 7.3. Test conditions for the reversal of density gradient 
experiments. 
 
 
 
  Table 7.4.  Test conditions for change in flame heat release 
experiments. 
 
 
 
Case ?o / ?f uf / uo Jo/Jf ?o ?f uo uf Jo Jf 
    (kg/m3) (kg/m3) (m/s) (m/s) (kg.m/s2) (kg.m/s2) 
1 7.99 5.27 0.86 1.3 0.163 4.47 23.57 0.0047 0.0055 
2 2.0 3.0 0.67 0.99 0.50 4.5 13.5 0.0036 0.0055 
 
Table 7.5. Test conditions for variation in jet momentum experiments. 
 
 
                                                 
? Baseline Case could be either H2+Ar ? O2+He ? H2+Ar or H2+He ? O2+Ar ? H2+He. 
Configuration Velocity  Mass Flow  Re 
 (m/s) (kg/s)  
 O2 H2 O2 H2 O2 H2 
H2-O2-H2 6 18 1.425E-3 1.825E-4 3700,4900,7300 1100,1300,1600 
 O2/N2 H2 O2/N2 H2 O2/N2 H2 
O2/N2-H2-O2/N2 17.8 5 2.603E-3 7.603 E-5 7320,8783,10980 450,600,900 
Configuration Velocity  Density Ratio Heat  Release Forcing 
 (m/s)  (kW)  
 Center Co-Flow    
Baseline? 4.5 13.5 7.0 or 15.2 15 Unforced 
H2+Ar ? O2+He ? H2+Ar 4.5 13.5 7.0 15 Forced, 1150Hz 
H2+He ? O2+Ar ? H2+He 4.5 13.5 15.2 15 Forced, 1150Hz 
 
 227 
 
Flow Conditions A D 
Density Ratio (?o/??f) 14.5 3 
O2 flow rate (g/s) 1.06 1.06 
Velocity (m/s) 4.5 4.5 
Oxygen 
Reynolds number 5500 5500 
H2 flow rate (g/s) 0.125 0.018 
CH4 flow rate (g/s) 0.015 0.231 
H2 mole fraction 98.53% 37.41% 
CH4 mole fraction 1.47% 62.59% 
 
 
Fuel 
Velocity (m/s) 13.0 4.6 
Velocity Ratio (uf/uo) 2.9 1.0 
Rate of Heat Release (kW) 15.9 13.8 
 
Table 7.6. Flow conditions for the simultaneous measurement of 
pressure and chemiluminescence oscillations. 
 
 
 
 
Case ?o / ?f uf / uo Jo/Jf ?o ?f uo uf Jo Jf 
    (kg/ m3) (kg/ m3) (m/s) (m/s) (kg.m/ s2) (kg.m/ s2) 
1 7.99 3.02 2.62 1.3 0.163 4.47 13.50 0.0047 0.0018 
2 7.99 3.36 2.12 1.3 0.163 4.47 15.03 0.0047 0.0022 
3 7.99 3.64 1.80 1.3 0.163 4.47 16.28 0.0047 0.0026 
4 7.99 4.01 1.49 1.3 0.163 4.47 17.91 0.0047 0.0032 
5 7.99 4.51 1.18 1.3 0.163 4.47 20.17 0.0047 0.0040 
6 7.99 5.03 0.94 1.3 0.163 4.47 22.50 0.0047 0.0050 
7 7.99 5.27 0.86 1.3 0.163 4.47 23.57 0.0047 0.0055 
 
Table 7.7.  Test conditions for velocity ratio experiments. 
 
 
 
 
 228 
 
 
 
 
 
 
Case ?o / ?f uf / uo Jo / Jf ?o ?f uo uf Jo Jf 
    (kg/m3) (kg/m3) (m/s) (m/s) (kg.m/s2) (kg.m/s2) 
1 6.0 3.0 1.99 1.21 0.20 4.5 13.5 0.0045 0.0022 
2 5.0 3.0 1.67 1.18 0.24 4.5 13.5 0.0044 0.0026 
3 4.0 3.0 1.33 1.15 0.29 4.5 13.5 0.0042 0.0032 
4 3.0 3.0 1.00 1.09 0.36 4.5 13.5 0.0040 0.0040 
5 2.0 3.0 0.67 0.99 0.50 4.5 13.5 0.0036 0.0055 
 
Table 7.8. Test conditions for variation in jet momentum through 
variation in jet densities. 
 
 
 
 
 
Case ?o / ?f uf / uo Jo/Jf ?o ?f uo uf Jo Jf 
    (kg/m3) (kg/m3) (m/s) (m/s) (kg.m/s2) (kg.m/s2) 
1 7.99 3.36 2.12 1.3 0.163 4.47 15.03 0.0047 0.0022 
2 7.99 3.64 1.80 1.3 0.163 4.47 16.28 0.0047 0.0026 
3 7.99 4.01 1.49 1.3 0.163 4.47 17.91 0.0047 0.0032 
4 7.99 4.51 1.18 1.3 0.163 4.47 20.17 0.0047 0.0040 
5 7.99 5.27 0.86 1.3 0.163 4.47 23.57 0.0047 0.0055 
 
Table 7.9. Test conditions for variation in jet momentum through 
variation in jet velocities. 
 
 
 
 
 
 
 
 
 
 
 229 
 
 
 
 
 
 
 
 
 
 
 
 
Case YCH4 YH2 ?o  / ?f uf / uo uo uf Heat Release ?f ?o 
     (m/s) (m/s) (kW) (kg/m3) (kg/m3) 
1 0.4 0.6 6 3 4.5 13.5 12.8 0.222 1.33 
2 0.5 0.5 6 3 4.5 13.5 11.2 0.227 1.36 
3 0.6 0.4 6 3 4.5 13.5 10.2 0.231 1.38 
4 0.7 0.3 6 3 4.5 13.5 9.53 0.233 1.40 
5 0.8 0.2 6 3 4.5 13.5 9.02 0.235 1.41 
6 0.9 0.1 6 3 4.5 13.5 8.62 0.236 1.42 
 
Table 7.10.  Test conditions for flame-acoustic experiments using 
GH2-GCH4 blended fuel and Oxygen. 
 
 
 230 
 
Appendix C: Gas Properties 
 
 
Gas     
 ? MW ? Q 
  (gm/mole) (kg/m.s) (Joules/Mole) 
Air 1.40 28.94 1.860860611x10E-5 - 
Helium 1.667 4.0026 - - 
Argon 1.667 39.95 - - 
Methane 1.31 16.00 - 814000 
Oxygen 1.40 32.00 2.0497443625x10E-5 - 
Hydrogen 1.41 2.00 8.8459046629x10E-6 242000 
 
 
Ambient Temperature (Ta): 300K 
Ambient Pressure (Pa) : 1 atm 
Universal Gas Constant (Ru) 8.314 (J/K/mole)  
Gas Specific Gas Constant : (Ru / MW) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 231 
 
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