an experimental study of the effect of a pilot flame …

The Pennsylvania State University

The Graduate School

College of Engineering

AN EXPERIMENTAL STUDY OF THE EFFECT OF A PILOT FLAME ON

TECHNICALLY PRE-MIXED, SELF-EXCITED COMBUSTION INSTABILITIES

A Dissertation in

Mechanical Engineering

by

Bridget C. O’Meara

2015 Bridget C. O’Meara

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

December 2015

The dissertation of Bridget C. O’Meara was reviewed and approved* by the following:

Domenic A. Santavicca

Professor of Mechanical Engineering

Dissertation Advisor

Chair of Committee

Richard Yetter


Jacqueline O’Connor

Assistant Professor of Mechanical Engineering

Michael M. Micci

Professor of Aerospace Engineering

Director of Graduate Studies in Aerospace Engineering

Karen A. Thole


Department Head of Mechanical and Nuclear Engineering

*Signatures are on file in the Graduate School

iii

Abstract

Combustion instabilities are a problem facing the gas turbine industry in the

operation of lean, pre-mixed combustors. Secondary flames known as “pilot flames” are a

common passive control strategy for eliminating combustion instabilities in industrial gas

turbines, but the underlying mechanisms responsible for the pilot flame’s stabilizing

effect are not well understood. This dissertation presents an experimental study of a pilot

flame in a single-nozzle, swirl-stabilized, variable length atmospheric combustion test

facility and the effect of the pilot on combustion instabilities.

A variable length combustor tuned the acoustics of the system to excite

instabilities over a range of operating conditions without a pilot flame. The inlet velocity

was varied from 25 – 50 m/s and the equivalence ratio was varied from 0.525 – 0.65. This

range of operating conditions was determined by the operating range of the combustion

test facility. Stability at each operating condition and combustor length was characterized

by measurements of pressure oscillations in the combustor. The effect of the pilot flame

on the magnitude and frequency of combustor stability was then investigated.

The mechanisms responsible for the pilot flame effect were studied using

chemiluminescence flame images of both stable and unstable flames. Stable flame

structure was investigated using stable flame images of CH* chemiluminescence

emission. The effect of the pilot on stable flame metrics such as flame length, flame

angle, and flame width was investigated. In addition, a new flame metric, flame base

distance, was defined to characterize the effect of the pilot flame on stable flame

anchoring of the flame base to the centerbody. The effect of the pilot flame on flame base

iv

anchoring was investigated because the improved stability with a pilot flame is usually

attributed to improved flame anchoring through the recirculation of hot products from the

pilot to the main flame base.

Chemiluminescence images of unstable flames were used to identify several

instability mechanisms and infer how these mechanisms are affected by the pilot flame.

Flame images of cases in which the pilot flame did not eliminate the instability were

investigated to understand why the pilot flame is not effective in certain cases. The phase

of unstable pilot flame oscillations was investigated to determine how the phase of pilot

flame oscillations may affect its ability to interfere with instability mechanisms in the

main flame.

A forced flame response study was conducted to determine the effect of inlet

velocity oscillation amplitude on the pilot flame. The flame response was characterized

by measurements of velocity oscillations in the injector and chemiluminescence intensity

oscillations determined from flame images. As the forcing amplitude increases, the pilot

flame’s effect on the flame transfer function magnitude becomes weaker. Flame images

show that as the forcing amplitude increases, the pilot flame oscillations increase, leading

to an ineffective pilot. The results of the flame response portion of this study highlight the

effect of instability amplitude on the ability of a pilot flame to eliminate a combustion

instability.

v

Table of Contents

List of Figures ............................................................................................................................... viii

List of Tables ................................................................................................................................ xiv

List of Symbols .............................................................................................................................. xv

Acknowledgements ...................................................................................................................... xvii

Chapter 1 Introduction ............................................................................................................. 1

1.1 Background ...................................................................................................................... 1

1.2 Types of experimental flame studies ............................................................................... 3

1.2.1 Fully pre-mixed and technically pre-mixed studies ................................................. 4

1.2.2 Self-excited and forced studies ................................................................................ 6

1.3 Instability mechanisms literature review ....................................................................... 10

1.3.1 Fully pre-mixed flame response ............................................................................. 11

1.3.2 Equivalence ratio oscillations and technically pre-mixed flames .......................... 21

1.4 Pilot flame literature review ........................................................................................... 26

1.4.1 Fuel injection considerations ................................................................................. 27

1.4.2 Pilot flames ............................................................................................................ 28

1.5 Objectives for current work ........................................................................................... 38

Chapter 2 Experimental Set Up ............................................................................................. 40

2.1 Combustion test facility ................................................................................................. 40

2.1.1 Overview of test facility ......................................................................................... 40

2.1.2 Inlet Section ........................................................................................................... 41

2.1.3 Injector Section ...................................................................................................... 43

2.1.4 Combustor section ................................................................................................. 45

2.2 Measurements Techniques ............................................................................................. 47

2.2.1 Pressure .................................................................................................................. 47

2.2.2 Velocity .................................................................................................................. 47

2.2.3 Chemiluminescence Intensity ................................................................................ 48

2.2.4 Basic processing of pressure and chemiluminescence measurements ................... 49

2.2.5 Two microphone method ....................................................................................... 51

2.3 Flame Imaging ............................................................................................................... 52

2.3.1 Camera set-up ........................................................................................................ 52

2.3.2 Basic image processing .......................................................................................... 54

2.3.3 Phase averaged image processing .......................................................................... 56

2.3.4 Flame image metrics .............................................................................................. 57

Chapter 3 Combustor stability characteristics ........................................................................ 59

vi

3.1 Experimental test conditions .......................................................................................... 59

3.2 Longitudinal Modes ....................................................................................................... 60

3.3 Combustor Stability ....................................................................................................... 62

3.3.1 Stability map of combustor pressure ...................................................................... 62

3.3.2 Maximum combustor pressure oscillation magnitude and frequency .................... 64

3.3.3 Effect of combustor length on instability frequency .............................................. 67

3.4 Acoustic model of the combustion test facility .............................................................. 67

3.5 Acoustic mode shapes .................................................................................................... 71

3.6 Conclusions .................................................................................................................... 74

Chapter 4 Pilot flame effect on technically pre-mixed, self-excited combustion instabilities

76

4.1 Injector geometry and pilot flame configuration ........................................................... 77

4.2 The effect of pilot flame on self-excited instabilities at various operating conditions .. 78

4.2.1 Defining unstable combustor regions .................................................................... 78

4.2.2 Instability I ............................................................................................................. 81

4.2.3 Instability II ............................................................................................................ 82

4.2.4 Instability III .......................................................................................................... 85

4.2.5 Instability IV .......................................................................................................... 86

4.3 The effect of pilot flame intensity on self-excited instabilities ...................................... 88

4.3.1 Case 1: Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55 .................................................... 88

4.3.2 Case 2: Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60 .................................................... 90

4.4 Role of main flame equivalence ratio on pilot flame effect ........................................... 93

4.4.1 Effect of main flame equivalence ratio on combustor stability ............................. 93

4.4.2 Comparison of stable flame structure .................................................................... 96

4.5 Conclusions .................................................................................................................... 97

Chapter 5 The effect of pilot flame on stable flame structure ................................................ 99

5.1 Comparison of stable flame images without and with a pilot flame ............................ 100

5.2 Effect of pilot flame on flame length and flame angle ................................................. 101

5.3 Effect of pilot flame on flame width ............................................................................ 105

5.4 Effect of pilot flame on flame base location ................................................................ 107

5.4.1 Definition of flame base distance ......................................................................... 107

5.4.2 Example of flame base contours without and with a pilot flame ......................... 110

5.4.3 Choice of flame contour value ............................................................................. 110

5.4.4 Effect of pilot flame on flame base location for all operating conditions ............ 113

5.5 Conclusions .................................................................................................................. 116

Chapter 6 Interaction of the main and pilot flames under unstable conditions .................... 118

6.1 Instability mechanisms ................................................................................................. 118

vii

6.2 Unstable flame images ................................................................................................. 119

6.2.1 Phase averaged flame images for a strong pilot effect case ................................. 119

6.2.2 Phase averaged flame images for a weak pilot effect case .................................. 126

6.3 Effect of pilot fuel injection location on pilot flame oscillations ................................. 132

6.3.1 Details of pilot injector modifications ................................................................. 133

6.3.2 Effect of pilot injection modification on combustor pressure oscillations ........... 134

6.4 Forced flame response ................................................................................................. 136

6.4.1 Comparison of PMT and high speed camera flame transfer function gain .......... 139

6.4.2 Separation of the main flame response and the pilot flame response .................. 140

6.4.3 Main flame transfer function with varying pilot flame intensity and forcing

amplitude ............................................................................................................. 141

6.4.4 Effect of pilot flame on forced instabilities at low forcing amplitudes ................ 142

6.4.5 Effect of pilot flame on forced instabilities at high forcing amplitudes ............... 144

6.4.6 Effect forcing amplitude on pilot flame stability ................................................. 146

6.5 Conclusions .................................................................................................................. 149

Chapter 7 Summary and future work ................................................................................... 150

7.1 Summary ...................................................................................................................... 150

7.2 Recommendations for future work .............................................................................. 154

Appendix A Uncertainty and repeatability of self-excited results ............................................... 157

Appendix B Effect of a perforated plate on self-excited instabilities .......................................... 160

B.1 Technically pre-mixed study perforated plate study ......................................................... 160

B.1.1 Effect of original plate location .................................................................................. 161

B.1.2 Effect of plate open area ............................................................................................. 163

B.1.3 Effect of reduced area plate location .......................................................................... 164

B.2 Fully pre-mixed study perforated plate study .................................................................... 168

References .................................................................................................................................... 172

viii

List of Figures

Figure 1.1: Combustion instability feedback loop ........................................................................... 3

Figure 1.2: Fully pre-mixed portion of the instability feedback loop .............................................. 5

Figure 1.3: Forced flame response portion of the instability feedback loop .................................... 7

Figure 1.4: Pathways for flame response to velocity perturbations [24] ....................................... 11

Figure 1.5: Schematic of a typical flow field in a swirl-stabilized combustor [35] ....................... 16

Figure 1.6: Schematic of a flow field with a central axial jet and annular swirling flow; Adapted

from [59] ........................................................................................................................................ 18

Figure 1.7: Schematic a) V-flame shape and b) M-flame shape. The flame is indicated by the red

lines. The flow direction is from the bottom to the top of the page ............................................... 19

Figure 1.8: (a) Combustor model (b) Illustration of the development of the equivalence ratio

oscillation [8] (Adapted from [82]) ................................................................................................ 22

Figure 1.9: Pathways for flame response to equivalence ratio perturbations [24] ......................... 23

Figure 1.10: Schematic of possible pilot fuel injection configurations ......................................... 29

Figure 1.11: Schematic of fuel nozzle including pilot fuel injection from Snyder et al. ............... 31

Figure 1.12: Example of a catalytic pilot design (Adapted from [59]) .......................................... 32

Figure 1.13: Schematic of pilot passage from [119] ...................................................................... 35

Figure 1.14: Schematic of pilot fuel injection designs used by Lee et al. Location (a) is a single

hole on the axis of the centerbody. Location (b) is an arrangement of 12 evenly spaced holes at a

45 angle around the outer circumference of the centerbody. Location (c) is an arrangement of 12

evenly spaced holes around the circumference of the dump plane. (Adapted from [122]) ........... 37

Figure 2.1: Schematic of test facility; Flow direction is from left to right .................................... 41

Figure 2.2: Top view of the combustion test facility inlet section ................................................. 43

Figure 2.3: Schematic of injector geometry and important features .............................................. 44

Figure 2.4: Cross section of combustor section ............................................................................. 46

Figure 2.5: Examples of initial image processing; a) Background subtracted projection image; b)

Emission image; c) Revolved image. Colors indicate intensity, and are self-scaled for each image.

....................................................................................................................................................... 55

Figure 2.6: Examples revolved a) Mean image; b) RMS fluctuation image; c) Phase image.

Colors bars are shown for each image; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, 0% pilot, Lcomb =

25 in., technically pre-mixed ......................................................................................................... 56

Figure 2.7: Example of a series of phase averaged CH* chemiluminescence flame images......... 57

ix

Figure 2.8: Stable CH* chemiluminescence flame image indicating center of heat release (+),

flame length Lf, flame width Wf, and flame angle α; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, 0%

pilot, technically pre-mixed ........................................................................................................... 57

Figure 3.1: Stability map of combustor pressure oscillations; Tin = 250C, Uin = 45 m/s, ϕoverall =

0.55, 0% pilot, technically pre-mixed ............................................................................................ 63

Figure 3.2: Single sided power spectral density for combustor length Lcomb = 25 in.; Tin = 250C,

Uin = 45 m/s, ϕoverall = 0.55, 0% pilot, technically pre-mixed ......................................................... 64

Figure 3.3: a) Frequency of the maximum pressure oscillation magnitude; b) Comparison of the

peak (solid circles) and total (open squares) RMS pressure oscillation magnitude; c) Ratio of peak

to total RMS pressure oscillations; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525, 0% pilot, technically

pre-mixed ....................................................................................................................................... 66

Figure 3.4: Schematic of the combustion test facility and corresponding duct sections used to

model the acoustics of the system .................................................................................................. 69

Figure 3.5: Comparison of natural frequencies predicted by the acoustic model (dashed lines) and

the measured instability frequencies (‘x’ markers); Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, 0%

pilot, technically pre-mixed ........................................................................................................... 71

Figure 3.6: Mode shapes predicted by acoustic model; a) Mode 1, 167 Hz; b) Mode 2, 457 Hz;

Mode 3, 646 Hz; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, 0% pilot, technically pre-mixed ........ 74

Figure 4.1: Injector schematic indicating the location of main and pilot paths and flames ........... 77

Figure 4.2: a) Peak combustor pressure fluctuations and b) corresponding frequencies ............... 80

Figure 4.3: Instability I combustor pressure oscillations vs a) inlet velocity and b) frequency;.... 82

Figure 4.4: Convective time vs inlet velocity for all operating conditions; Black box indicates

operating conditions at which Instability II occurred; ................................................................... 83

Figure 4.5: Instability II combustor pressure oscillations vs a) inlet velocity and b) frequency; .. 85

Figure 4.6: Instability III combustor pressure oscillations vs a) inlet velocity and b) frequency; . 86

Figure 4.7: Instability IV combustor pressure oscillations vs a) inlet velocity and b) frequency; . 88



Figure 4.10: Peak combustor pressure fluctuations and corresponding frequency for three

combinations of main flame equivalence ratio and pilot flame intensity; Tin = 250C, Uin = 50

m/s, ϕoverall = 0.55; Case 1, Case 2, Case 3 ....................................................................... 95

Figure 4.11: CH* chemiluminescence intensity images of stable flames; Tin = 250C, Uin = 50m/s,

a) ϕmain = 0.514, 6.5% pilot; b) ϕmain = 0.514, 0% pilot .................................................................. 97

Figure 5.1: Comparison of CH* stable flame images (a) without a pilot flame and (b) with 6.5%

pilot flame; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525 ................................................................. 100

x

Figure 5.2: Stable flame center of heat release locations for all operating conditions, Tin = 250C

..................................................................................................................................................... 102

Figure 5.3: Percent change in flame length (change in flame length divided flame length with 0%

pilot) for all operating conditions, Tin = 250C ............................................................................ 104

Figure 5.4: Change in flame angle for all operating conditions, Tin = 250C .............................. 105

Figure 5.5: Stable flame width (Wf) versus flame length (Lf) ..................................................... 106

Figure 5.6: Percent change in flame width (change in flame width divided flame width with 0%

pilot) for all operating conditions, Tin = 250C ............................................................................ 107

Figure 5.7: Stable flame CH* chemiluminescence intensity image with contour of 5% maximum

image intensity; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525, 0% pilot .......................................... 108

Figure 5.8: Comparison of 5% maximum intensity contours without a pilot flame and with 6.5%

pilot flame; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525 ................................................................. 110

Figure 5.9: Varying flame contour values for stable flames a) without and b) with 6.5% pilot

flame; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525 ......................................................................... 112

Figure 5.10: Effect of flame contour value on a) Calculated main flame base distance and b)

relative difference in main flame base distance between unpiloted and 6.5% pilot cases; .......... 113

Figure 5.11: Flame base distance for all operating conditions, Tin = 250C ................................ 115

Figure 5.12: Percent change in flame base distance (change in flame base distance divided flame

base distance with 0% pilot) for all operating conditions, Tin = 250C ....................................... 115

Figure 6.1: Phase averaged CH* chemiluminescence images of an unstable flame with an

instability frequency of 158 Hz. Images are scaled to the overall maximum intensity. ‘+’ symbol

indicates the center of heat release. Outline indicates 5% of maximum image intensity. Operating

conditions: Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, Lcomb = 25 in., 0% pilot .............................. 120

Figure 6.2: Phase averaged CH* chemiluminescence images at a frequency of 167 Hz. Images are

scaled to the overall maximum intensity. ‘+’ symbol indicates the center of heat release. Outline

indicates 5% of maximum image intensity. Operating conditions: Tin = 250C, Uin = 45 m/s, ϕoverall

= 0.55, Lcomb = 25 in., 6.5% pilot .................................................................................................. 123

Figure 6.3: Comparison of the stable flame structure characterized by (a) mean flame position and

(b) flame shape defined by contours 5% of the maximum image intensity. Operating conditions:

Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55; Blue: 0% pilot; Black: 6.5% pilot ................................ 124




conditions: Tin = 250C, Uin = 35 m/s, ϕoverall = 0.55, Lcomb = 27 in., 0% pilot .............................. 127




conditions: Tin = 250C, Uin = 35 m/s, ϕoverall = 0.55, Lcomb = 27 in., 6.5% pilot ........................... 129

xi

Figure 6.6: Example of a CH* chemiluminescence intensity flame image with the flame base

region indicated with a white box and the main flame and pilot flame region divided by a pink

line. .............................................................................................................................................. 130

Figure 6.7: Normalized CH* intensity oscillations from the main flame base and the pilot flame

over a period of instability; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55; 6.5% pilot ........................ 131

Figure 6.8: Phase difference between flame base and pilot flame CH* chemiluminescence

intensity oscillations for operating conditions where the pilot flame did not eliminate a self-

excited instability ......................................................................................................................... 132

Figure 6.9: Redesigned pilot fuel injector indicating Lpilot, the distance from the edge of the pilot

fuel nozzle to the exit of the injector ........................................................................................... 133

Figure 6.10: Effect of the pilot fuel injection location on the magnitude of combustor pressure

oscillations; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55 ................................................................... 136

Figure 6.11: a) Peak combustor pressure fluctuations and b) corresponding inlet velocity

oscillation magnitude; Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60; 0% pilot, 4% pilot, 6.5%

pilot, 8% .................................................................................................................................. 138

Figure 6.12: Comparison of flame transfer function measured by a PMT () and high speed

camera images () ...................................................................................................................... 140

Figure 6.13: Example of a flame image with a dashed line dividing the main flame region from

the pilot flame region ................................................................................................................... 141

Figure 6.14: CH* intensity based flame transfer function gain at various forcing amplitude for

three levels of pilot flame; Operating conditions: Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60,

Frequency = 170 Hz ..................................................................................................................... 142

Figure 6.15: Phase averaged CH* chemiluminescence images of a forced flame; Images are



= 0.60, Forcing Frequency = 170 Hz, Amplitude = 5%, 0% pilot ............................................... 143




= 0.60, Forcing Frequency = 170 Hz, Amplitude = 5%, 6.5% pilot ............................................ 144




= 0.60, Forcing Frequency = 170 Hz, Amplitude = 50%, 0% pilot ............................................. 145




= 0.60, Forcing Frequency = 170 Hz, Amplitude = 50%, 6.5% pilot .......................................... 146

Figure 6.19: Axial location of the pilot flame center of heat release for three forcing amplitudes;

Operating conditions: Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60, Forcing Frequency = 170 Hz; .. 147

xii

Figure 6.20: CH* intensity fluctuations in the pilot flame region for three forcing amplitudes;

Operating conditions: Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60, Forcing Frequency = 170 Hz; .. 148

Figure A.1: Peak combustor pressure fluctuations with error bars indicating two standard

deviations of the mean; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55; 0% pilot, 6.5% pilot ..... 157

Figure A.2: Frequency of peak combustor pressure fluctuation for all eight data sets; Tin = 250C,

Uin = 45 m/s, ϕoverall = 0.55; 0% pilot ........................................................................................... 158

Figure A.3: : Peak combustor pressure fluctuations with error bars indicating two standard

deviations of the mean taken on two different days; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55;

0% pilot, Day 1; 6.5% pilot, Day 1; 0% pilot, Day 2; 6.5% pilot, Day 2; ....................... 159

Figure B.1: Magnitude and frequency of self-excited, technically pre-mixed combustor pressure

fluctuations for all operating conditions with the original perforated plate. ................................ 162

Figure B.2: Stability map showing the effect of perforated plate location on self-excited,

technically pre-mixed instabilities. Operating condition: Tin = 250°C, u = 40 m/s, φ = 0.55,

technically pre-mixed, original plate. Plate Location: Location1, Location 2, Location 3

..................................................................................................................................................... 163

Figure B.3: Stability map showing the effect of perforated plate open area on self-excited,


technically pre-mixed, Location 1 (original location). Plates: Original, Reduced area ...... 164

Figure B.4: Stability map showing the effect of plate location self-excited, technically pre-mixed

instabilities with the reduced area plate. Operating condition: Tin = 250°C, u = 40 m/s, φ = 0.55,

technically pre-mixed, reduced area plate. Plate Locations: Location1, Location 2,

Location 3 .................................................................................................................................... 165

Figure B.5: Stability map for a case where moving the perforated plate upstream increases the

magnitude of a self-excited, technically pre-mixed instability. Operating condition: Tin = 250°C,

u = 40 m/s, φ = 0.60, technically pre-mixed, reduced area plate. Plate Locations: Location1,

Location 2, Location 3............................................................................................................. 166

Figure B.6: Natural frequency mode shape predicted for Tin = 250°C, u = 40 m/s, φ = 0.55, Lcomb

= 41in. .......................................................................................................................................... 167

Figure B.7: Natural frequency mode shape predicted for Tin = 250°C, Uin = 40 m/s, φ = 0.60,

Lcomb = 32in. ................................................................................................................................. 167

Figure B.8 Stability map showing the effect of plate location self-excited, fully pre-mixed

instabilities with the reduced area plate. Operating condition: Tin = 250°C, Uin = 35 m/s, φ = 0.60,

fully pre-mixed, reduced area plate. Plate Locations: Location1, Location 2, Location 3

..................................................................................................................................................... 169

Figure B.9: Magnitude and frequency of self-excited, fully pre-mixed combustor pressure

fluctuations for all operating conditions with the reduced area perforated plate. Plate Locations:

Location1, Location 2, Location 3 ................................................................................. 170

xiii

Figure B.10: Effect of perforated plate location on the phasing. a) Phase difference between heat

release rate and velocity fluctuations; b) Phase difference between velocity and pressure

fluctuations; c) Phase difference between pressure and heat release rate fluctuations. Operating

condition: Tin = 250°C, Uin = 35 m/s, φ = 0.60, fully pre-mixed, reduced area plate. Plate

Locations: Location1, Location 2, Location 3 ............................................................... 171

xiv

List of Tables

Table 1.1: Summary of passive pilot flame studies ....................................................................... 29

Table 3.1: Summary of self-excited, technically pre-mixed operating conditions ........................ 60

Table 6.1: List of operating conditions in from Figure 6.8 .......................................................... 132

xv

List of Symbols

A = Forcing amplitude u′ u̅⁄ or Area

c = Speed of sound

cp = Specific heat at constant pressure

cv = Specific heat at constant volume

D = Diameter

f = Frequency [Hz]

fs = Sampling rate [1/s]

fst = Stoichiometric fuel air ratio

FPM = Fully pre-mixed

FTF = Flame transfer function

Gxx = Single sided power spectral density (SSPSD)

HR = Heat of reaction

i = Index variables

j = Imaginary unit (√−1 )

I = Chemiluminescence intensity

Im = Imaginary part of complex number

J = Bessel function

k = Wave number

L = Length [in.]

m = Index of frequency domain or Mass

Ma = Mach number

MW = Molecular weight

n = Index of time domain

N = Number of samples

NOx = Nitrogen oxides

p = Pressure [Pa]

q, Q = Heat release

r, R = Radius

Re = Real part of complex number

Ru = Universal gas constant

S = Cross sectional area

SL = Laminar flame speed

Sw = Swirl number

t, τ = Time [s]

T = Temperature [°C] or Period [s]

TMM = Two microphone method

TPM = Technically pre-mixed

U = Axial velocity [m/s]

V = Volume

W = Width

x = Axial coordinate or Time domain signal or Mole fraction

xvi

X = Linear spectrum

Z = Acoustic impedance

Greek Letters

α = Flame angle [°]

γ = Specific heat ratio

ε = Image intensity

Δ = Difference

φ = Equivalence ratio

λ = Wavelength

θ = Phase angle [°]

ρ = Density [kg/m3]

ω = Angular frequency [rad/s]

Subscripts

co = Cutoff

CoHR = Center of heat release

comb = Combustor

conv = Convective

ds = Downstream

exp = Exposure

f = Flame

fb = Flame base

in = Inlet

main = Main flame only

mean = Mean quantity

mix = Air/fuel mixture quantity

overall = Main and pilot

peak = Peak quantity

pilot = Pilot flame only

us = Upstream

Superscripts

* = Excited species

( )′ = Fluctuating quantity

( )̅̅ ̅̅ ̅ = Average quantity

( )̇ = Rate

( )̂ = Complex quantity

xvii

Acknowledgements

I would like to thank my advisor, Dr. Domenic Santavicca, for his guidance and

support during my graduate studies. Many thanks also to my doctoral committee, Dr.

Jacqueline O’Connor, Dr. Richard Yetter, and Dr. Michael Micci.

The research presented in this dissertation was supported by Solar Turbines. I

would like to thank in particular James Blust for his mentorship while I interned with

Solar Turbines, and for his support and insights.

Several people’s assistance has been invaluable in completing my graduate

research. Dr. Bryan Quay designed the combustion test facility. Larry Horner fabricated

the test facility. Dr. Stephen Peluso patiently shared his knowledge and experience from

working with this test facility before me. I appreciate all of his help and advice on

technical problems and research questions. Thank you to all the past and current graduate

students in the Turbulent Combustion Lab, Alex Borsuk, Dr. Nicholas Bunce, Dr. Alex

De Rosa, Jihang Li, Dr. Poravee Orawannukul, Janith Samarasinghe, and Dr. Michael

Szedlmayer, for their support, advice, and friendship. Thank you also to Sally Mills and

Mary Newby.

Finally, I would like to thank my friends and family. In particular, thank you to

my mom and dad, my brother Will, my sister-in-law Yuxiao, and my nephew Colin for

providing the happiness and comfort that only family can. Thank you Dave, for being

there on all the good and bad days.

1

Chapter 1

Introduction

1.1 Background

Nitrogen oxide, or NOx, is a pollutant that contributes to smog and acid rain, and

is therefore subject to strict emissions regulations [1]. Most land based gas turbines burn

natural gas, generating nitrogen oxides as a product of combustion. The majority of NOx

from natural gas combustion is produced through the following reactions [2]:

𝑂 + 𝑁2 ↔ 𝑁𝑂 + 𝑁

𝑁 + 𝑂2 ↔ 𝑁𝑂 + 𝑂

𝑁 + 𝑂𝐻 ↔ 𝑁𝑂 + 𝐻

NOx produced by these reactions is referred to as “thermal” NOx because the reactions

occur at high temperatures. The best way to reduce NOx emissions is to operate at low

temperatures to inhibit thermal NOx production. Diffusion flame combustors, which were

once widely used, are very stable, but the high temperatures associated with diffusion

flames resulted in unacceptably high NOx levels. Methods of reducing diffusion flame

temperatures, such as water injection could meet initial NOx emissions targets of 100

ppm, but recently even stricter regulations made lean pre-mixed combustion necessary

[3]. Unfortunately, while modern lean pre-mixed combustors have very low emissions,

they are susceptible to high amplitude pressure fluctuations known as combustion

instabilities. Instabilities are undesirable because they can lower the efficiency of the

system, cause flame blowout and flashback, and produce vibrations that can damage the

system components [4].

2

Combustion instabilities occur more often in lean pre-mixed systems than in

traditional diffusion systems for two main reasons. First, they operate close to the lean

blowout limit where small perturbations may produce large responses [5]. In addition,

diffusion style combustors use film cooled liners that inject air through perforated liners

to lower the temperature of the exhaust gas entering the turbine. This type of cooling

system has the beneficial side effect of damping out acoustic disturbances. Lean pre-

mixed combustors operate at much lower temperatures, so less dilution air is used and the

damping effect is not significant [6].

Understanding the mechanisms that cause instabilities is important for designing

combustors. Rayleigh's criterion states that in order for an instability to occur, pressure

and heat release rate fluctuations must be in phase (within 90) [7]. While Rayleigh's

criterion is necessary for an instability, it does not completely describe the conditions at

which instabilities occurs. In order for an instability to grow, more energy must be added

to the system than is dissipated or transferred across system boundaries. Dissipation

includes mechanisms such as viscous dissipation at the combustor walls and radiation

from inflow and outflow [8]. This is expressed mathematically in Equation (1.1) [9]. In

this equation, 𝑝′(𝑥, 𝑡), 𝑞′(𝑥, 𝑡), V, T, and Li represent combustor pressure oscillations,

heat release oscillations, combustor volume, the period of oscillation, and acoustic energy

loss mechanisms, respectively.

∬ 𝒑′(𝒙, 𝒕)𝒒′(𝒙, 𝒕)

𝑽𝑻

𝒅𝒕𝒅𝑽 ≥ ∬ ∑ 𝑳𝒊

𝒊

(𝒙, 𝒕)𝒅𝒕𝒅𝑽

𝑽𝑻

(1.1)

Energy is added to the system via a feedback loop illustrated in Figure 1.1. When

the heat release peak occurs in phase with pressure, the expansion of hot gases performs

3

work on the system, and the pressure oscillations grow [9]. The energy density associated

with combustion is large compared to the energy required to drive a pressure oscillation,

so only a small fraction of the total energy available in the system is necessary to drive

the instability [8]. The pressure oscillations then propagate upstream and perturb the flow

rates of air and fuel. Unsteady air flow rates produce velocity fluctuations, and both

unsteady air and fuel flow rates produce equivalence ratio fluctuations Velocity

fluctuations and equivalence ratio fluctuations affect heat release rate through various

flame response mechanisms which will be discussed later in this chapter.

Figure 1.1: Combustion instability feedback loop

1.2 Types of experimental flame studies

Experimental studies of lean, pre-mixed flames can be categorized in different

ways. One category is based on how air and fuel are mixed. If air and fuel are mixed far

upstream of a choke plate to ensure a spatially and temporally uniform mixture, the flame

is considered “fully pre-mixed”. If fuel is injected further downstream, allowing the

possibility of equivalence ratio oscillations as well as velocity oscillations, the flame is

“technically pre-mixed”. In the literature, fully pre-mixed may also be referred to as pre-

4

mixed or perfectly pre-mixed, and technically pre-mixed may be referred to as practically

or partially pre-mixed.

Another way of categorizing flame studies is based on how the flame is perturbed.

In self-excited studies, the feedback loop from Figure 1.1 sustains the instability. In a

forced flame experiment, a velocity or equivalence ratio disturbance is imposed at a

specific forcing amplitude and frequency on an otherwise stable flame.

While the current study focuses on technically pre-mixed, self-excited

experiments, much of the literature in the field of combustion instabilities focuses on

fully pre-mixed and forced flame response studies. These fully pre-mixed and forced

experiments are simplifications of the instability feedback loop from Figure 1.1, but the

results are still useful for understanding the more complicated technically pre-mixed and

self-excited cases. Therefore this literature review will include fully pre-mixed and forced

studies as well as technically pre-mixed and self-excited studies. The remainder of

Section 1.2 discusses fully and technically pre-mixed flames, and forced and self-excited

studies in greater detail in order to understand the similarities and differences between

each type of study and some of the benefits and limitations of each.

1.2.1 Fully pre-mixed and technically pre-mixed studies

Fully pre-mixed studies eliminate equivalence ratio oscillations a by mixing the

air and fuel far upstream of the injector to ensure a uniform air/fuel mixture. A choke

plate prevents pressure fluctuations from propagating upstream and modulating the flow

rates of air and fuel at the fuel injection location. The mixture that enters the combustor is

uniform both spatially and temporally. Fully pre-mixed studies simplify the feedback

5

loop shown in Figure 1.1 by eliminating equivalence ratio fluctuations. This simplified

feedback loop is shown in Figure 1.2.

Figure 1.2: Fully pre-mixed portion of the instability feedback loop

Many studies have been performed on fully pre-mixed flames because the

absence of equivalence ratio makes this type of flame relatively straightforward to study.

Only velocity perturbations are present, so the flame response can be traced back to

velocity oscillation mechanisms. Heat release from the flame is also easier to study in

fully pre-mixed flames than in technically pre-mixed flames for reasons that are

discussed in greater detail in Section 1.2.2. Fully pre-mixed flame studies have been

critical in identifying mechanisms that control the flame response to velocity

perturbations. However, while fully pre-mixed experiments provide valuable insights into

flame response mechanisms, a constant equivalence ratio mixture is not realistic for

actual combustors.

In industrial combustors, fuel is injected near the swirler, and the air and fuel mix

over a short distance before entering the combustion chamber. This type of fuel air

mixture is referred to as technically pre-mixed. Unlike fully pre-mixed flames,

technically pre-mixed flames are subject to equivalence ratio fluctuations as well as

6

velocity fluctuations. Equivalence ratio fluctuations arise from either fluctuations in fuel

flow rate or in air flow rate at the fuel injection location. The presence of equivalence

ratio fluctuations makes the analysis of technically pre-mixed flames more complicated,

and fewer studies have addressed combustion instabilities in flames with both

equivalence ratio oscillations and velocity oscillations present.

1.2.2 Self-excited and forced studies

In industrial gas turbines, combustion instabilities occur due to the feedback loop

shown in Figure 1.1. Unsteady heat release from the flame couples with the acoustic of

the system and unsteady flow to sustain an instability [4, 10]. Experimental studies of

self-excited instabilities are designed to study this phenomenon in a laboratory setting. In

self-excited experiments, naturally occurring unstable modes of the combustor are

excited, and the feedback loop discussed above sustains an instability.

The experimental study of self-excited instabilities is important because this type

of experiment reflects how combustion instabilities actually occur. However, self-excited

instabilities can be difficult to study for several reasons. Instability mechanisms can be

difficult to identify because the steps of the feedback loop are coupled. In addition, the

instability amplitude and frequency cannot be controlled. Many studies simplify the

problem and allow systematic variation of forcing frequency and amplitude by focusing

on the section of the feedback loop where velocity and/or equivalence ratio fluctuations

cause fluctuations in heat release rate. Figure 1.3 shows the simplified feedback loop

investigated in forced flame response studies.

7

Figure 1.3: Forced flame response portion of the instability feedback loop

In these forced flame response studies, large pressure fluctuations are eliminated

by operating at stable conditions that do not excite resonant modes. The frequency and

amplitude of the velocity or equivalence ratio disturbance can be systematically varied

with a device such as a loudspeaker or a siren, and the response of the flame to these

specific disturbance inputs can be investigated.

Forced flame response studies characterize the response of the flame to the

imposed disturbance in terms of a flame transfer function [11, 12]. Understanding the

concept of a flame transfer function is necessary for understanding the literature on

forced flame response. A flame transfer function relates heat release rate fluctuations to

velocity or equivalence ratio fluctuations. Equations (1.2) and (1.3) show the equations

for velocity and equivalence ratio flame transfer functions:

𝐹𝑇𝐹𝑢(𝑓, 𝐴) =

�̇�′(𝑓) �̅̇�⁄

𝑢′(𝑓) �̅�⁄ (1.2)

𝐹𝑇𝐹𝜑(𝑓, 𝐴) =

�̇�′(𝑓) �̅̇�⁄

𝜑′(𝑓) �̅�⁄

(1.3)

where u, φ, �̇�, f, and A are the velocity, equivalence ratio, heat release rate, forcing

frequency, and forcing amplitude respectively. The prime symbol denotes a fluctuating

8

quantity and the overbar represents a mean quantity. The flame transfer function is a

complex quantity, with both a magnitude and phase. The magnitude is called the gain,

and it represents whether the flame amplifies or damps a disturbance. The phase indicates

the time lag between the imposed disturbance and the heat release fluctuation.

Peluso et al. demonstrated that at a particular operating condition and frequency,

the fully pre-mixed flame response for forced and self-excited flames are the same [13],

suggesting that results of forced flame response studies are applicable to understanding

combustion instabilities in actual gas turbines. Flame transfer functions can be measured

experimentally or computationally [14], and are useful in predicting instabilities using a

simple linear acoustic model [14, 15]. Flame response studies have been used in multi-

nozzle test facilities as well as single nozzle test facilities [16, 17].

In order to experimentally determine the flame transfer function, heat release rate

fluctuations must be measured. Heat release rate fluctuations are commonly determined

using global chemiluminescence intensity measurements. Experimental studies have

shown that for a fixed equivalence ratio, inlet temperature, and air flow rate the

chemiluminescence intensity increases linearly as fuel flow rate increases [18, 19]. The

fuel flow rate determines the heat release rate, so chemiluminescence intensity is linearly

related to heat release rate. However, the slope of that line increases with increasing

equivalence ratio. Equivalence ratio was been shown to be exponentially related to

chemiluminescence intensity [19], leading to the following expression [10]:

𝐼 = 𝑘�̇�𝑎𝑖𝑟𝜑𝛼𝑝𝛽 (1.4)

where �̇�𝑎𝑖𝑟 is the mass flow rate of the mixture flowing through the injector, and k, 𝛼,

and 𝛽 are constants. An equation for heat release oscillations can be derived from the

definition of heat release rate.

9

�̇� = �̇�𝑓𝑢𝑒𝑙𝐻𝑅 (1.5)

where �̇�𝑓𝑢𝑒𝑙 is the mass flow rate of fuel, and 𝐻𝑅 is the heat of reaction. Substituting for

�̇�𝑓from the definition of equivalence ratio yields:

�̇� = 𝑓𝑠𝑡�̇�𝑎𝑖𝑟𝜑𝐻𝑅 (1.6)

where 𝑓𝑠𝑡 is the stoichiometric fuel air ratio. Linearizing Equations (1.4) and (1.6) leads

to the following expression for the normalized fluctuating chemiluminescence intensity

and heat release:

𝐼′

𝐼 ̅=

𝑚′̇𝑎𝑖𝑟

�̇�𝑎𝑖𝑟̅̅ ̅̅ ̅̅

+ 𝛼𝜑′

�̅�

(1.7)

�̇�′

�̅̇�=

𝑚′̇𝑎𝑖𝑟

�̇�𝑎𝑖𝑟+

𝜑′

�̅�

(1.8)

Pressure terms were neglected because they are relatively small compared to other terms.

The relationship between chemiluminescence intensity and heat release rate

shows an important difference between fully pre-mixed and technically pre-mixed

flames. For fully pre-mixed flames, equivalence ratio fluctuations, 𝜑′, are zero and

fluctuating intensity and heat release rate terms are equal. Normalized

chemiluminescence intensity can then be used as a direct measure of normalized global

heat release rate. Balachandran et al. compared various methods for measuring heat

release in fully pre-mixed flames. These methods were global OH* and CH* emission

measurements, two-dimensional phase-synchronized OH* images, flame surface density

from OH* planar laser-induced fluorescence (PLIF), and local heat release rate from

simultaneous OH and CH2O PLIF. These methods all showed similar results, indicating

10

that global chemiluminescence intensity measurements are an acceptable method for

determining fully pre-mixed global flame transfer functions [20].

In the absence of air mass flow rate oscillations (i.e. no inlet velocity oscillations),

equivalence ratio oscillations are caused by the oscillating fuel flow rate only, and heat

release rate is related to chemiluminescence intensity by the constant 𝛼 which is

determined from a steady state calibration. For technically pre-mixed flames, both

velocity and equivalence ratio fluctuations are present. Heat release rate cannot be

measured directly from chemiluminescence, but some methods have been proposed to

overcome this problem. These methods will be discussed when technically pre-mixed

studies are reviewed in Section 1.3.2.

1.3 Instability mechanisms literature review

Now that the concepts of fully pre-mixed, technically pre-mixed, forced, and self-

excited flames have been introduced, a literature review involving these types of

experiments will be presented. The following literature review focuses on studies of

turbulent, swirl-stabilized flames similar to the type of flame that will be investigated in

the current study. However, some studies of laminar flames and simple combustor

geometries will be discussed in cases where they provide relevant background

information. The first section focuses on fully pre-mixed flames to introduce flame

response mechanisms associated with velocity oscillations. The second section discusses

both flame response to equivalence ratio fluctuations only, and flame response to both

velocity and equivalence ratio fluctuations in technically pre-mixed flames. Both forced

flame response and self-excited studies will be included in this literature review.

11

1.3.1 Fully pre-mixed flame response

Heat release rate in laminar flames is related to the unburned mixture density, 𝜌𝑢,

flame speed, 𝑆𝐿, flame surface area, 𝐴𝑓, and heat of reaction per unit mass of unburned

mixture, ∆ℎ𝑅 by the following equation [21, 22]:

�̇� = 𝜌𝑢𝑆𝐿𝐴𝑓∆ℎ𝑅 (1.9)

This relationship comes from the definition of heat release rate. Pressure

fluctuations are generally small, so the density of the unburned mixture is approximately

constant. If equivalence ratio is constant, as it is in the fully pre-mixed case, flame speed

and heat of reaction per unit mass are also constant. That leaves flame area as the only

pathway through which velocity fluctuations can affect heat release rate in a fully pre-

mixed flame. This is shown schematically in Figure 1.4. Variations in flame area may be

caused by large-scale coherent structures or, in turbulent pre-mixed flames, small-scale

turbulent eddies [23].

Figure 1.4: Pathways for flame response to velocity perturbations [24]

Fully pre-mixed flames have been studied extensively and important flame

response mechanisms have been identified and reviewed [4, 23, 25]. For single, turbulent,

fully pre-mixed flames, these mechanisms include vortex shedding, swirl number

fluctuations, and the interactions between these two mechanisms. Flame structure also

influences flame response. These mechanisms will be discussed in further detail in the

following sections.

12

1.3.1.1 Vortex Shedding

The effects of large-scale coherent structures on combustion dynamics have been

studied from as early as the 1970s [26]. Vortices are generated in the shear layer of the

flow [27]. When velocity fluctuations at the exit of the injector reach a maximum, a

vortex is shed and it convects downstream [28, 29]. Usually, vortex shedding is related to

the Kelvin Helmholtz instability, but when the flow is forced by either a resonant

acoustic frequency of the combustor or by an external source, much larger vortices can be

produced at the instability frequency [30].

As the vortex moves downstream, it interacts with the flame and produces

fluctuations in heat release. This phenomenon is known as flame-vortex interaction. The

flame can wrap around vortical structures which distorts the flame and produces

fluctuations in flame surface area. Variations in flame surface area then lead to

fluctuations in heat release rate [9]. Vortices also entrain fresh reactants and hot

combustion products and convect them downstream. After a time delay, the vortex

interacts with the combustor wall or another vortex. The reactants contained within the

vortex ignite, causing increased heat release [4].

Although the presence of vortex shedding has been known for quite some time,

the effects of flame-vortex interactions continue to be of interest in current combustion

dynamics studies. For example, a recent experimental study by Lee et al. observed flame-

vortex interactions in fully pre-mixed, self-excited instabilities in the nonlinear regime

[31]. They found that the mode of the instability was strongly dependent on the

convection time of the vortex, i.e. the time for the vortex to convect from the dump plane

to the center of heat release.

13

1.3.1.2 Swirl Number Fluctuations

Swirlers are a common feature of lean pre-mixed gas turbines. They create a

region of high mixing of the fuel/air mixture, and they help to stabilize the flame. The

swirling flow creates a region of recirculating flow at the center of the combustor that

carries combustion products from the combustion zone of the flame back to the base of

the flame, which increases flame stability [27]. The swirl number S is defined as the ratio

of the axial flux of swirl momentum to the axial flux of axial momentum times a

characteristic radius. Neglecting pressure in the axial momentum term results in Equation

(1.10) for swirl number [32]:

𝑆𝑤 =∫ 𝑢𝑧𝑢𝜃𝑟2𝑑𝑟

𝑅

0

𝑅 ∫ 𝑢𝑧2𝑟𝑑𝑟

𝑅

0

(1.10)

Both axial and azimuthal velocity fluctuations can lead to swirl number fluctuations.

Swirl number fluctuations then cause the flame angle to fluctuate, producing heat release

fluctuations.

Pailes et al. proposed that destructive and constructive interference between

vortex roll-up near the tip of the flame and flame angle fluctuations at the base of the

flame causes the gain minimum and maximum in a flame transfer function [33]. Bunce et

al. found that analysis was sensitive to the choice of upstream and downstream

interrogation windows. An alternative mechanism was suggested in which the gain

minimum occurs when the flame angle fluctuates and damps vortices shed in the shear

layer. When the gain maximum occurs, the flame angle does not fluctuate and therefore

the vortices are not damped [34].

14

1.3.1.3 Flow Structure

Typical combustor flow field

The flow field of a turbulent, swirl-stabilized combustor with a center body has

been studied extensively, and important features of the flame structure have been

identified [23, 35]. Figure 1.5 illustrates an example of important flow field regions in a

typical single nozzle combustor. Regions (1) and (2) are recirculation zones which are

regions where the flow is directed upstream. The reverse flows from the recirculation

zones help to stabilize the flame by carrying hot products to the base of the flame. These

hot products mix with incoming reactants to provide heat and radicals promote

combustion [2, 36–38].

The recirculation zone indicated by Region (1) is called the outer recirculation

zone (ORZ). It forms as a result of a sudden expansion when the flow enters the

combustor. When the flow expands into the combustor, the shear layer separates and

impinges on the wall downstream in what is known as the reattachment zone. An adverse

pressure gradient directs some flow upstream to produce a corner recirculation zone [39].

Heat transfer across the combustor wall will cool the hot gases in the outer recirculation

zone, which influences the stabilization of the flame in the outer shear layer [40–42].

Region (2) is the inner recirculation zone (IRZ). It is caused by vortex breakdown

in a swirling flow and is therefore also referred to as the “vortex breakdown bubble.” A

vortex breakdown bubble is characterized by a stagnation point at the leading edge of the

vortex breakdown bubble and a region of reverse flow [43]. Vortex breakdown occurs

due to the conversion of axial and radial vorticity to negative azimuthal vorticity [44, 45].

Vortex breakdown has been studied extensively by several authors [43, 44, 46–53].

15

The size, shape, and location of the vortex breakdown bubble can be affected by

combustion instabilities, particularly for high amplitudes and for frequencies below the

natural frequency of the vortex bubble, conditions at which lock-in occurs [54]. In certain

combustor configurations, the flame stabilizes at the vortex breakdown stagnation point,

and, under certain forcing conditions, the vortex breakdown bubble oscillates causing the

flame to oscillate as well [55]. Time averaged velocity fields also show evidence of

change in the vortex breakdown under large amplitude oscillations as compared to under

stable conditions [56]. In addition, the phase averaged vortex breakdown structure varies

over an instability period [56, 57].

Region (3) indicates the high speed jet that enters the combustor. Region (4)

shows the shear layers that divide the jet from the recirculation zones. These shear layers

form as a result of the large velocity difference between the high speed jet and the

ambient fluid in the combustor. Large velocity gradients exist in the shear layers. The

flame stabilizes in the low velocity regions of the shear layer where the local flow

velocity is similar to the flame speed [2, 58]. As mentioned in the previous section on

vortex shedding, the shear layers are the regions responsible for vortex shedding. Shear

layers respond strongly to harmonic excitations. Acoustic waves excite the shear layer

disturbance which then excite the flame [45].

16

Figure 1.5: Schematic of a typical flow field in a swirl-stabilized combustor [35]

Flow field with coaxial inlet flow

In the present study, a pilot flame is injected along the centerline of the

combustor. The axial jet of reactants and their subsequent combustion will likely produce

a flow structure within the combustor that is different from the typical swirl stabilized

combustor flow field discussed above. Many studies have investigated the effect of

coaxial flow on combustion and shown that the presence of a central jet can alter the

associated combustor flow field.

In non-premixed flames, fuel is often injected through an axial jet while air is

injected through an outer swirling flow. Figure 1.6 illustrates how an unswirled jet

injected along the centerline of a swirling flow field will influence flow field [59]. A jet

issues from the central nozzle with a velocity UF. When swirl is introduced to the outer

flow, a recirculation zone will form. The negative velocity UV produced by the

recirculating flow will slow the jet velocity. The resulting axial centerline velocity UCL is

less than the velocity would be in the presence of only a jet Uj. Depending on the velocity

of the jet and the intensity of the swirl, the resulting centerline velocity may be positive

or negative.

17

PIV measurements from Olivani et al. showed that for a particular configuration,

a stagnation point formed where the fuel jet and reverse flow velocity were equal in

magnitude. Their results showed some penetration of the jet into the recirculation zone

along the centerline. The jet flow then reversed and was forced outwards around the

recirculation bubble into the swirling outer flow. A central sooting luminous plume was

produced as a result of intermittent fuel penetration into the recirculation zone [60]. As

the jet momentum increases, the jet can penetrate and weaken the inner recirculation zone

[61]. For relatively high jet momentum, the flow field is unaffected by swirl and the flow

field resembles that of a typical jet [62]. Similarly, increasing the swirl strength with

strengthen the inner recirculation zone and prevent penetration by the jet [63, 64]. Jets

were shown to penetrate the recirculation zone more easily with combustion than in cold

flow cases, likely because heat release causes gas expansion which leads to an increase in

axial velocity and a decrease in swirl number. [65]. These studies of coaxial, non-

premixed flows show that the presence of a central jet will influence the flow field within

the combustor, but the effect of the jet is dependent on the combustor geometry, swirl

strength, and flow rates.

Similar interactions between a central jet and recirculating flow were observed in

flow behind a disc stabilizer with a central fuel jet [66–70] and in a bluff body burner

[71]. In addition to the size and shape of the inner recirculation zone, Sengissen et al.

noted a suppression of the precessing vortex core associated with the recirculation vortex

breakdown bubble with sufficiently high central pilot flame intensity in a combustor with

a central, swirling pilot flow [72].

18

Figure 1.6: Schematic of a flow field with a central axial jet and annular swirling flow; Adapted

from [59]

1.3.1.4 Stable flame shape

Stable flame structure can be characterized from CH* chemiluminescence flame

images obtained at stable operating conditions [19, 73]. Various metrics are used to

quantify the flame structure including flame length Lf, flame angle α, and flame width Wf

[12, 74–76]. Flame length is typically defined as the distance from the edge of the

centerbody to the center of heat release of the flame. Flame width is the width at half the

maximum of the axial heat release distribution. Flame angle is the angle between the

flame length vector and the flow direction.

The flame structure may also be characterized by the flame shape. The flame

shapes observed in this study fall into the category of either V-flames or M-flames [40,

41, 74]. V-flames are attached only to the edge of the centerbody and are stabilized in the

inner shear layer. M-flames, in contrast, have two attachment points. They anchor both to

the edge of the centerbody and the edge of the dump plane and are stabilized in the inner

19

and outer shear layers. These two flame shapes are illustrated in Figure 1.7. Studies have

shown that increasing the heat transfer across the combustor wall tends to leads to a V-

shaped flame. Heat transfer leads to a lower temperature in outer recirculation zone

which inhibits flame from stabilizing in the outer shear layer [40–42].

Figure 1.7: Schematic a) V-flame shape and b) M-flame shape. The flame is indicated by the red

lines. The flow direction is from the bottom to the top of the page

The effect of stable flame structure on combustion instabilities has been

investigated by several authors in both experiments and modeling. Many early studies

conducted on laminar flames have noted the influence of stable flame parameters such as

flame angle, flame length, flame width, Strouhal number, and flame shape on laminar

flame response [56–58]. Durox et al. studied the effect of several flame shapes, including

V- and M-flames, on laminar flame response [78]. They found that V-flames amplified

flame response more than M-flames. Flame tip displacement in V-flames provided a

major contribution to the flame surface area perturbation. They also found that at very

large modulation amplitudes, the M-flame detaches from the burner lip and takes a V-

flame shape.

Kim et al. [73] investigated the effect of flame shape on fully pre-mixed flames.

Two flame shapes were observed: an enveloped M-flame which lies in the compact flame

regime, and a dihedral V-flame which is non-compact. The center of heat release (defined

20

as the location of the maximum CH* intensity) for 95 different stable operating

conditions fell onto a well-defined curve. The shorter flames fell into M-flame category,

and the longer flames that impinged on the wall fell into the V-flame category. The two

flames showed distinctly different behavior. For example, when forced at the same

frequency and amplitude, the V-flame showed more significant interactions with a

vortex-ring structure than the M-flame. This behavior is attributed to the M-flame’s short

flame length which does not allow enough time for the vortex to grow and interact with

the flame as it convects downstream. The V-flame oscillates in the flow direction when

the vortex impinges on it, allowing the flame and vortex to interact as the vortex-ring is

convected downstream. The self-excited behavior for V- and M-flames also differed. The

V-flame instability corresponded to the frequencies amplified by the flame response

while the M-flame instability resulted from the 1/4 wave mode of the mixing section.

Kim et al. also used hydrogen to manipulate flame shape and study the effect of

flame shape on the fully pre-mixed flame response [79]. Pure natural gas flames were

found to be longer and exhibit a V-flame shape while hydrogen enrichment produced

shorter flames with an M-flame shape. Results showed the gain of the M-flames was

much lower than the gain of V-flames. They found that the flame response was governed

by the flame length (the distance from the edge of the centerbody to the location of

maximum heat release), the flame angle (the angle between the flame length and the flow

direction), and the Strouhal number. Because these three parameters determine the flame

response, flame response of flames with similar shapes is similar regardless of inlet flow

conditions.

21

1.3.2 Equivalence ratio oscillations and technically pre-mixed flames

In technically pre-mixed flames, the total heat release oscillations occur due to a

combination of velocity and equivalence ratio oscillations, so there are two sources for

heat release perturbations, making the underlying mechanisms of the instabilities difficult

to determine. Depending on the magnitude and phase of the velocity and equivalence

ratio oscillations, one disturbance may dominate the other, or they can amplify or damp

each other [80, 81]. In addition, the flame response is difficult to study because

chemiluminescence intensity is not directly related to heat release rate, as was discussed

in Section 1.2.1. The difficulties associated with the study of technically pre-mixed

flames have resulted in far fewer studies of technically pre-mixed flames than fully pre-

mixed flames. However, there are some technically pre-mixed studies that will be

discussed in this section.

Lieuwen and Zinn explained how equivalence ratio oscillations can cause heat

release oscillations [82]. The evolution of the equivalence ratio oscillation is illustrated in

Figure 1.8. Pressure oscillations propagate upstream from the combustor into the injector

after a time delay τ, causing oscillations in the mass flow rates of air and fuel at the fuel

injection location. These flow rate oscillations cause equivalence ratio oscillations

through the following relationship which can be derived from the definition of

equivalence ratio:

𝜑′

�̅�=

𝑚𝑓̇′

𝑚𝑓̇̅̅ ̅̅ −𝑚𝑎̇

′

𝑚𝑎̇̅̅ ̅̅

1 +𝑚𝑎̇

′

𝑚𝑎̇̅̅ ̅̅

(1.11)

This equation shows that equivalence ratio oscillations will be largest when air and fuel

flow rate oscillations are out of phase at the injector. The phase of the air flow rate

22

oscillations depend on the upstream boundary condition [83]. The phase of the resulting

equivalence ratio is then different than the initial pressure oscillations at the fuel injector.

The equivalence ratio perturbation then convects downstream and reaches the flame after

a time delay τconv. Finally, the combustion process responds to the equivalence ratio

perturbation after some time τcomb. If the resulting heat release perturbation occurs in

phase with pressure oscillations, then a combustion instability may occur.

Figure 1.8: (a) Combustor model (b) Illustration of the development of the equivalence ratio

oscillation [8] (Adapted from [82])

Cho and Lieuwen studied the response of laminar pre-mixed flames to

equivalence ratio oscillations. They found that the flame response to equivalence ratio is

determined by the superposition of disturbances in heat of reaction, flame speed, and

flame area. Fully pre-mixed flames, on the other hand, respond to velocity perturbations

via fluctuations in flame area only. Equivalence ratio flame response mechanisms are

shown schematically in Figure 1.9. Equivalence ratio fluctuations are directly responsible

for fluctuations in heat of reaction and flame speed. Flame area fluctuations occur as a

result of flame speed fluctuations and are therefore an indirect result of equivalence ratio

fluctuations.

23

Figure 1.9: Pathways for flame response to equivalence ratio perturbations [24]

Several authors have investigated the flame response to equivalence ratio

oscillations only. Kim et al. studied the linear and non-linear response to equivalence

ratio oscillations. In the linear regime, they found the flame behaves like a low-pass filter.

Heat release oscillations are amplified at low frequencies and fall off rapidly at high

frequencies. The phase increases linearly with frequency, indicating a convective

mechanism is responsible for the flame response [84]. Orawannukul et al. observed

similar gain and phase results in an experimental study of flame response to equivalence

ratio oscillations over a wide range of operating conditions. The presence of a convective

mechanism was supported with flame images. Phase synchronized fluctuation images

(phase synchronized images with the mean flame image subtracted) showed negligible

changes in the overall flame shape while a high intensity region was shown to convect

downstream, indicating that the flame response to equivalence ratio fluctuations are

caused by a convective mechanism [85].

Kim et al. [33] also studied the nonlinear response to equivalence ratio

oscillations. The nonlinear effects were most noticeable at high frequency and low

equivalence ratios. At low frequencies, lean blow out occurs before forcing amplitudes

24

large enough to produce nonlinear effects can be reached. Nonlinear effects were

attributed to the nonlinear dependence of flame speed and heat of reaction on equivalence

ratio. Similar results were noted for laminar flames by Shreekrishna et al. [86]. Flame

images showed no variation in flame length over a forcing cycle, indicating that changes

in heat of reaction, not flame speed, are the primary cause of the nonlinear flame

response. Sengissen et al. also observed almost no motion in a flame subjected to

equivalence ratio oscillations in their LES simulations [72]

Technically pre-mixed flames have been studied experimentally for both forced

and self-excited cases. Kim et al. experimentally studied the forced response of

technically pre-mixed flames to velocity and equivalence ratio perturbations. Their work

showed that the magnitude of an instability for a technically pre-mixed flame can be

amplified or damped by changing the phase between the velocity and equivalence ratio

perturbations [87]. Lee, Kim, and Santavicca used infrared laser measurements to study

equivalence ratio fluctuations during self-excited instabilities. They found that for a

particular instability, equivalence ratio fluctuations were primarily responsible for the

fluctuations in heat release [88].

Kim et al. also studied flame structure in technically pre-mixed flames. They

observed flame images in M-shaped flames with both equivalence ratio and inlet velocity

oscillations [62, 28]. While M-flames were shown to be more stable in fully pre-mixed

cases, these experiments showed that M-flames are susceptible to local extinction when

velocity and equivalence ratio oscillations occur in phase. In a case where velocity and

equivalence ratio oscillations occurred in phase, the flame divided into an upstream and

downstream region. Unsteady local extinction eventually occurred in the middle of these

25

two regions, and the downstream portion convected downstream with the mean flow and

eventually extinguished. In contrast, when equivalence ratio and velocity oscillations

occurred out of phase, the effects of these two mechanisms canceled. High equivalence

ratio mixture impinged on a relatively long flame and low equivalence ratio mixture

impinged on a relatively short flame, and the effects cancel. Flame images showed local

flame extinction did not occur and a clear M-flame shape was maintained over the

forcing period.

Several studies have addressed the problem of relating chemiluminescence

intensity to heat release rate in technically pre-mixed flames. Both Schuermans et al. and

Guyot and Paschereit have proposed similar methods for determining heat release rate

using multiple chemiluminescence signals [10, 31]. A different approach was proposed

by Huber and Polifke. If velocity and equivalence ratio fluctuations are uncoupled, then

the total flame response is a superposition of the flame response to velocity fluctuations

and to equivalence ratio fluctuations. They supported this hypothesis with results from a

computer simulation [80]. Orawannukul et al. applied Huber and Polifke’s hypothesis to

experimental techniques and demonstrated a reverse reconstruction process in which heat

release rate fluctuations for a forced, technically pre-mixed flame are derived from

chemiluminescence intensity measurements of a forced technically pre-mixed flame and

a forced fully pre-mixed flame [92]. Results from this study showed large differences

between the measured chemiluminescence intensity based transfer function and the

reconstructed heat release based transfer function. Unfortunately, these methods cannot

be directly validated because there is no way of directly measuring heat release from a

technically pre-mixed flame.

26

Orawannukul et al. also applied the reverse reconstruction process to flame

images of technically pre-mixed flames. Although the measured and reconstructed

images showed some differences, there were quantitative similarities in flame shape and

locations of high and low intensity [93]. These results suggest that while the exact values

of local heat release from a technically pre-mixed flame cannot be determined from

chemiluminescence flame images, these images can provide useful qualitative

information about the unsteady flame structure of a technically pre-mixed flame.

1.4 Pilot flame literature review

Knowledge of combustion instabilities can be put into practical use by developing

methods for suppressing them. Instabilities are suppressed by disrupting the feedback

loop between unsteady heat release and the system acoustics through either passive or

active control methods. Passive controls systems often involve modifications of the

system’s fuel injection or acoustics. The flame dynamics can be controlled passively by

modifying flow and flame configurations [94]. The acoustics can be modified by

changing the system geometry or installing damping devices such as acoustic liners,

Helmholtz resonators, and quarter wave cavities [23]. However, these acoustic

modifications often require too much space to be practical and are limited to a specific

frequency. Active controls generally include sensors to detect instabilities. The feedback

loop is modified as the flame is running, often by adjusting secondary fuel injection.

Passive methods for controlling instabilities tend to be more practical to implement than

active control methods which are often complicated and expensive.

A common method for controlling combustion instabilities is by modifying fuel

injection either through fuel staging or through a pilot flame. These fuel staging and pilot

27

flame control methods can be either passive or active. The current study investigates a

passive pilot flame in which fuel is diverted from the main flame to a secondary pilot

flame located on the centerline of the combustor. Pilot flame studies will be reviewed to

determine the current understanding of why pilot flames affect combustion instabilities.

Studies of fuel staging and varying fuel injection locations are relevant to the present

study because the pilot design in the injector used in this study involves diverting fuel

from the main fuel flow to the pilot flame. Fuel injection studies provide insight into the

effect of varying fuel injection and therefore will therefore also be reviewed in addition to

pilot flame studies.

1.4.1 Fuel injection considerations

Fuel injection location plays an important role in combustion oscillations driven

by equivalence ratio fluctuations. The τf time-lag model is commonly used to explain

how an equivalence ratio disturbance convected by the mean flow leads to a self-excited

instability. If the convective delay time τ occurs at an appropriate multiple of the acoustic

period T = 1/f, then the resulting heat release oscillation will occur in phase with the

pressure oscillation peak. Richards and Straub used multiple fuel injection locations to

reduce or eliminate instabilities that were observed when fuel was injected in only one

location [95].

Active control methods that modulate fuel injection been shown to be very

successful in eliminating combustion instabilities [8, 96]. Several studies have found that

the location of secondary fuel injection as well as the amount of secondary fuel injected

affect the effectiveness of the secondary fuel injection [97–99]. By using active control to

optimize the phasing of the fuel injection, the instability can be reduced with smaller

28

amounts of secondary fuel than for cases without active control. Phasing the fuel

injection allows the flow of fuel to the flame to be adjusted to reduce heat release

fluctuations. These studies of strategic fuel injection demonstrate the influence of the fuel

injection design and show how fuel injection can affect combustion instabilities driven by

equivalence ratio fluctuations. They also show the importance of the phasing of the

secondary fuel injection. The effect of fuel injection and equivalence ratio perturbations

will be considered in the present study of a pilot flame.

1.4.2 Pilot flames

Pilot flames are secondary flames that can be run in addition to the main flame to

help improve the stabilization of the main flame. The term “pilot flame” can refer to a

variety of secondary flame configurations in different types of burners. For example,

many studies of laboratory scale diffusion flames use an arrangement of pilot flames

around the nozzle exit to prevent the main flame from becoming lifted [100–103].

For lean, pre-mixed, swirl stabilized combustors, pilots are often used during the

transition from one operating regime to another to provide continuous ignition sources to

the incoming flow [104]. Several different pilot fuel injection geometries are noted in the

literature. A pilot flame may refer to a secondary pilot injector within a combustion

system or a separate pilot fuel passage within an individual injector, as noted by Davis et

al. in their review of dry low NOx combustion systems for heavy duty gas turbines [104].

For single nozzle experimental studies, three pilot flame geometries that are most

common in the literature. These configurations are illustrated in Figure 1.10. The first is a

single opening along the central axis of the injector. This configuration directs the pilot

into the central recirculation zone. This is configuration (a) in Figure 1.10. Pilot fuel may

29

also be injected through an arrangement of evenly spaced holes around the exit of the

injector at the centerbody or the dump plane. These locations are indicated by

configuration (b) and configuration (c), respectively, in Figure 1.10. Injecting the fuel

around the injector exit directs the pilot directly towards the base of the flame. The

injector considered in this study contains a pilot that falls into the first category, but

studies on either configuration provide insight into the mechanisms responsible for the

pilot’s stabilizing effect.

Figure 1.10: Schematic of possible pilot fuel injection configurations

The effects of pilot flames have been observed experimentally and in

computational simulations. A summary of relevant pilot flame studies is provided in

Table 1.1.

Table 1.1: Summary of passive pilot flame studies

Authors

(Year)

Pilot

Configuration

Pilot

Mix

Flame

images?

Passive/

Active? Additional Notes

Experimental Studies

Snyder et al.

(1996)

6 holes

at nozzle exit Diffusion No Passive

Pandalai et al.

(1998)

8 holes

at nozzle exit Diffusion No Passive

Lee et al

(2000)

Centerline and

12 holes at

nozzle exit

Diffusion Yes Both

Phase averaged CH*

images without pilot

Studied effect of

secondary fuel

injection location

30

Shinjo et al.

(2007)

12 holes

at nozzle exit Diffusion Yes Both

OH* intensity

without and with

secondary fuel

injection

Comparison of

experimental and

computational results

Albrecht

(2010)

9 holes

at nozzle exit Pre-mixed Yes Both

Phase averaged and

time averaged OH*

intensity images

Rosentsvit et

al.

(2014)

Slit around

nozzle exit

Hot

products No Passive

Hot products injected

directly to main flame

base

Kendrick et al.

(1999) centerline

Diffusion

and

pre-mixed

Yes Passive

Phase averaged CH*

intensity contours

without pilot

Time averaged CH*

intensity contours

with pilot

Steele et al.

(2000) centerline Diffusion No Passive

Pachereit


Variable axial pilot

location

Dhanuka et al.


PIV flow field

measurements

Jet-A fuel

Farber et al.

(2010) centerline Pre-mixed Yes Passive

Time averaged CH*

chemiluminescence

images

LDV velocity

measurements

Fu et al.

(2015) Centerline Pre-mixed Yes Passive

Studies pilot flame

dynamics without

main flame

Muruganandam

et al.

(2005) centerline Pre-mixed Yes Active

Computational Studies

Sengissen et al.

(2007) centerline Pre-mixed No Passive

Includes mean velocity

profiles, and

instantaneous

temperature, pressure

and equivalence ratio

fields.

Wang et al.

(2010) centerline Pre-mixed No Passive

Includes flame

response to pulsating

pilot jet for two forcing

frequencies and

amplitudes

31

An early study of an injector including a pilot flame was conducted by Snyder et

al. Experiments were performed on an aeroderivative engine, and the authors noted that

various combinations of pilot fuel injected into the recirculation zone and pre-mixed main

fuel could produce stable flames over the entire operating range [105].

Figure 1.11: Schematic of fuel nozzle including pilot fuel injection from Snyder et al.

(Adapted from [105])

With increasingly stringent NOx emissions regulations, some studies have found

pilot flames may lead to unacceptable high NOx levels. For example, Steele et al. found

that for their specific injector, 10% pilot fuel eliminated large pressure oscillations, but

increased NOx above their 25 ppm goal [106]. A more efficient pilot design could reduce

the amount of pilot fuel required to reduce an instability, and thereby keep NOx

emissions acceptably low. Some pilot flame research has focused on catalytic pilot

32

flames to produce lower NOx emissions than traditional pilots. For example, Karim et al.

incorporated the catalytic pilot design shown in Figure 1.12 into a modified Solar Taurus

70 injector.

Figure 1.12: Example of a catalytic pilot design (Adapted from [59])

Studies have demonstrated that this type of pilot successfully reduces combustion

instabilities with very low NOx emission levels. However these studies tend to focus on

developing functional catalytic pilots and demonstrating emissions reductions, and do not

discuss in detail the underlying mechanisms that cause pilot flames to reduce instabilities

[107, 108].

A common assumption about pilot flames is that they enhance the stability by

increasing the concentration of hot products recirculated to the base of the main flame.

As discussed in Section1.3.1.3, hot products from the flame promote combustion and

increase temperatures in the flame base, so increasing the concentration of hot products

through a pilot flame should improve flame anchoring. Pandalai and Mongia noted a

reduction in combustion instabilities when they injected pilot fuel through an

33

arrangement of holes located at the injector exit. While they speculated the pilot effect

was due to enhanced recirculation and improved anchoring of the flame to the injector

exit, no attempts were made to validate this hypothesis [109]. Dhanuka et al. came to a

similar conclusion in their study of an LPP gas turbine combustor for aircraft

applications. In these types of engines, a diffusion pilot flame is necessary to stabilize the

main pre-mixed flame. They concluded that the interactions between the main and pilot

flames are not responsible for stabilization because the main flame exists upstream of the

location where the main flame and pilot flame interact. Instead they suggest that a

recirculation zone brings hot products from the pilot flame upstream to the base of the

main flame and which helps to stabilize the main flame [110].

Many studies that attempt to explain the effect of pilot flames focus on

instabilities that occur near the lean blowout limit. These studies focus on the effect of the

pilot on static stability. Static stability refers to the ability of the system to anchor a flame

over the desired range of operating conditions [111, 112]. The hot products recirculation

explanation of the pilot flame effect is particularly relevant for lean blowout conditions.

Strong velocity gradients in the shear layers cause stretching of the flame. The flame can

extinguish locally if the flame stretch rate is greater than the extinction stretch rate [45].

Flame blowout has been studied in bluff body stabilized flames. Holes in the flame near

lean blow out lead to the mixing of fresh reactants with hot products from the wake

recirculation zone. The hot products ignite the reactants and “repair” the holes [45, 113–

115]. This demonstrates the importance of hot products in preventing lean blowout.

Experimental studies of swirl stabilized flames have also found that blow out originates

from extinctions of the flame near the exit of the nozzle in a region referred to as the

34

flame root. Stohr et al. studied extinction in this region. This flame root region is unstable

due to high strain rates. During stable operation, this region is stabilized by relatively fuel

rich conditions and hot products carried by the inner recirculation zone from the

downstream portion of the flame. While this study did not include a pilot flame, it

demonstrated how a pilot could prevent blowout by stabilizing the base of the flame

[116].

Muruganandam et al. developed an active control system to stabilize the flame

near lean blow out by injecting pilot fuel into the flame base region when measured OH*

intensity levels dropped below a threshold value [117]. A study by Rosentsvit et al. [118]

directly investigated the hypothesis that increasing the hot products at the base of the

flame improves flame stability. The mechanism was isolated by creating a simple

combustor geometry with no swirl and a gradual area increase rather than a dump plane

to prevent complicated flow structures. The pilot flame was ignited in a separate

chamber, and the hot products exited through a narrow slit directly into to the main

combustion zone. Experimental results showed that by increasing the percent of total fuel

sent through the pilot, the lean blow out limit could be extended to lower equivalence

ratios, thus increasing the range of stable operating conditions near blowout.

Results of the present study, however, have shown an effect of pilot flame at both

high and low equivalence ratios, so extending the flame blow out limit cannot be the only

mechanism through which the pilot flame prevents instabilities. Some pilot flame studies

have investigated the dynamic stability of a flame with the addition of a pilot flame.

Dynamic stability refers to the unsteadiness due to self-excited combustion driven

oscillations, and involves chemical energy fed into acoustic oscillations [111, 112]. There

35

is evidence in the literature that pilot flames may affect instabilities by altering the flow

structure. Using a large eddy simulation (LES), Sengissen et al. studied the effects of

different amounts of pilot fuel on flame stability. The pilot design used by Sengissen et

al. is shown in Figure 1.13.

Figure 1.13: Schematic of pilot passage from [119]

For 2% of the total fuel injected through the pilot, they found that the flame was

unstable, but when 6% of the total fuel was injected through the pilot, the flame was

stable. They concluded that the higher pilot fuel case prevents the formation of a

precessing vortex core by creating a roughly stoichiometric region near the burner

entrance where the flame can propagate. In the lower pilot fuel case, the flow rate of fuel

was very low and the region near the burner entrance was lean. This lean region prevents

the flame from stabilizing and leads to the formation of a precessing vortex core

containing lean cold gases. They confirmed experimentally that the 2% case was unstable

and the 6% case was stable but they did not attempt to experimentally identify the

proposed stability mechanisms [119]. Wang et al. also used LES to demonstrate that a

36

pilot flame located along the central axis suppresses the precessing vortex core [120]. In

an experimental study with a similar configuration, Färber et al. used measurements of

mean velocity profiles to show the pilot flame results in a wider inner recirculation zone.

This wider flow structure corresponded to more stable combustion [121]. It should be

noted that in the three studies mentioned, the pilot flow as well as the main flow was

swirled, whereas in the current study, the pilot flow is not swirled. The fluid mechanics

would then be expected to differ.

Lee et al. [122] tested different pilot fuel injection designs, shown schematically

in Figure 1.14, and noted several mechanisms that could be responsible for the observed

effects. They investigated self-excited instabilities at two operating conditions. In both

cases, they used chemiluminescence imaging to determine the mechanism responsible for

the instability and found that passively adding a pilot flame likely reduced the

instabilities by interfering with that mechanism. For example, one case showed evidence

of periodic flame separation which the pilot flame likely prevents. The other case showed

evidence of flame-vortex interaction. They suggested that the addition of the pilot flame

along the centerline of the combustor, Location (a) in Figure 1.14, changed the location

of the reaction zone and reduced the flame-vortex interaction. However, no phase

averaged images with the pilot flame were presented to confirm their theories on the pilot

flame effect. They also investigated a closed loop control strategy and found it was most

effective when the pilot fuel was injected with appropriate phasing into a region of either

positive or negative Rayleigh index [122]. This location corresponded to Location (c) in

Figure 1.14. Shinjo et al. noted similar results. They found that a passive pilot flame

37

altered flame shape and may have reduced flame-vortex interactions. They further

reduced instabilities through phasing of pilot fuel injection [123].

Figure 1.14: Schematic of pilot fuel injection designs used by Lee et al. Location (a) is a single

hole on the axis of the centerbody. Location (b) is an arrangement of 12 evenly spaced holes at a

45 angle around the outer circumference of the centerbody. Location (c) is an arrangement of 12

evenly spaced holes around the circumference of the dump plane. (Adapted from [122])

In most pilot flame studies, the pilot flame itself is stable. However, Fu et al.

demonstrated that the dynamic stability of the pilot flame influences the overall stability

of the combustor [124]. The found that for low intensity pilot flames, the pilot does not

interact with the main flame and an instability occurred with a frequency of 33 Hz. As the

pilot fuel was increased, large scale extinction of the flame base was eliminated and the

33 Hz instability was eliminated. However, for the highest pilot flame intensity tested, a

130 Hz instability occurred. In the absence of the main flame, the highest intensity pilot

flame was found to become unstable with a frequency of 130 Hz. This result shows the

importance of the pilot flame stability in controlling the main flame stability.

While these studies have provided some insight into the behavior of pilot flames,

there has yet to be a thorough study that encompasses a wide range of operating

conditions. There is also only limited experimental evidence for the mechanisms

proposed in these papers. The stability of a combustor with and without pilot is still very

38

unpredictable. The current study will investigate the behavior of a pilot flame over a wide

range of operating conditions in order to determine when the pilot flame is and is not

effective. Flame imaging will be used to investigate the underlying instability

mechanisms that are affected by the pilot flame.

1.5 Objectives for current work

This literature review shows that research on combustion instabilities has focused

primarily on fully pre-mixed flames. While there have been some studies on technically

pre-mixed flames, more work needs to be done in this area. Industrial combustors are run

technically pre-mixed, so understanding this type of flame is critical to understanding

combustion instabilities. Therefore, this study will focus on technically pre-mixed flames.

The stability of the combustion test facility will be investigated under a wide range of

operating conditions to determine under what conditions the flame becomes unstable.

In addition, the suppression of instabilities is an important application for

combustion research. Pilot flames are commonly used in gas turbines as a means of

reducing instabilities. While numerous studies have noted that pilot flames reduce

combustion instabilities, further research is needed to explain why pilot flames affect

instabilities. The current work focuses on a detailed investigation of the effect of a

centrally located pilot flame on the magnitude of combustion instabilities. The effect of

the pilot flame will be investigated over a range of operating conditions and instability

frequencies and magnitudes to determine under what conditions the pilot flame does or

does not eliminate instabilities. This wide range of operating conditions allows for

conclusions that are not specific to one operating condition.

39

Flame images are used to determine how the presence of a pilot flame modifies

the behavior of the main flame. Both stable, time averaged and unstable, phase averaged

images will be investigated. Stable flame images show the effect of the pilot flame on

stable flame structure which has been shown to affect flame response. Phase averaged

images show the dynamics of unstable flames both without and with a pilot flame. These

images show how interactions between the main and pilot flames may affect instabilities.

Operating conditions where the pilot flame affects combustion instabilities as well as

conditions where the pilot flame is ineffective are investigated. A better understanding of

the mechanisms that control the pilot flame will help to optimize the design and use of

the pilot flame.

40

Chapter 2

Experimental Set Up

All experimental results in this study were obtained in single nozzle, swirl-

stabilized, atmospheric combustion test facility. Details of the experimental facility are

provided in Section 2.1. Various experimental measurements and data processing

techniques are explained in Section 2.2. Flame imaging, including camera set-up and

image processing, is explained in Section 2.3.

2.1 Combustion test facility

2.1.1 Overview of test facility

Experiments for this study were performed using a lean, pre-mixed, swirl-

stabilized, variable length combustor with a single industrial gas turbine injector. Figure

2.1 illustrates the combustion test facility which consists of an inlet section, an injector, a

combustion chamber, and an exhaust section. Each section of the test facility will be

explained in greater detail in the following sections.

The air and fuel required for the combustion reaction are brought into the system

to achieve a desired operating condition. Thermal mass flow meters measure flow rates,

and needle valves adjust the flow rates of air and fuel to achieve the desired equivalence

ratio and mean inlet velocity. High pressure air enters the system from a compressor, and

a dome pressure sets the air pressure to 180 psig. An 88kW electric heater preheats the

incoming air to a maximum temperature of 250°C. The fuel for this study is natural gas,

41

and it enters the system at a pressure of 200 psig. Pressure regulators and heaters prevent

the gas from cooling excessively as it expands to this pressure.

Figure 2.1: Schematic of test facility; Flow direction is from left to right

2.1.2 Inlet Section

The first section of the test facility is the inlet section. The inlet is illustrated in

Figure 2.2 and important features are labeled. Adjustments to the inlet section allow

different types experimental flame studies to be performed, i.e. forced flame response or

self-excited, and fully or technically pre-mixed. Section 1.2 discusses these different

types of experimental flame studies in greater detail.

In forced flame response studies, a siren device driven by a motor imposes

velocity oscillations on the flow entering the test facility at a specified frequency and

amplitude. The siren and motor are labeled in Figure 2.2. The frequency of the forced

velocity perturbation is determined by the rotational speed of the motor. The forcing

amplitude is determined by the fraction of the inlet flow that is diverted from the main

42

flow path to the siren. The amount of inlet flow that passes through the siren is

determined by adjusting the siren valve and main valve, which are labeled in Figure 2.2.

For self-excited experiments, the siren section is bypassed. Solid plates block

Locations “C” and “D” in Figure 2.2 to prevent leakage of the main inlet flow into the

siren pathway. A choke plate is inserted at location “B” to create an approximately closed

inlet acoustic boundary. During self-excited experiments, the length of the combustor is

varied to excite unstable combustor modes. Coupling between unsteady heat release rate,

the system acoustics, inlet velocity, and equivalence ratio leads to large instabilities under

certain conditions. This feedback loop is shown schematically in Figure 1.1

This test facility is also capable of running in both fully pre-mixed (FPM) and

technically pre-mixed modes (TPM). For fully pre-mixed experiments, the fuel is injected

upstream of a choke plate and a uniform mixture of air and fuel enters the system through

the inlet section. Mixing the air and fuel upstream of a choke plate prevents equivalence

ratio fluctuations by ensuring pressure oscillations cannot propagate to the fuel injection

location. Injecting the fuel far upstream of the combustor also ensures that the air and fuel

are well mixed when the mixture reaches the combustor.

However, the present study focuses primarily on technically pre-mixed

experiments (TPM). For technically pre-mixed experiments, only air is present in the

inlet section. Fuel is added downstream at the swirler in the injector section. The fuel

mixes with air over a short distance between the swirler and the injector exit. Pressure

oscillations at the fuel injection location can cause oscillations in both the air and fuel

flow rates which then lead to equivalence ratio oscillations. The injector section is

explained in more detail in the next section.

43

Figure 2.2: Top view of the combustion test facility inlet section

2.1.3 Injector Section

This test facility uses a single, swirl stabilized, industrial gas turbine injector. A

schematic of this injector is shown in Figure 2.3. There are two pathways for flow

entering the injector. Approximately 95% of the total air enters through the main annular

pathway between the outer wall of the combustor and the centerbody. A swirler in the

main passage introduces an azimuthal velocity component to the flow. As discussed in

Section 1.3.1.3, the swirling component helps to stabilize the flame.

The swirler is also the location at which the main fuel is added to the air in

technically pre-mixed flames. During unstable combustion, pressure fluctuations

propagate to the fuel injector and can cause fluctuations in fuel flow rate. If the fuel

injector is chocked (i.e. the pressure drop across the injector is large), pressure

fluctuations do not affect the flow rate of fuel. However, in this study, the fuel injection

holes are unchoked (i.e. the pressure drop is small). Pressure fluctuations in the fuel

44

injector cause fluctuations in fuel flow rate, that then lead to equivalence ratio

fluctuations. Equivalence ratio fluctuations are also caused by fluctuations in the air flow

rate at the fuel injection location. Pressure fluctuations modulate the flow rate of air in the

injector. Variations in the amount of air at the fuel injection location lead to fluctuations

in equivalence ratio.

Figure 2.3: Schematic of injector geometry and important features

The remaining 5% of the flow entering the injector travels into the secondary

pathway through the centerbody. The flow through the centerbody is split between two

possible pathways through the centerbody. Some of the flow passes through the outer

passage between the outer wall of the centerbody and the pilot fuel path. This flow cools

the face of the centerbody exposed to the combustor and prevents damage from

overheating. The remainder of the flow enters the pilot fuel passage and mixes with any

pilot fuel that may be added. This two centerbody flow paths combine just before

entering the combustor.

45

For the technically pre-mixed case, air enters the pilot passage, and fuel may be

added to produce a pilot flame. The flow rate of fuel can be varied to adjust the intensity

of the pilot flame. The pilot flame tends to help in flame stabilization. The effect of the

pilot flame on self-excited instabilities and the mechanisms driving the pilot flame effect

are focus of the current study.

In the fully pre-mixed case, the flow entering the centerbody passage is a mixture

of air and fuel. This mixture produces a secondary flame with the same equivalence ratio

as the main flame. With the current injector design, a secondary flame is always present

in the fully pre-mixed case. The study of a fully pre-mixed pilot flame would require

modifications to the injector to remove the secondary flame from the baseline case with

no additional pilot fuel.

2.1.4 Combustor section

The combustion chamber is depicted in Figure 2.4. The combustor consists of two

sections: an optically accessible quartz window section and a stainless steel section. The

flame is located within the quartz section. This quartz window allows for

chemiluminescence emission measurements and flame imaging. The quartz section is

made of a GE214 fused quartz tube with the following dimensions: inner diameter =

150mm, wall thickness = 3mm, length = 305mm. High-temperature RTV silicone secures

the upstream and downstream ends of the quartz to the dump plane and the stainless steel

transition section, respectively. A cooling ring delivers room temperature air to the

outside quartz surface prevent the quartz from overheating.

The downstream section where optical access is not necessary is made of a

stainless steel, double walled tube. It is cooled by room temperature air flowing through

46

the space between the inner and outer walls. A stainless steel, cone-shaped plug sits on

two bearings inside the stainless steel combustor section. To cool the plug, distilled water

sprays on the back surface of the plug. A pump increases the water pressure to increase

the flow through the spray nozzles and to prevent vaporization within the plug by raising

the boiling temperature.

Figure 2.4: Cross section of combustor section

The plug is used to vary the combustor length Lcomb (the distance from the dump

plane to the plug) from 25 to 59 inches. The resonant acoustic mode of the combustor

changes with combustor length, so varying the plug position allows the system to be

tuned for either stable or unstable combustion. The plug position is adjusted with a

translation stage driven by a stepper motor. The plug also reduces the open area of the

stainless steel combustion section by approximately 90%. The exhaust products exit the

combustor through the passage between the edge of the plug and the inner wall of the

stainless steel combustion chamber. Mufflers reduce the noise of both the main and

cooling air exhausts.

47

2.2 Measurements Techniques

The primary measurements acquired in this experimental study are pressure,

velocity, and chemiluminescence intensity. The set up and methods for each of these

measurements are explained in the following sections. Methods for processing the

acquired data are also explained.

2.2.1 Pressure

Static pressure inside of the combustor was measured using a digital static

pressure gauge (Omega model DPG1000B-05G). Pressure fluctuations were measured at

three different locations (see Figure 2.3) using dynamic pressure transducers (PCB model

112A22 and 112A04). All pressure transducers are water cooled and recessed mounted.

The transducer located at the dump plane was used to measure pressure

fluctuations within the combustor. These measurements were used to characterize the

self-excited instabilities. Measurements from the upstream and downstream transducers

in the injector were used to calculate velocity fluctuations using the two microphone

method (TMM) which will be explained Section 2.2.5.

2.2.2 Velocity

The mean velocity of the flow in the injector was calculated from the mass flow

rates of the fuel and air, the cross sectional area of the injector, and the density of the

mixture. The density was calculated from the measured temperature and static pressure

using the ideal gas law.

Velocity fluctuations in the injector were calculated from a pressure gradient

measured using the two microphone method (TMM). The pressure measurements were

obtained from two pressure transducers located between the swirler and the injector exit

48

and separated by a distance of 1.25 inches. The location of the velocity fluctuation

measurements was selected to be as close to the flame as possible to approximate velocity

fluctuations at the flame. Section 2.2.5 includes the details of how velocity fluctuations

are calculated from pressure measurements using the two microphone method.

Velocity fluctuation measurements can be used for forced flame response studies

to determine input of the flame transfer function. In self-excited studies, velocity

fluctuations provide information on an important part of the self-excited feedback loop

that drives the instability. In addition, velocity oscillation measurements are important

because all phase measurements are referenced to the peak velocity fluctuation in order to

keep a consistent reference point across all data sets.

2.2.3 Chemiluminescence Intensity

Chemiluminescence emission from the flame was measured using three

photomultiplier tubes (PMTs), each equipped with a narrow band-pass filters to isolate

OH* (307± 5nm), CH*(432 ± 5nm), or CO2 (365 ± 5nm) emissions. For fully pre-

mixed flames, chemiluminescence intensity can be used as a direct measure of global

heat release rate. In technically pre-mixed flames, quantitative measurements of heat

release cannot be obtained directly from chemiluminescence intensity. However,

qualitative information can be obtained from chemiluminescence. In addition, some

studies have developed methods for deriving global heat release rate from

chemiluminescence intensity measurements using a reconstruction procedure. The effect

of equivalence ratio on chemiluminescence intensity measurements are explained in

Section 1.3.2.

49

2.2.4 Basic processing of pressure and chemiluminescence measurements

The pressure and chemiluminescence measurements described in the previous

sections were acquired simultaneously using a LabVIEW interface combined with a

National Instruments data acquisition board (PCI-6259 data acquisition board with BNC

2110 connector block). The signals were acquired at a sampling rate of fs = 8192

samples/second for 8 seconds. The data was then processed using a MATLAB program.

Each 8 second record was divided into 1 second sets for a frequency resolution of Δf = 1

Hz, and each set was processed individually. The oscillation magnitude and frequencies

reported in this study are the mean RMS oscillation amplitude and the mode of the

oscillation frequencies for these 8 one second records.

For each record, the linear spectrum of the measured time series data is calculated

from the discrete Fourier Transform shown in Equation (2.1). This transform converts the

measured data from the time domain to the frequency domain.

𝑋𝑚 = ∑ 𝑥𝑛

𝑁−1

𝑛=0𝑒−𝑗2𝜋

𝑛𝑚𝑁 ∆𝑡 (2.1)

In the above equation, Xm is the linear spectrum, xn is the time domain signal, j indicates

an imaginary number, N is the number of data points, Δt is the time between data points,

n is the index of the time domain and m is the index of the frequency domain. The linear

spectrum is a complex value with a magnitude and phase.

The phase is calculated from angle of the complex number

𝜃𝑋 = tan−1 (

𝐼𝑚(𝑋𝑚)

𝑅𝑒(𝑋𝑚)) (2.2)

where Im and Re represent the imaginary and real parts of the complex number. The

phase is referenced from start time of the data acquisition, so the phase value varies for

each set of data. In order to compare phase values across data sets, phase values are

50

referenced relative to the peak velocity oscillation. For example, if the combustor

pressure oscillations are measured on two separate occasions for the same operating

condition, the calculated phase will be different, but the phase difference between the

pressure and velocity fluctuations should be consistent between the two data sets.

The frequency and amplitude of the oscillations were found from GXX, the single

sided power spectral density (SSPSD). Gxx was calculated from Equation (2.3) [125].

𝐺𝑋𝑋 =1

𝑇|𝑋0|2 for m = 0

𝐺𝑋𝑋 =2

𝑇|𝑋|2 for 1 < m < N/2 - 1

𝐺𝑋𝑋 =1

𝑇|𝑋𝑁

2

|2

for m = N/2

(2.3)

The frequency of the instability is the frequency corresponding to the maximum

oscillation amplitude found from the SSPSD. The root mean square (RMS) fluctuation

amplitude at the peak frequency is calculated from the modified version of Parseval’s

theorem in Equation (2.4).

𝑅𝑀𝑆 = √∑ 𝐺𝑋𝑋(𝑓)𝑓+10

𝑓−10⋅ ∆𝑓 (2.4)

For self-excited experiments, it is necessary to sum around the peak frequency to account

for uncertainty in the oscillation frequency. The frequency resolution in this study is 1

Hz. If the frequency is not exactly an integer value, “leakage” will occur and some

energy will be contained in adjacent frequency bins. In addition, some variation in the

frequency may occur while over the time the data is recorded which will also cause

energy to spread across several frequencies. The sum of the amplitude from 10 Hz below

51

the peak frequency to 10 Hz above the peak frequency accounts for the spread of energy

over multiple frequency bins.

2.2.5 Two microphone method

Velocity fluctuations in the injector were calculated from pressure measurements

at an upstream and a downstream location using the two microphone method (TMM)

[125, 126]. The TMM comes from the linearized conservation momentum equation for an

incompressible and inviscid fluid with negligible body forces:

𝜌𝑑𝑢

𝑑𝑡= −

𝑑𝑝

𝑑𝑥 (2.1)

The velocity, u, at a point, x, between two pressure transducers separated by a small

distance Δx can be calculated by applying a finite difference approximation:

𝑈(𝑥) =𝑃𝑢𝑠−𝑃𝑑𝑠

jωρΔ𝑥 (2.2)

where U is the linear spectrum of velocity, ω is the angular frequency, ρ is the mixture

density, Δx is the distance between the two microphones, and Pus and Pds are the upstream

and downstream pressure linear spectra, respectively.

The assumptions for the TMM apply to the conditions investigated in this study.

The incompressible assumption applies for low Mach numbers, i.e. Ma ≤ 0.3 [127]. Mach

numbers are below approximately 0.1 for this experiment. Fluctuations in pressure are

small (under 10% of the mean) and therefore fluctuations in density are also small. The

Reynolds number represents the ratio of inertial forces to viscous forces [127]. For this

study, Reynolds numbers are high, so the impact of viscous forces is negligible. Finally,

there are no axial body forces present. Spatial variation of the velocity field between the

two microphones assumed to be negligible, so the convective acceleration term is

52

ignored. Therefore, the TMM may be used to measure velocity fluctuations in the

injector.

The two microphone method is only accurate within high and low frequency

limits. The finite difference approximation used in the two microphone method is not

accurate when the wavelength of the pressure perturbation is on the same order as or

smaller than the spacing between the microphones [128]. This leads to a high frequency

limit above which the two microphone method cannot be used. The wavelength, λ, at a

given operating condition can be calculated from the speed of sound, c, and the

frequency, f.

𝜆 = 𝑐𝑓⁄ (2.3)

For the frequencies considered in this study, the 1.25 inch microphone spacing is

sufficient avoid the high frequency limit.

At low frequencies, wavelength of the pressure perturbation is very long, and the

difference in pressure measured by the two microphones is very small [129]. Errors in the

two microphone method can occur because attenuation of the pressure wave between the

two measurement locations has a significant effect. In addition, if the difference in

pressure measurements is on the same order as the turbulent pressure fluctuations, the

two microphone results will not be accurate. The frequencies of interest in this study are

well above the low frequency limit.

2.3 Flame Imaging

2.3.1 Camera set-up

Two-dimensional CH* chemiluminescence emission flame images were used to

study flame structure. Line of sight images were taken using an ICCD (intensified

53

charged-coupled device) camera with a 430 ± 5nm narrow bandpass filter, which

corresponds to the wavelength of CH* chemiluminescence emissions.

Two types of flame images were taken: time averaged and phase averaged. Time-

averaged images were taken for stable and unstable flames during self-excited

experiments using a Princeton Instruments model 576G ICCD camera. Phase-averaged

images of unstable flames were acquired with a high-speed Phantom model 7.1 camera

and Video Scope VS4-1845HS intensifier. Several camera settings are important to note

because they affect the image acquired by the camera. These settings include exposure

time τexp and camera gain.

For time averaged images, the exposure time is relatively long. In this study, the

exposure time was set to 70 ms. Twelve images were acquired and then summed during

processing. The long exposure time of time averaged images produce images that are

averaged over many cycles of an instability. These long exposure times result in

increased acquired signal, so the camera gain was set as low as possible to reduce noise

amplification. In this study, the gain was typically set to 2.

Phase averaged images are acquired with a high speed camera capable of

acquiring thousands of images per second. In this study, images are acquired at a

sampling rate fs of either 4000 or 5400 samples per second, depending on the instability

frequency. In order to adequately capture phase averaged images, at least 1/12 of the

instability cycle was captured in each image. For lower frequencies, 4000 samples per

second is a high enough sampling rate to ensure at least 1/12 of the instability cycle is

captured in each frame. However, for frequencies above approximately 330 Hz, a higher

sampling rate is necessary to capture at least 1/12 of a cycle. A sampling rate of 5400

54

samples per second allows an adequate fraction of the instability to be captured for the

higher range of frequencies observed in this study. Because higher sampling rates result

in larger files that require more time to process, fs = 4000 samples per second was used

whenever possible. The exposure time for high speed images varied depending on

sampling rate. For fs = 4000, the exposure time was set to τexp = 200 μs and for fs = 5400,

the exposure time was set to τexp = 160 μs.

The exposure time for the high speed images is very small in order to capture a

fraction of an instability cycle. Because the exposure time is low, only a small amount of

signal is captured in each image, so the gain must be set to a high value in order to

amplify the signal. For phase averaged images in this study, the gain was set to the

highest possible value that could be used without causing saturation. This gain value

varied depending on the operating condition and magnitude of the instability.

2.3.2 Basic image processing

The images captured by the camera are line of sight, integrated images referred to

as “projection images”. In a line of sight integrated image, each pixel value represents the

total the intensity across the flame at that point. The flame is approximately

axisymmetric, so the raw image were deconvoluted using the Hankel-Fourier method for

a discrete inverse Abel transform [130]. The deconvolution process allows a line of sight

integrated image to be converted to a two dimensional, infinitesimally thin slice of the

flame.

Initial image processing is the same for both time-averaged and phase-

synchronized images. A background image, i.e. an image of the combustor without the

flame, was taken and subtracted from each raw image. The flame is nearly axisymmetric,

55

so an inverse Abel transform is used to deconvolute the background subtracted images

using the Hankel-Fourier method. The result of the deconvolution process is an

infinitesimally thin, two dimensional slice of the flame referred to as an “emission

image.” Finally, each pixel is weighted by 2πr where r is the radial distance from the

centerline of the combustor. This weighted image is referred to as the “revolved image.”

Each pixel is weighted by its distance from the centerline to account for the fact that the

flame is three dimensional.

Figure 2.5 shows examples of stable, time averaged images at each stage of the

initial processing procedure. The images are presented in a pseudo color scale with cool

colors corresponding to low intensity and warm colors corresponding to high intensity.

Only the top half of the emission and revolved images are shown due to symmetry of the

image. The flow direction is from left to right.

a) b) c)

Figure 2.5: Examples of initial image processing; a) Background subtracted projection image; b)

Emission image; c) Revolved image. Colors indicate intensity, and are self-scaled for each image.

This is the final step for processing the time-averaged images. Additional steps

for the phase averaged images are explained in the following section. The phase

synchronized images require further processing.

Increasing intensity

56

2.3.3 Phase averaged image processing

For phase averaged images, a series of images are acquired over 1 second. Each

image pixel can be treated like an individual sensor, resulting in an intensity time series

for each pixel. The time series of each pixel is filtered at the frequency of the instability

and the mean, RMS fluctuations, and phase relative to the velocity oscillation are

calculated for each pixel. The values of these individual pixels can be displayed as mean,

fluctuation and phase images. Examples of each of these types of images are shown in

Figure 2.6.

a) b) c)

Low High -π π

Figure 2.6: Examples revolved a) Mean image; b) RMS fluctuation image; c) Phase image.

Colors bars are shown for each image; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, 0% pilot, Lcomb =

25 in., technically pre-mixed

A time series of the CH* chemiluminescence image is reconstructed from the

fluctuation and phase images using the following equation:

𝐶𝐻𝑖,𝑗∗ = 𝐶𝐻𝑖,𝑗

∗̅̅ ̅̅ ̅̅ + √2𝐶𝐻𝑖,𝑗∗ ′

∗ cos(2𝜋𝑓𝑡 + 𝜑𝑖,𝑗) (2.5)

Where CH* is the chemiluminescence intensity, f is the instability frequency, t is the

time, 𝜑 is the phase, the overbar indicates the mean value, the prime symbol indicates the

RMS fluctuation, and i and j are the row and column indices indicating the pixels location

in the image. An example of a reconstructed time series of images is shown in Figure 2.7.

100 200 300 400 500 600 700

50

100

150

200

100 200 300 400 500 600 700

50

100

150

200

57

Figure 2.7: Example of a series of phase averaged CH* chemiluminescence flame images

2.3.4 Flame image metrics

Flame metrics such as flame center of heat release CoHR, flame length Lf, flame

angle α, and flame width Wf, are used to characterize flame structure and have been

shown to have a strong effect on flame response [12, 77, 79]. These metrics are identified

from flame images and are labeled in Figure 2.8. This figure is a deconvoluted, r-

weighted time averaged, stable CH* chemiluminescence image. Only the top half of the

image is shown due to symmetry. The grey rectangles indicate the injector centerbody

and the dump plane.

Figure 2.8: Stable CH* chemiluminescence flame image indicating center of heat release (+),

flame length Lf, flame width Wf, and flame angle α; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, 0%

pilot, technically pre-mixed

The center of heat release represents where the majority of heat release occurs in

the flame. A black ‘+’ sign indicates the location of the center of heat release in Figure

0 30 60

90 120 150

180 210 240

270 300 330

Lf

Wf

58

2.8. The center of heat release is calculated using the equations for calculating the center

of mass where intensity is substituted for mass. Only the pixels within 10% of the

maximum intensity are considered. The equations for the center of heat release for the

radial, r, and axial, x, coordinates are given by the following equations:

𝑟𝐶𝑜𝐻𝑅 = ∑ 𝜀𝑖

′𝑟𝑖

𝑁

𝑖=1∑ 𝜀𝑖

′𝑁

𝑖=1⁄ (2.6)

𝑥𝐶𝑜𝐻𝑅 = ∑ 𝜀𝑖

′𝑥𝑖

𝑁

𝑖=1∑ 𝜀𝑖

′𝑁

𝑖=1⁄

(2.7)

where εi’ is the top 10% of the image intensity. This center of mass calculation is used

rather than simply the maximum image intensity because there may be several pixels

with equal or similar values or an abnormally high intensity in one pixel. Simply

choosing the maximum intensity could then give a misleading center of heat release

location. The flame length is defined as the distance from the edge of the centerbody

where the flame anchors to the center of heat release. This distance represents the

distance a disturbance must travel before interacting with region of highest heat release of

the flame. The flame angle is the angle between the horizontal and the line connecting the

edge of the centerbody to the center of heat release.

The flame width is calculated from the full width at half maximum of the intensity

profile at the radial center of heat release location. It characterizes the degree of

spreading of the flame along the combustor wall. All flames in this study interact with the

wall of the combustor.

59

Chapter 3

Combustor stability characteristics

The purpose of this study is to investigate self-excited, technically pre-mixed

combustion instabilities and the effect of a secondary pilot flame on reducing the

magnitude of these instabilities. Before investigating the pilot flame effect, this chapter

presents an investigation of the baseline combustor stability with no pilot flame. Section

3.1 summarizes the operating conditions investigated in this study. Section 3.2 presents

background information on the acoustics of the combustor to explain the plane wave

nature of the observed instabilities. Measurements of pressure oscillation magnitude in

the combustor and the corresponding oscillation frequencies are presented in Section 3.3.

In Section 3.4, experimental measurements of self-excited combustor instabilities are

compared to a simple acoustic model that predicts the natural frequencies of the

combustion system. The results of this chapter and their importance to the remainder of

this study are summarized in Section 3.6.

3.1 Experimental test conditions

Self-excited experiments were performed over the range of technically pre-mixed

operating conditions summarized in Table 3.1. Each operating condition was defined by

an inlet temperature Tin, a mean inlet velocity Uin, and an equivalence ratio ϕ. The inlet

velocity ranged from 30 m/s to 50 m/s. Inlet velocities below 30 m/s were avoided to

prevent the centerbody from overheating. At velocities above 50 m/s the flame tended to

blow off. The equivalence ratio was varied from 0.525 to 0.65. The equivalence ratio was

kept above ϕ = 0.525 to avoid the lean blowout limit. Above ϕ = 0.65, high combustor

60

temperatures caused the quartz window of the combustor to overheat. The inlet air

temperature was set to 250C, the highest inlet temperature that could be reached by the

heater used in this experimental set up. The variable length capability of test facility,

explained in detail in Section 2.1.4, allowed the combustor length to be varied from 25 in.

< Lcomb < 59 in. at increments of 1 in. for each operating condition. The minimum and

maximum combustor lengths were limited by the geometry of the test facility. Varying

the combustor length tuned the acoustics of the system to either excite or damp self-

excited instabilities. The instability frequency also changed with combustor length.

Table 3.1: Summary of self-excited, technically pre-mixed operating conditions

Parameters Self-excited test conditions

pressure, P 1atm

inlet temperature, Tin 250C

inlet velocity, Uin 30, 35, 40, 45, 50 m/s

equivalence ratio, ϕ 0.525, 0.55, 0.60, 0.65

combustor length, Lcomb 25 in. – 59 in., ΔLcomb = 1 in.

3.2 Longitudinal Modes

Before presenting the results of the combustor stability measurements, some

background information is given on the acoustics of the pressure oscillations observed in

this study. For the conditions investigated in this study, all resonant modes are

longitudinal. There are no radial or azimuthal modes excited at the operating conditions

listed in Table 3.1 in this test facility. The absence of non-longitudinal modes is

explained by considering the cutoff frequency associated with the combustor geometry.

The combustion system used in this experiment is made up of a series of ducts of circular

61

cross sections. The first non-longitudinal mode of a waveguide with circular cross section

occurs at the following frequency [131]:

𝑓𝑐𝑜 =

𝐽11

𝜋𝐷𝑐 (3.1)

where 𝑓𝑐𝑜 is the cutoff frequency, c is the speed of sound, D is the diameter of the

combustor section, and 𝐽11 is the zero value of the derivative of the Bessel function of the

first kind for the first non-planar mode. The lowest possible cutoff frequency occurs at

the largest diameter and the lowest speed of sound. The largest cross section of the test

rig is the quartz combustor section with an inner diameter of 0.15 m. The speed of sound

for an ideal gas mixture is given by:

𝑐 = √𝛾𝑚𝑖𝑥𝑅𝑢𝑇𝑖𝑛

𝑀𝑊𝑚𝑖𝑥 (3.2)

where 𝛾𝑚𝑖𝑥 is the specific heat ratio of the mixture, 𝑅𝑢 is the universal gas constant, 𝑇𝑖𝑛 is

the inlet temperature, and 𝑀𝑊𝑚𝑖𝑥 is the molecular weight of the mixture. Assuming the

mixture is composed entirely of air and methane, 𝛾𝑚𝑖𝑥 and 𝑀𝑊𝑚𝑖𝑥 are calculated from

the following equations:

𝛾𝑚𝑖𝑥 =

𝑥𝑐�̅�,𝐶𝐻4 + (1 − 𝑥)𝑐�̅�,𝑎𝑖𝑟

𝑥𝑐�̅�,𝐶𝐻4 + (1 − 𝑥)𝑐�̅�,𝑎𝑖𝑟 (3.3)

𝑀𝑊𝑚𝑖𝑥 = 𝑥𝑀𝑊𝐶𝐻4 + (1 − 𝑥)𝑀𝑊𝑎𝑖𝑟 (3.4)

where 𝑥 is the mole fraction of 𝐶𝐻4, 𝑐�̅� is the molar specific heat at constant pressure and

𝑐�̅� is the molar specific heat at constant volume. The value of 𝑥 depends on the

equivalence ratio.

For the operating conditions tested, the minimum speed of sound was calculated

to be approximately 460 m/s. For the 0.15 m diameter quartz combustor, this speed

62

corresponds to a cutoff frequency of approximately 1800 Hz. The instability frequencies

observed in the study are well below this frequency, indicating that only longitudinal

modes need to be considered.

3.3 Combustor Stability

The feedback loop that sustains a self-excited instability was discussed in Section

1.1. Varying the combustor length changes the acoustics of the system, which affects this

feedback loop. At stable combustor lengths, damping mechanisms dominate the driving

mechanisms, and an instability does not occur. However, over certain ranges of

combustor lengths, unstable heat release couples with a resonant mode of the combustor

to produce self-excited instabilities. For all of the operating conditions listed in Table 3.1,

at each combustor length, the stability of the combustor was characterized by measuring

oscillations in combustor pressure, pcomb, inlet velocity, Uin, and global

chemiluminescence intensity, ICH*. These parameters are related to the instability

feedback loop.

The following section presents the results of measurements of pressure

oscillations measured at the dump plane of the combustor. These measurements are used

to determine whether the combustor is stable or unstable at a given operating condition

and combustor length.

3.3.1 Stability map of combustor pressure

The spectrogram in Figure 3.1 presents the single sided power spectral densities,

SSPSD, of the combustor pressure oscillations for each combustor length at typical

operating condition. The process for calculating the SSPSD was explained in Section

2.2.4. In this figure, the x-axis indicates the combustor length and the y-axis indicates the

63

frequency of the pressure oscillation. The magnitude of the pressure oscillations are

shown using a color scale in which and warm colors indicate large amplitude oscillations

and cool colors indicate low amplitude oscillations.

This spectrogram illustrates the stability characteristics of the combustor, and

demonstrates the effect of combustor length on the magnitudes and frequencies of self-

excited combustor pressure fluctuations. At each combustor length, the turbulent nature

of the flow produces pressure oscillations across all frequencies, indicated by the color

values ranging from 90dB to 160dB. However, for each combustor length, a single,

preferred frequency tends to dominate. In Figure 3.1, large instabilities at preferred

frequencies are indicated by narrow bands of yellow or red. This dominant frequency is

determined by the operating condition and the geometry of the combustor. As the

combustor length varies from 25 in. < Lcomb < 59 in., both the preferred frequency and the

magnitude of the oscillations change due to changes in the acoustics of the system.

Figure 3.1: Stability map of combustor pressure oscillations; Tin = 250C, Uin = 45 m/s, ϕoverall =

0.55, 0% pilot, technically pre-mixed

Combustor Length [in.]

Fre

quency [H

z]

25 30 35 40 45 50 55100

200

300

400

500

600

700

800

900

1000

Com

busto

r P

ressure

Oscill

atio

n [dB

re 2

.9e-9

psi]

90

100

110

120

130

140

150

160

64

3.3.2 Maximum combustor pressure oscillation magnitude and frequency

In order to study self-excited instabilities and compare the stability of the

combustor across different operating conditions and combustor lengths, peak combustor

pressure oscillation magnitude and frequency are identified for each condition. The

stability map in Figure 3.1 shows that for each combustor length, a single frequency tends

to dominate the instability. This section explains how the peak frequency and

corresponding instability magnitude is identified from the single sided power spectral

density of combustor pressure oscillations. The validity of using this peak pressure

oscillation for characterizing the instability is demonstrated.

Figure 3.2 shows the single sided power spectral density for Lcomb = 25 in. for the

same example operating condition as the spectrogram in Figure 3.1. In this case, a very

strong peak occurs at a frequency of f = 173 Hz. The magnitude of the pressure

oscillations at f = 173 Hz is several orders of magnitude larger than the fluctuations at all

other frequencies, and the combustor stability is characterized by this frequency and the

RMS pressure oscillation at this frequency.

Figure 3.2: Single sided power spectral density for combustor length Lcomb = 25 in.; Tin = 250C,

Uin = 45 m/s, ϕoverall = 0.55, 0% pilot, technically pre-mixed

0 1000 2000 3000 40000

0.01

0.02

0.03

0.04

0.05

Frequency [Hz.]

Am

plitu

de

[psi

/p

Hz]

65

Similar instability maxima and dominant frequencies were observed for all

combustor lengths. Peaks were identified in the single sided power spectral densities for

all combustor lengths. Figure 3.3a shows the frequencies of the maximum combustor

pressure oscillations for each combustor length. Figure 3.3b compares the RMS (root

mean square) combustor pressure oscillations at these peak frequencies (solid circle

markers) with the total RMS combustor pressure oscillations (open square markers)

across all frequencies for each combustor length. The total pressure oscillations follow

the same trends as the peak oscillations, with maxima and minima occurring at the same

combustor lengths. The magnitudes of pressure oscillations are also similar, indicating

that most of the energy in the oscillations is contained at the peak frequency. Figure 3.3c

shows the ratio between the RMS pressure oscillations at the peak frequency and the total

RMS pressure oscillations. For conditions where large pressure oscillations occur, over

90% of the total RMS fluctuations occurred at the peak frequency. At conditions where

the oscillations are weak, the percent of the oscillation energy contained within a single

frequency drops to as low as 30%. At these stable conditions, the pressure oscillations are

distributed over a wider range of frequencies, resulting in a lower percentage of the total

energy occurring at a single frequency.

The results presented in this section demonstrate that a single frequency tends to

dominate the self-excited response at a given operating condition and combustor length.

This dominant frequency will therefore be used to characterize the combustor stability

throughout the remainder of this study.

66

Figure 3.3: a) Frequency of the maximum pressure oscillation magnitude; b) Comparison of the

peak (solid circles) and total (open squares) RMS pressure oscillation magnitude; c) Ratio of peak

to total RMS pressure oscillations; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525, 0% pilot, technically

pre-mixed

25 30 35 40 45 50 55 60150

200

250

300

350

400

450


Fre

quen

cy [

Hz]

25 30 35 40 45 50 55 600

1

2

3

4


p /p

mea

n [%

]

25 30 35 40 45 50 55 600

20

40

60

80

100


p pe

ak/p to

tal [

%]

67

3.3.3 Effect of combustor length on instability frequency

Figure 3.3a shows that over certain ranges of combustor lengths, the instability

frequency varies slightly with increasing combustor length. This variation is expected

because the combustor length affects the acoustics of the system. For example, over the

ranges 25 in. < Lcomb < 34 in. and 35 in. < Lcomb < 53 in. the frequency decreases with

combustor length which is expected since the resonant longitudinal mode of a tube tends

to decrease with increasing length.

However, the combustor is made up of many acoustic elements, so the resonant

frequencies and mode shapes are not simply proportional to the length of the combustor.

While the instability frequencies show small, gradual change over relatively small ranges

of combustor lengths, abrupt jumps in the frequency are also observed. For example, the

plot of frequency in Figure 3.3a shows a large jump in frequency between a lower

frequency instability when Lcomb = 32 in. and high frequency instability when Lcomb = 33

in. For Lcomb < 32 in., the instability frequency is approximately 170 Hz. At Lcomb = 33

in., the frequency jumps to 445 Hz. Sudden jumps in the instability frequency likely

occur due to a switch in the resonant mode of the combustor.

Investigating the acoustics of the combustion test facility will provide insight into

the resonant modes of the combustor. The acoustics of the test facility are investigated

using an acoustic network model. The next section explains the acoustic model and

compares the model results with the experimental results presented in this section.

3.4 Acoustic model of the combustion test facility

The instability feedback loop discussed in Section 1.1 explains how the acoustics

of the combustion system couple with the flow field and heat release oscillations in the

68

flame to produce a self-excited instability. The frequencies of the self-excited instabilities

should be similar to the natural frequencies of the system because of this coupling with

the system acoustics. Dowling and Stow [10] explain how a combustion system can be

modeled as a series of ducts of uniform area and flow properties. In this acoustic model,

the disturbance is linearized and one-dimensional. The complex amplitude of the pressure

and volume velocity is given by:

�̂�(𝑥) = 𝐴𝑒𝑥𝑝(−𝑖𝑘+𝑥) + 𝐵𝑒𝑥𝑝(𝑖𝑘−𝑥) (3.5)

�̂�(𝑥) = (𝑆/𝜌𝑐)[𝐴𝑒𝑥𝑝(−𝑖𝑘+𝑥) − 𝐵𝑒𝑥𝑝(𝑖𝑘−𝑥)] (3.6)

where A and B are constants, and S is the cross-sectional area of a duct. The

wavenumbers, 𝑘+ and 𝑘−, are defined as:

𝑘+ = 𝜔 (𝑐 + 𝑈𝑜)⁄

(3.7a)

𝑘− = 𝜔 (𝑐 − 𝑈𝑜)⁄

(3.7b)

where ω is the frequency, c is the speed of sound, and Uo is the mean velocity.

Figure 3.4 shows how the relatively complicated combustion test facility

geometry was simplified into a series of ducts to model the acoustics of the combustor.

The choked inlet and end plug were modeled as closed end boundary conditions. The

acoustic pressure and volume velocity are continuous across the junction of two ducts, so

a pressure and velocity matching condition is applied to the boundary between two ducts.

The duct temperature affects the natural frequencies of the combustion system through

both the speed of sound c and the density ρ of the mixture. The temperature is equal to

the preheated inlet temperature Tin from the Inlet section to the Injector section. At the

Quartz Combustor section, the temperature increases to the adiabatic flame temperature

69

Tad. This combustor temperature assumes there is no heat transfer across the boundary of

the combustor and the temperature profile is constant throughout the combustor.

Figure 3.4: Schematic of the combustion test facility and corresponding duct sections used to

model the acoustics of the system

The first two ducts, Section 1 (Inlet) and Section 2 (Plenum), are used as an

example to demonstrate how the equations for the acoustic pressure and volume velocity

of each section are used to solve for the natural frequencies of the system. An impedance

boundary condition is applied to the end of Section 1 at x1 = 0. From the definition of

acoustic impedance, 𝑍 = �̂� 𝑆�̂�⁄ , and substituting Equations (3.5) and (3.6) results in the

following equation:

𝑍1 =

𝐴1𝑒𝑥𝑝(−𝑖𝑘1+𝑥1) + 𝐵1𝑒𝑥𝑝(𝑖𝑘1

−𝑥1)

(𝑆1/𝜌1𝑐1)[𝐴1𝑒𝑥𝑝(−𝑖𝑘1+𝑥1) − 𝐵1𝑒𝑥𝑝(𝑖𝑘1

−𝑥1)] (3.8)

Rearranging Equation (3.8) leads to:

𝐴1 (

𝑆1𝑍1

𝜌1𝑐1− 1) + 𝐵1 (

−𝑆1𝑍1

𝜌1𝑐1− 1) = 0

(3.9)

The Sections 1 and 2 are connected at x1 = L1 / x2 = 0. The resulting equations at

this boundary are:

70

𝐴1𝑒𝑥𝑝(−𝑖𝑘1

+𝐿1) + 𝐵1𝑒𝑥𝑝(𝑖𝑘1+𝐿1) − 𝐴2 − 𝐵2 = 0

(3.10)

𝐴1

𝑆1

𝜌1𝑐1𝑒𝑥𝑝(−𝑖𝑘1

+𝐿1) + 𝐵1

−𝑆1

𝜌1𝑐1𝑒𝑥𝑝(𝑖𝑘1

+𝐿1) + 𝐴2

−𝑆2

𝜌2𝑐2+ 𝐵2

𝑆2

𝜌2𝑐2= 0

(3.11)

A similar analysis conducted on the remaining ducts results in a set of 2n

equations in 2n unknowns, where n is the number of duct sections. These equations can

be rewritten in matrix from as [M]x = 0 where x is a vector of the coefficients A and B.

Solving det([M]) = 0 results in the frequencies that solve the system of equations. A

program developed by Scarborough et al. was used to solve for the natural frequencies of

the combustion facility used in this study.

Figure 3.5 shows the results of this acoustic model compared to the actual

frequencies measured experimentally in this study for a typical operating condition. The

first three modes predicted by the model are shown in dashed lines and the frequencies

obtained from experiments are shown with ‘x’ symbols. For combustor lengths from 25

in. < Lcomb < 50 in., the model accurately predicts the frequency of the instability. The

low frequency instability that occurs for short combustor lengths Lcomb < 30 in.

corresponds to the first mode predicted by the model. The predicted frequencies for this

range of combustor lengths are within 10 Hz of the experimentally measured values. The

high frequency instability that occurs from 30 in. < Lcomb < 52 in. corresponds to the

second mode predicted by the model.

This model is less successful for predicting the instability frequency for the longer

range of combustor lengths investigated in this study, Lcomb > 50 in. In this simple model

the temperature throughout the entire combustor is assumed to be the adiabatic flame

temperature. Heat transfer across the combustor walls as well as cooling of the variable

71

length plug will create a more complicated temperature distribution in the combustor.

This temperature profile becomes more important as the combustor length increases

because there is a greater length over which heat transfer occurs. However, detailed

measurements of the temperature distribution within the combustor were out of the scope

of this study.

While this model does not fully capture the resonant mode of the combustor for

long combustor lengths, it does demonstrate that there are different resonant modes

associated with the combustor. The frequency of the instability depends on which mode

is excited at a particular combustor length. The presence of these various resonant modes

explains why large jumps in the instability frequency were observed in experiments.

Figure 3.5: Comparison of natural frequencies predicted by the acoustic model (dashed lines) and

the measured instability frequencies (‘x’ markers); Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, 0%

pilot, technically pre-mixed

3.5 Acoustic mode shapes

For each combustor length, each predicted resonant frequency has an associated

mode shape. The pressure mode shape is calculated using the following equations [10]

25 30 35 40 45 50 55 60100

200

300

400

500

600

700

Combustor Length [in]

Fre

quency [H

z]

72

�̂�(𝑥) = 𝐴𝑠𝑖𝑛[(2𝑛 − 1)𝜋𝑥/2𝑙] (3.12)

where A is an arbitrary constant. Mode shapes are useful in understanding the

experimentally observed instability frequencies [10, 132]. Nodes and antinodes can be

identified from the mode shape plots. For example, if a pressure node occurs at the flame

location, the flame will not amplify the instability and an instability will not occur at this

frequency.

The first three mode shapes predicted by the acoustic model for a combustor

length Lcomb = 25 in. are shown in Figure 3.6. The x-axis shows the axial location in the

test facility and the y-axis shows the relative amplitude of the pressure oscillations. Each

section of the combustor is labeled in the plot. The flame location indicates the flame

length determined from the stable flame image (see Chapter 5 for more information on

determining stable flame length). Figure 3.6a and Figure 3.6c show the flame is located

near relative peaks in pressure oscillation magnitude for the first and third modes,

respectively, while Figure 3.6b indicates a pressure node at the flame location for the

second mode. These results suggest the second mode will not be amplified because of the

presence of the pressure node at the flame.

The flame response will determine whether the first or third modes will dominate.

Flames tend to act as low-pass filters, where the flame transfer function gain generally

decays with increasing perturbation frequency for both velocity [4, 12, 20, 23, 74, 77]

and fuel flow rate oscillations [85]. Therefore it is expected that the flame is more likely

to amplify the first, lower frequency mode. In this case, the first mode shown in Figure

3.6a is, in fact, the dominant frequency observed experimentally. However, caution must

be taken in assuming that a lower frequency instability will be the dominant mode,

particularly with technically pre-mixed flames. Velocity and equivalence ratio

73

oscillations may interact constructively or destructively [80, 89, 92], depending on the

phase of the disturbance, so the lower frequency mode may not necessarily dominate.

Further work is required to investigate the technically pre-mixed flame response and

incorporate the flame response into this acoustic model. However, this is left to future

work.

a)

b)

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

Axial location [m]

Am

plit

ude

Injector Plenum

Injector Combustor

Flame

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

Axial location [m]

Am

plit

ude

Injector

Flame

CombustorPlenum Injector

Inlet

Inlet

74

c)

Figure 3.6: Mode shapes predicted by acoustic model; a) Mode 1, 167 Hz; b) Mode 2, 457 Hz;

Mode 3, 646 Hz; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, 0% pilot, technically pre-mixed

3.6 Conclusions

The stability of the combustion test facility was investigated over a range of

operating conditions and combustor lengths. The acoustic modes were shown to be

longitudinal, and the resonant modes of the combustor were predicted using an acoustic

network model. For each combustor length, combustor pressure oscillations were

measured and the dominant pressure oscillation frequencies and magnitudes were

identified. The dominant frequencies were shown to be related to the resonant acoustic

modes of the combustor predicted by the acoustic model.

Plots of the RMS pressure oscillation magnitude at the dominant frequency allow

stable and unstable conditions to be identified. Regions of very strong self-excited

combustion instabilities can be observed from the pressure oscillation magnitudes plotted

in Figure 3.3b. Clear maxima in pressure oscillations can be observed at Lcomb = 25 in.,

36 in., 45 in., and 59 in. Due to the changes in the system acoustics as the combustor

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

Axial location [m]

Am

plit

ude

CombustorPlenumInjector InjectorFlame

Inlet

75

length varies, the frequency associated with these instabilities is different for each

maximum.

The investigation of the effect of pilot flame on self-excited technically pre-mixed

instabilities discussed in the remainder of this study will focus on the effects of a pilot

flame on regions of large amplitude oscillations across a range of operating conditions.

The effectiveness of the pilot flame is characterized by the reduction of the combustor

pressure oscillation magnitude caused by the pilot flame. The pilot flame effect will be

considered weak if the combustor is still unstable when the pilot flame is present.

76

Chapter 4 Pilot flame effect on

technically pre-mixed, self-excited combustion instabilities

In industrial gas turbine combustors, fuel is typically injected into a main passage

where it mixes with air before entering into the combustor and producing a flame. In

addition to this main flame, many injector designs include an additional fuel passage for a

secondary flame known as a “pilot flame”. This pilot flame can be turned on during

operation to help eliminate self-excited instabilities. While pilot flames are known to

affect self-excited combustion instabilities, the underlying mechanisms that cause a pilot

flame’s effect are not well understood.

This chapter presents the results of a detailed study of the effects of a pilot flame

on the technically pre-mixed, self-excited combustion instabilities introduced in Chapter

3. Background information on the injector geometry and pilot flame configuration is

provided in Section 4.1. Measurements of combustor pressure fluctuations for several

self-excited, technically pre-mixed operating conditions are presented in Section 4.2. The

effect of pilot flame intensity is investigated in Section 4.3. When operating with a pilot

flame, the main flame equivalence ratio is lowered in order to maintain a constant overall

equivalence ratio. The effect of the main flame equivalence ratio on the pilot flame effect

is discussed in Section 4.4. Results from this chapter show the pilot flame is an effective

method for eliminating or reducing instabilities only in certain cases. The reduction in the

magnitude of a self-excited instability by the pilot is strongly dependent on both the

operating condition and the instability mode.

77

4.1 Injector geometry and pilot flame configuration

A schematic of the injector used in this study, including the main and pilot

pathways and the location of the main and pilot flames, is shown in Figure 4.1. The

location of the pilot fuel injection influences how well the pilot stabilizes the main flame

[122]. In this study, the pilot fuel passage is located within the centerbody, and air and

fuel exit the pilot passage along the centerline of the combustor. The resulting pilot flame

is located in the center of the combustor, surrounded by the main flame produced by the

mixture of fuel and air exiting the injector from the main, annular passage.

Figure 4.1: Injector schematic indicating the location of main and pilot paths and flames

The amount of air sent through the pilot passage, approximately 5% of the total

air flow, is constant. It is determined by the injector design and cannot be varied. The

flow rate of pilot fuel is adjusted to control the intensity of the pilot flame. Typically,

when operating with a pilot flame, fuel is diverted from the main flame to the pilot in

order to keep the overall equivalence ratio, ϕoverall, constant. The equivalence ratio of the

main flame is then slightly lower when running with a pilot flame than it is when running

without. The intensity of the pilot flame is expressed in terms of the percent of the total

fuel diverted from the main flame to the pilot. For example, in this study, a typical pilot

78

intensity level is 6.5%, a condition commonly used in industry because the equivalence

ratio of the pilot is approximately equal to the equivalence ratio of the main flame. This

pilot intensity means that 6.5% of the total fuel enters the combustor through the pilot

fuel path. While most cases investigated in this study use 6.5% pilot, the amount of pilot

fuel can be varied to adjust the intensity of the pilot flame. As the intensity of the pilot

flame increases, so does the equivalence ratio of the pilot flame, leading to higher

temperatures and increased NOx production. This is why pilot flame intensity is not

typically higher than 6.5% for this injector under actual industrial operation.

4.2 The effect of pilot flame on self-excited instabilities at various operating conditions

4.2.1 Defining unstable combustor regions

Figure 4.2a and Figure 4.2b show the magnitudes and frequencies of combustion

instabilities for a typical operating condition without a pilot and with a 6.5% intensity

pilot flame over combustor lengths from 25 in. < Lcomb < 59 in. This pilot intensity was

chosen because it was shown to have a strong effect in certain cases, and it is an intensity

commonly used in actual gas turbine applications. 6.5% pilot is considered a “neutral

pilot” because the equivalence ratio of the pilot flame is approximately equal to the main

flame.

For the operating condition shown in Figure 4.2b, the instability frequencies

remain similar (within 6 Hz at peak instability frequencies) in the unpiloted and piloted

cases, indicating that the pilot flame does not change the acoustics of the system. While

the instability frequencies are not affected by the pilot flame, the addition of the pilot

flame does tend to affect the magnitudes of the self-excited instabilities. Four regions of

large amplitude combustor pressure oscillations are observed in the case without a pilot

79

flame, shown in blue circles. These four instabilities, referred to as Instabilities I, II, III,

and IV are labeled in Figure 4.2.

Due to changes in the system acoustics caused by varying the combustor length,

each of these unstable regions corresponds to a different instability frequency. Instability

I is a low frequency instability that occurs over the shortest combustor lengths tested. The

magnitude of the instability is highest at the shortest combustor length tested and

gradually decreases as combustor length increases. For the operating condition shown in

Figure 4.8, the shortest combustor length tested is Lcomb = 25 in., and the corresponding

frequency is 170 Hz.

As the combustor length increases, the instability frequency decreases, which is

expected when the length of an acoustic element increases. At a combustor length of

Lcomb = 31 in., an abrupt jump in frequency occurs, indicating a change in the resonant

mode of the combustor. The various instability modes of the combustor are explained in

greater detail in Chapter 3. The change in the instability mode marks a transition from

Instability I to Instability II. Instability II is a higher frequency mode. It reaches a peak at

Lcomb = 32 in. with a frequency of 450 Hz. The next peak in combustor pressure

oscillations, Instability III, occurs at Lcomb = 42 in., and has a frequency of 370 Hz.

Finally, Instability IV occurs at the longest range of combustor lengths tested. The

instability magnitude reaches a maximum at the longest combustor length tested. In this

case, the combustor length Lcomb = 59 in. and the frequency of the instability is 220 Hz.

The effect of the pilot flame is observed to vary with the instability frequency. For

Instabilities I, II, and III, the large amplitude pressure oscillations are eliminated with

6.5% pilot, but Instability IV still exists. The effect of 6.5% pilot flame on self-excited

80

instabilities is investigated over a range of operating conditions to determine whether the

effects observed for the operating condition shown in Figure 4.2 are consistent as inlet

velocity and equivalence ratio vary. The following sections compare the peak of each of

the four instabilities without and with 6.5% pilot flame. The effect of equivalence ratio,

inlet velocity, and instability mode are considered.

a)

b)

Figure 4.2: a) Peak combustor pressure fluctuations and b) corresponding frequencies

Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55; 0% pilot, 6.5% pilot

25 30 35 40 45 50 55 600.0

1.0

2.0

3.0

4.0


p/

pm

ean [

%]

25 30 35 40 45 50 55 600.0

1.0

2.0

3.0

4.0


p/

pm

ean [

%]

0% pilot

6.5% pilot

25 30 35 40 45 50 55 60150

200

250

300

350

400

450

500


Fre

quency [

Hz]

25 30 35 40 45 50 55 60150

200

250

300

350

400

450

500


Fre

quency [

Hz]

I

II

III

IV

81

4.2.2 Instability I

For Instability I, the maximum values of combustor pressure fluctuations were

achieved at the shortest combustor length tested. Therefore, the instabilities presented in

Figure 4.3 are for the shortest combustor length tested for each operating condition at

which this instability occurred. Combustor pressure fluctuations are plotted against inlet

velocity in Figure 4.3a) and against the corresponding instability frequency in Figure 4.3

b). Without the pilot flame, this instability tends to be largest for the frequency range

from 160 Hz and 170 Hz. For low equivalence ratios, this frequency range is reached at

higher velocities, whereas at higher equivalence ratios, this frequency corresponds to

lower velocities. This explains why the magnitude of this instability increases with

increasing velocity at low equivalence ratios and decreases with increasing velocity at

high equivalence ratios. It also explains why the low instability magnitude is lowest in

the highest equivalence ratio case, ϕoverall = 0.65, and why the instability was not observed

at this equivalence ratio for velocities greater than Uin = 40 m/s.

The pilot flame is very successful at reducing the magnitude of this instability.

The effect of the pilot flame tends to increases as velocity increases. For example, in the

lowest equivalence ratio case, ϕoverall = 0.525, the pilot flame only reduces the pressure

fluctuations from 1.21% to 0.94% when Uin = 35m/s. However, when the velocity is

increased to Uin = 50m/s, the unpiloted pressure fluctuations reach a maximum value of

1.47%, while the piloted pressure fluctuations reach a minimum value of 0.08%.

In the higher equivalence ratio cases, ϕoverall = 0.60 and ϕoverall = 0.65, the

magnitude of the instability without pilot decreases at high velocities, so the absolute

value of the difference in magnitude between the unpiloted and piloted cases decreases,

but the pilot still successfully eliminates the instability. For example, when ϕoverall = 0.60

82

and Uin = 30m/s, the pilot flame has the smallest effect, reducing the instability from

1.05% to 0.68%. The pilot effect becomes much stronger at the next higher inlet velocity

tested, Uin = 35m/s. In this case, the instability is reduced from 1.00% to 0.14% with the

pilot flame. At Uin = 45m/s, the instability frequency is 180 Hz, well above of the highly

unstable 160-170 Hz range. At this increased velocity and high instability frequency, the

magnitude of the unpiloted instability is 0.47%. With the pilot flame, the instability is

reduced to 0.17%. Although the magnitude of this reduction is not as great as for Uin =

35m/s, the pilot still successfully reduces this instability from a magnitude that would be

considered unstable to a magnitude that is considered stable.

a) b)

Figure 4.3: Instability I combustor pressure oscillations vs a) inlet velocity and b) frequency;

Tin = 250C; ϕoverall = 0.525, ϕoverall = 0.55, ϕoverall = 0.60, ϕoverall = 0.65

0% pilot cases: Filled shapes, solid lines; 6.5% pilot cases: Open shapes, dashed lines

4.2.3 Instability II

Instability II occurs when the combustor length is between 29 in. < Lcomb < 36 in.

This instability does not occur for all operating conditions. It tended to become stronger

as equivalence ratio increased, and was not observed at low inlet velocities for the lower

equivalence ratios tested. Lower equivalence ratios correspond to a longer flame length.

A longer flame length combined with a lower inlet velocity results in a longer convective

30 35 40 45 500.0

0.5

1.0

1.5

Uin

[m/s]

p/

pm

ean [

%]

30 35 40 45 500.0

0.5

1.0

1.5

Uin

[m/s]

p/

pm

ean [

%]

155 160 165 170 175 1800.0

0.5

1.0

1.5

Frequency [Hz]

p/

pm

ean [

%]

155 160 165 170 175 1800.0

0.5

1.0

1.5

Frequency [Hz]

p/

pm

ean [

%]

83

time for a disturbance to reach the flame. The response of a flame to a disturbance is

dependent on the associated convection time, and the convection time for the lower

equivalence ratios and inlet velocities may not excite Instability II. The calculation of

convective time is discussed in greater detail in Section 2.3.4. Convection time based on

stable flame length for all operating conditions is shown in Figure 4.4. All operating

conditions contained within the black box excite Instability II while conditions with

convective times above approximately 2.5ms do not. The addition of a 6.5% pilot flame

does not have a significant effect of the convective time for these operating conditions.

The pilot flame effect is therefore not due to a change in convective time caused by the

presence of the pilot flame.

Figure 4.4: Convective time vs inlet velocity for all operating conditions; Black box indicates

operating conditions at which Instability II occurred;



Figure 4.5 shows the peak of Instability II versus inlet velocity and instability

frequency for all operating conditions, both without and with 6.5% pilot flame. This

30 35 40 45 501.5

2.0

2.5

3.0

3.5

4.0

Inlet Velocity [m/s]

Convective t

ime [

ms]

30 35 40 45 501.5

2.0

2.5

3.0

3.5

4.0

Inlet Velocity [m/s]

Convective t

ime [

ms]

84

instability corresponds to frequencies between 435 Hz and 510 Hz. The difference in the

instability frequency compared to Instability I indicates a switch in the instability mode.

For this instability, the pilot flame has a very strong effect when the equivalence

ratio is low. For the two lowest equivalence ratio cases, ϕoverall = 0.525 and ϕoverall = 0.55,

the instability is eliminated with the addition of the pilot flame. However, for higher

equivalence ratios, the pilot flame does not eliminate the instability. The influence of

equivalence ratio on the effect of the pilot flame is illustrated by considering cases where

the inlet velocity Uin = 50m/s. In the lowest equivalence ratio case, ϕoverall = 0.525, the

pressure fluctuations are reduced from 4.22% to 0.17%. When the equivalence ratio

increases to ϕoverall = 0.55, the unpiloted pressure fluctuations increase to 5.2%. However,

the pilot still eliminates the instability, reducing the fluctuations to 0.34%. In the next

highest equivalence ratio case, ϕoverall = 0.60, the unpiloted pressure fluctuations further

increase to 7.35%. In this case, the pilot flame only reduces the instability to 4.97%.

Similarly for ϕoverall = 0.65, the unpiloted instability magnitude increase to 7.74%, and the

pilot flame only reduces the magnitude of the fluctuations to 6.31%. These results show

that not only does the pilot fail to eliminate the instability in the two highest equivalence

ratio cases, but the magnitude of the reduction of the instability also decreases as

equivalence ratio increases.

85

a) b)

Figure 4.5: Instability II combustor pressure oscillations vs a) inlet velocity and b) frequency;



4.2.4 Instability III

A third instability peak with frequencies ranging from 320 Hz to 375 Hz occurs

when the combustor length is increased to 35 in. < Lcomb < 55 in. The maximum

combustor pressure fluctuations for Instability III are plotted against the inlet velocity and

corresponding frequency in Figure 4.6a and Figure 4.6b. Unlike Instability II which

increased with increasing inlet velocity and equivalence ratio, the magnitude of this

instability tends to decrease with increasing inlet velocity and equivalence ratio. As with

Instability II, this dependence on velocity and equivalence ratio suggests convective time

is important to exciting this instability. This instability occurs for operating conditions

with convective times above approximately 2.5 ms, as shown in Figure 4.4.

Similar to Instability II, the pilot is most effective for lower equivalence ratios.

As the equivalence ratio increases, the effect of the pilot flame is reduced. For example,

in the lowest equivalence ratio case, ϕoverall = 0.525, when the inlet velocity is Uin = 30

m/s, the pilot flame reduces the magnitude of the self-excited instability from 4.26% to

1.85%. As the inlet velocity increases, the magnitude of the unpiloted instability

35 40 45 500.0

2.0

4.0

6.0

8.0

Uin

[m/s]

p/

pm

ean [

%]

35 40 45 500.0

2.0

4.0

6.0

8.0

Uin

[m/s]

p/

pm

ean [

%]

420 440 460 480 500 5200.0

2.0

4.0

6.0

8.0

Frequency [Hz]

p/

pm

ean [

%]

420 440 460 480 500 5200.0

2.0

4.0

6.0

8.0

Frequency [Hz]

p/

pm

ean [

%]

86

decreases. The instability is lowest when the inlet velocity is Uin = 50 m/s. The pilot

continues to successfully reduce the instability magnitude as velocity increases. When Uin

= 50 m/s, the magnitude of the instability is reduced from 1.43% to 0.18%. Although the

magnitude of this reduction is smaller than in the Uin = 30 m/s, the pilot flame does not

have to reduce the instability by as much to achieve a stable flame.

When the equivalence ratio is increased to ϕoverall = 0.55, the unpiloted instability

at an inlet velocity of 30 m/s is 5.52%, which is higher than the ϕoverall = 0.525 case. The

pilot flame only reduces this instability to 3.83%. This is a reduction of 1.69 compared to

a reduction of 2.41 for ϕoverall = 0.525. For the highest equivalence ratio case, ϕoverall =

0.65, and the lowest velocity tested at this equivalence ratio, Uin = 35m/s, the pilot flame

only reduces the instability from 1.77% to 1.68%. This reduction in the magnitude of the

pressure oscillations is negligible.

a) b)

Figure 4.6: Instability III combustor pressure oscillations vs a) inlet velocity and b) frequency;



4.2.5 Instability IV

The final instability occurred at the longest combustor lengths tested, Lcomb > 55

in. with frequencies ranging from190 Hz to 250 Hz. As with Instability I, test facility

30 35 40 45 500.0

1.0

2.0

3.0

4.0

5.0

6.0

Uin

[m/s]

p/

pm

ean [

%]

30 35 40 45 500.0

1.0

2.0

3.0

4.0

5.0

6.0

Uin

[m/s]

p/

pm

ean [

%]

320 340 360 3800.0

1.0

2.0

3.0

4.0

5.0

6.0

Frequency [Hz]

p/

pm

ean [

%]

320 340 360 3800.0

1.0

2.0

3.0

4.0

5.0

6.0

Frequency [Hz]

p/

pm

ean [

%]

87

geometry prevented a clear maximum from being achieved, so the results reported in

Figure 4.7 are for the longest combustor length tested for each operating condition. The

longest combustor length corresponded to the maximum observed pressure oscillations

for this instability. The results in Figure 4.7 show the maximum magnitude of the

pressure fluctuations at all operating conditions for which this instability occurred. The

instability tends to become worse as the velocity and equivalence ratio increase. In

general, the pilot flame has very little effect on this instability.

In some cases, particularly at low velocities and at low equivalence ratios, there is

a slight reduction in the instability magnitude with the pilot flame. For example, for

ϕoverall = 0.525 and Uin = 30 m/s, the pilot reduces the instability magnitude from 1.38% to

0.83%. However, as velocity and equivalence ratio increases, the effect of the pilot flame

decreases. When the equivalence ratio is kept at ϕoverall = 0.525 and the inlet velocity is

increased to Uin = 50 m/s, both the unpiloted and piloted pressure fluctuations are worse

than in lower velocity case. The unpiloted instability magnitude is 3.06% while the

piloted magnitude is 3.07%. This 0.01% difference is not significant. Similarly, for the

highest equivalence ratio case, ϕoverall = 0.65 and lowest velocity at this equivalence ratio,

Uin = 35 m/s, the pilot flame only reduces the magnitude of the pressure oscillations from

2.27% to 2.09%. This reduction in the instability is small compared to the ϕoverall = 0.525

case with the same inlet velocity.

88

a) b)

Figure 4.7: Instability IV combustor pressure oscillations vs a) inlet velocity and b) frequency;



4.3 The effect of pilot flame intensity on self-excited instabilities

The results presented so far in this chapter have only addressed the effect of a

6.5% pilot flame. However, studies such as Steele et al. [106] have shown the pilot flame

intensity affects the magnitude of combustor pressure oscillations. This section

investigates the effect of pilot flame intensity for the current combustion test facility.

Combustor pressure fluctuations were measured over a range of combustor lengths with

pilot flame intensity ranging from 0% to 12%. The effects of pilot flame intensity on self-

excited combustion instabilities for two operating conditions are discussed.

4.3.1 Case 1: Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55

Figure 4.8a and Figure 4.8b show the magnitudes and frequencies, respectively,

of these combustor pressure fluctuations for a typical self-excited, technically pre-mixed

operating condition. The pilot flame has a different effect on the instability depending on

the frequency of the instability and the pilot intensity.

For example, Instability I gradually decreases in magnitude as the pilot flame

intensity increases. With 6.5% pilot, the large combustor pressure fluctuations are

30 35 40 45 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Uin

[m/s]

p/

pm

ean [

%]

30 35 40 45 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Uin

[m/s]

p/

pm

ean [

%]

180 200 220 240 2600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Uin

[m/s]

p/

pm

ean [

%]

180 200 220 240 2600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Uin

[m/s]

p/

pm

ean [

%]

89

reduced to 0.15%, an amplitude low enough to be considered stable. Instabilities II and

III, on the other hand, require as little as 3% pilot to eliminate the instability.

The pilot flame does not have a strong effect on the magnitude of Instability IV.

Strong instabilities exist with as much as 12% pilot. This pilot intensity creates a rich

pilot flame and would likely not be used in industry due to increased NOx emissions, and

was used in this study simply to demonstrate the effect of a very strong pilot rather than a

realistic operating condition. Despite this unrealistically high intensity pilot, the large

amplitude instability still persists. Instability IV demonstrates that conditions exist where

the pilot flame does not effectively reduce the magnitude of the self-excited instability.

a)

25 30 35 40 45 50 55 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


Fre

quency [

Hz]

25 30 35 40 45 50 55 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


Fre

quency [

Hz]

0%

3%

4%

5%

6.5%

12%I

II

III

IV

90

b)


Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55

0% pilot, 3% pilot, 4% pilot, 5% pilot, 6.5% pilot, x 12% pilot

4.3.2 Case 2: Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60

Results presented in the previous section showed varying the instability frequency

as well as the pilot flame intensity changed the ability of the pilot flame to reduce the

magnitude of a self-excited instability. This section investigates how operating condition

changes the effectiveness of the pilot flame. Figure 4.9 shows the maximum combustor

pressure oscillations and corresponding frequency for a different operating condition than

that shown in Figure 4.8. For this operating condition, the inlet velocity is decreased to

Uin = 40 m/s and the overall equivalence ratio is increased to φoverall = 0.60. Changing the

operating condition changes the stability of the combustor through various mechanisms.

For example, an increase in temperature due to increased equivalence ratio changes the

speed of sound which then changes the instability frequency. In addition, both inlet

velocity and equivalence ratio affect the flame length. Flame length and inlet velocity

both affect the convective time for disturbances in the flow field to reach the flame. The

25 30 35 40 45 50 55 60100

200

300

400

500

600

700


p/

pm

ean [

%]

25 30 35 40 45 50 55 60100

200

300

400

500

600

700


p/

pm

ean [

%]

91

convective time strongly affects a flame’s response to a disturbance. The differences in

the combustor stability caused by operating condition can be observed by comparing the

instability magnitudes and frequencies without a pilot flame presented in Figure 4.8 and

Figure 4.9.

While the frequencies of these instabilities are within approximately 10 Hz for the

operating conditions shown in Figure 4.8 and Figure 4.9, the pilot flame does not affect

these instabilities the same. In contrast with the operating condition from Figure 4.8, the

case in Figure 4.9 shows the pilot has a much stronger effect on the low frequency

instability that occurs for Lcomb < 30 in. For the case shown in Figure 4.8, a pilot flame

with 4% intensity only decreases the magnitude of the instability from 1.54% to 1.24%,

but for the case shown in Figure 4.9 the instability which occurs at Lcomb = 25 in. is

reduced from 1.05% to .033%. However, the high frequency instability that occurs from

30 in. < Lcomb < 35 in. requires a pilot intensity of as much as 8% to eliminate the

instability. In the previous case, only 3% pilot was required to eliminate this instability.

Several factors are affected by the change in operating condition which may

influence the pilot flame effect. Increasing the equivalence ratio leads to lead to higher

intensity pilot flames which produce hotter products with a higher concentration of

radicals. Higher temperatures and increased concentration of radicals should improve

flame anchoring, but increasing the equivalence ratio did not consistently produce a

stronger pilot flame effect, so this does not appear to be the cause of the difference in

pilot effect. Changes in the inlet velocity and combustor temperature due to a change in

equivalence ratio likely influence the flow field of the combustor. Changes in the flow

field affect the recirculation time for hot products to be carried from the pilot flame to the

92

main flame base. Coupling of the recirculation time with the instability frequency causes

different pilot effects, depending on the operating condition and instability frequency.

The pilot effect is similar for these two operating condition for the instability that

occurs when Lcomb > 55 in. The pilot flame does not have a strong effect on this

instability. The fact that the instability that occurs for Lcomb > 55 in. is unaffected by pilot

flame across a range of operating conditions suggests that the pilot injector design is not

optimized for this instability. The pilot is likely more susceptible to instabilities due to

the relationship between the instability frequency and the convective time for a

disturbance to reach the flame.

a)

25 30 35 40 45 50 55 600.0

1.0

2.0

3.0

4.0

5.0


p/

pm

ean [

%]

25 30 35 40 45 50 55 600.0

1.0

2.0

3.0

4.0

5.0


p/

pm

ean [

%]

0%

4%

6.5%

8%

I

II

III

IV

93

b)


Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60; 0% pilot, 4% pilot, 6.5% pilot, 8%

4.4 Role of main flame equivalence ratio on pilot flame effect

4.4.1 Effect of main flame equivalence ratio on combustor stability

When the pilot flame is added, the equivalence ratio of the main flame is reduced

to maintain a constant overall equivalence ratio. For example, if the overall equivalence

ratio is ϕoverall = 0.55 and 6.5% of the total fuel is used for the pilot flame, then the main

flame equivalence ratio must be reduced to ϕmain = 0.514. This reduction in the main

flame equivalence ratio may cause the main flame to behave differently, and thereby

change the stability characteristics of the combustor. This section investigates the effect

of the reduction in the equivalence ratio of the main flame on the pilot flame effect.

Three cases of varying overall equivalence ratio and pilot level are considered in

this section. The overall equivalence ratio and the pilot flame intensity are listed for each

case:

Case 1. ϕoverall = 0.55, ϕmain = 0.55, and no pilot

Case 2. ϕoverall = 0.55, ϕmain = 0.514, and 6.5% pilot, and

25 30 35 40 45 50 55 60150

200

250

300

350

400

450

500


Fre

quency [

Hz]

25 30 35 40 45 50 55 60150

200

250

300

350

400

450

500


Fre

quency [

Hz]

94

Case 3. ϕoverall = 0.514, ϕmain = 0.514, and no pilot

For all three cases, the inlet velocity and inlet temperature are Uin = 50 m/s and Tin =

250°C. The reduced equivalence ratio in the Case 3 matches the main flame equivalence

ratio in Case 2, the 6.5% pilot case. If the main flame equivalence ratio is the primary

cause of the pilot flame effect, the piloted case (Case 2) should closely match the reduced

main flame equivalence ratio case with no pilot (Case 3).

The self-excited combustor pressure oscillations and corresponding frequencies

for combustor lengths ranging from 25 in. < Lcomb < 59 in. are shown in Figure 4.10 for

all three cases. Case 1 shows three regions of instability excited by varying the combustor

length. Each of these regions corresponds to a different frequency. The first instability

occurs for combustor lengths Lcomb < 30 in. and has a frequency of approximately 165

Hz. The frequency of instability switches to approximately 450 Hz for 30 in. < Lcomb < 36

in. Finally, for Lcomb > 54 in., the instability frequency is approximately 230 Hz.

In Case 2, with 6.5% pilot flame added and the main flame equivalence ratio

reduced, the magnitudes of the 165 Hz and 450 Hz instabilities are greatly reduced. In the

pilot case, the instability for Lcomb < 30 in. switches to the higher frequency at a much

shorter combustor length. This change in mode may contribute to the reduction of the

instability magnitude. The magnitude of the 230 Hz instability that occurs for Lcomb > 54

in., on the other hand does not change when a 6.5% pilot flame is added.

To determine the effect of the reduced main flame equivalence ratio, the reduced

equivalence ratio main flame was studied without pilot flame in Case 3. In this case, there

is no instability for Lcomb < 30 in. However, the frequency does not match the frequency

for Case 2, the case with 6.5% pilot. In the reduced equivalence ratio case, an instability

95

is excited for 39 in. < Lcomb < 45 in. This instability was not present in the case with a

pilot flame. The instability that was present in the pilot case for Lcomb > 54 in. is

eliminated in the reduced equivalence ratio case. These differences in the self-excited

results between the piloted case and the reduced equivalence ratio case with no pilot

suggest that the main flame equivalence ratio does not dominate the pilot flame effect.

The effect of the pilot flame is more likely due to the presence of the pilot itself and

interactions between the main and pilot flames. The interactions of the main and pilot

flames are studied in greater detail using flame images in Chapter 5 and Chapter 6.

a)

b)

Figure 4.10: Peak combustor pressure fluctuations and corresponding frequency for three

combinations of main flame equivalence ratio and pilot flame intensity; Tin = 250C, Uin = 50

m/s, ϕoverall = 0.55; Case 1, Case 2, Case 3

25 30 35 40 45 50 55 600.0

1.0

2.0

3.0

4.0

5.0


p/

pm

ean [

%]

25 30 35 40 45 50 55 600.0

1.0

2.0

3.0

4.0

5.0


p/

pm

ean [

%]

Case 1

Case 2

Case 3

25 30 35 40 45 50 55 600

100

200

300

400

500

600

700


Fre

quency [

Hz]

25 30 35 40 45 50 55 600

100

200

300

400

500

600

700


Fre

quency [

Hz]

96

4.4.2 Comparison of stable flame structure

Several studies have discussed the effect of stable flame structure on flame

response [12, 77, 79]. Stable CH* chemiluminescence intensity flame images are shown

in Figure 4.11 for Case 2 and Case 3 discussed in the previous section. Figure 4.11a

shows Case 2 with an overall equivalence ratio of ϕoverall = 0.55 and a 6.5% pilot flame

leading to a main flame equivalence ratio of ϕmain = 0.514. Figure 4.11b shows Case 3

with ϕoverall = 0.514 and no pilot flame. These flames are clearly not similar to each other.

The case with the pilot flame is characterized by strong anchoring to the centerbody,

likely due to the recirculation of hot products from the pilot flame to the flame base. The

improved flame anchoring is indicated by high CH* intensity in the flame base extending

towards the centerbody. Figure 4.11b shows that when the main flame equivalence ratio

is reduced without a pilot flame, the main flame does not anchor to the centerbody. The

strong CH* region of the flame base that was observed in the case with a pilot flame is

not observed when the main flame equivalence ratio is reduced without a pilot flame.

This poor anchoring is expected because the equivalence ratio is very low and the flame

is approaching lean blow out. This low main flame equivalence ratio results in a low

flame speed so the flame tends to anchor further downstream. In addition, a lower

equivalence ratio means there is a lower concentration of hot products for the

recirculation zone to transport to the flame base to promote combustion in the flame base

region and create a strongly anchored flame.

In addition to differences in the flame base and flame anchoring, the unpiloted

flame intensity is higher in the outer recirculation zone. This suggests these two flames

will have different flame responses. With such different flame structures, a similar flame

response is not expected. These stable flame images support the evidence from the

97

previous section showing that the main flame equivalence ratio is not responsible for the

effect of the pilot flame observed in this study. Therefore, the pilot flame itself likely

causes the observed effects.

a)

b)

Figure 4.11: CH* chemiluminescence intensity images of stable flames; Tin = 250C, Uin = 50m/s,

a) ϕmain = 0.514, 6.5% pilot; b) ϕmain = 0.514, 0% pilot

4.5 Conclusions

Four distinct instabilities were identified from measurements of combustor

pressure oscillations over a range of combustor lengths and self-excited, technically pre-

mixed operating conditions. The magnitudes of these instabilities varied depending on the

inlet condition and the instability mode. The effect of the pilot flame tended to increase

with increasing pilot intensity. However, the pilot flame intensity required to reduce the

magnitude of a self-excited instability varied with operating condition and instability

mode.

While measurements of combustor pressure fluctuations demonstrated the effect

of the pilot flame, the mechanisms driving the instability and the effect of the pilot flame

on these mechanisms cannot be determined from these measurements alone. A study of

98

the main flame equivalence ratio showed the effect of the main flame equivalence ratio is

not responsible for the observed effect of the pilot flame. Chapter 5 will address the effect

of the pilot flame on stable flame structure, which has been shown to influence flame

response. Chapter 6 will use phase averaged images to identify the mechanisms driving

the self-excited instabilities and ways the pilot flame may interact with these

mechanisms.

99

Chapter 5

The effect of pilot flame on stable flame structure

The previous chapter presented results showing pressure oscillations over a wide

range of self-excited, technically pre-mixed operating conditions and instability modes.

These results showed that the pilot flame’s ability to reduce or eliminate a self-excited

instability changes depending on the operating condition and the instability frequency, as

well as the intensity of the pilot flame. The reason for the variation in the pilot flame’s

ability to reduce self-excited instabilities must be determined. As discussed Section

1.3.1.4, several studies have shown the importance of stable flame shape on self-excited

combustion instabilities. The effect of the pilot flame on stable flame structure must be

investigated to determine the effect of the pilot flame on static stability, and determine

whether the observed effect of pilot flame on technically pre-mixed, self-excited

instabilities occurs due to changes stable flame structure.

Section 5.1 presents a qualitative comparison of two stable flames, one with no

pilot and one with 6.5% pilot, with the same inlet temperature, velocity and overall

equivalence ratio. Section 5.2 compares flame length Lf and flame angle αf for all

operating conditions tested in this study. These two metrics of stable flame shape have

been shown in the literature to influence on flame response. Another flame metric, flame

width Wf, is discussed in Section 5.3. Section 5.4 introduces an additional metric, the

flame base distance Lfb, to determine how the presence of the pilot flame affects

anchoring of the flame base to the centerbody.

100

5.1 Comparison of stable flame images without and with a pilot flame

CH* chemiluminescence intensity images of stable flames were obtained for all

operating conditions in this study. Figure 5.1a shows an example of stable flame without

a pilot flame and Figure 5.1b shows an example with 6.5% pilot flame. The inlet

temperature, velocity, and overall equivalence ratio are the same for both flames. The

image colors are scaled to the maximum intensity of each image. The images are

presented in a linear pseudo color scale. Colors transition from cool colors to warm

colors as the intensity increases. Black and dark blue indicate low intensity and red and

white indicate high intensity.

a)

b)

Figure 5.1: Comparison of CH* stable flame images (a) without a pilot flame and (b) with 6.5%

pilot flame; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525

Differences in flame shape clearly exist between these two cases. For example,

when the pilot flame is added, the main flame appears to be wider and extend further into

the outer recirculation zone. The main flame equivalence ratio is reduced in the 6.5%

pilot case to maintain a constant overall equivalence ratio. This lower main flame

equivalence ratio likely causes the flame width to increase in the 6.5% pilot case.

101

Another observable difference is in the anchoring location of the main flame base.

The unpiloted case shows evidence of an M-flame structure with weak anchoring of the

flame base to both the edge of the dump plane and the edge of the centerbody. When the

pilot flame is added, the flame no longer shows evidence of attachment to the dump

plane. Instead, the flame appears to anchor more strongly to the centerbody and shows a

clear V-flame structure. Improved flame base anchoring likely occurs due to the

recirculation of hot products from the pilot flame to the base of the main flame. These hot

products promote combustion in the region near the centerbody, so the flame is attached

more strongly. Fewer reactants are left to burn in the region closer to the dump plane, so

there is no longer evidence of flame base attachment in this region. According to the

results of Kim et al. [79], an M-flame structure tends to be more stable than a V-flame

structure. However, the results presented in Chapter 4 show the pilot flame does not make

stability worse, despite promoting a transition from an M-flame structure to a V-flame

structure. In fact, in many cases the pilot flame improves stability. Flame shape alone is

not sufficient to predict whether a flame will be stable.

This section highlighted differences in flame structure that are observable simply

by comparing two images. However, while several differences may be observed by

comparing the unpiloted and piloted flame images, differences in flame structure must be

quantified. The following sections discuss a variety of metrics to characterize changes in

stable flame structure caused by the addition of a 6.5% intensity pilot flame.

5.2 Effect of pilot flame on flame length and flame angle

Several authors have found that flame length Lf and flame angle αf, are important

parameters controlling flame response [12, 77, 79]. These parameters were defined in

102

2.3.4. Kim et al., for example, found that fully pre-mixed flames with similar flame

structure, i.e. similar flame length and flame angle, had similar flame responses,

regardless of inlet conditions. They also found that shorter, more compact flames fell into

the M-flame regime while longer flames fell into the V-flame regime. A critical flame

angle separated these two regimes [79].

Flame length and angle are calculated based on the location of the center of heat

release of the flame. Figure 5.2 shows the location of the center of heat release of the

main flame for all of the stable flames in this study, including cases both without and

with a pilot flame. The center of heat release locations fall along the combustor wall. All

flames in this study experience interactions with the combustor wall. As equivalence ratio

increases and velocity decreases, the location of the center of heat release tends to move

upstream. However, the presence of the pilot flame causes negligible change in center of

heat release location.

Figure 5.2: Stable flame center of heat release locations for all operating conditions, Tin = 250C

0% pilot cases: ϕoverall = 0.525, ϕoverall = 0.55, ϕoverall = 0.60, ϕoverall = 0.65

6.5% pilot cases: ϕoverall = 0.525, ϕoverall = 0.55, ϕoverall = 0.60, ϕoverall = 0.65

0 0.5 1 1.5 2 2.5 3 3.5 40.0

0.5

1.0

1.5

2.0

2.5

3.0

x location [in]

y l

ocati

on

[in

]

0 0.5 1 1.5 2 2.5 3 3.5 40.0

0.5

1.0

1.5

2.0

2.5

3.0

x location [in]

y l

ocati

on

[in

]

103

Flame length is defined as the distance from the edge of the centerbody to the

center of heat release, and the flame angle is the angle between the horizontal and the line

connecting the centerbody to the center of heat release. The center of heat release is the

only variable parameter in these metrics, so if the center of heat release location does not

change significantly, the flame length and flame angle will not change significantly

either. To demonstrate that the change in flame length is negligible, Figure 5.3 shows the

percent difference in flame length between the unpiloted and piloted cases for all of the

operating conditions tested. The percent change in flame length is calculated by finding

the difference between the unpiloted (0% pilot) and piloted (6.5% pilot) flame lengths

and dividing by the unpiloted flame length. The percent change is defined as:

% 𝑐ℎ𝑎𝑛𝑔𝑒 =

𝐿𝑓,0% − 𝐿𝑓,6.5%

𝐿𝑓,0%× 100 =

∆𝐿𝑓

𝐿𝑓,0%× 100 (5.1)

The pilot has the largest effect on flame length at low equivalence ratios. When

fuel is diverted from the main flame to the pilot flame, the main flame equivalence ratio

is reduced. When equivalence ratio decreases, the flame speed decreases leading to a

longer flame length. A small change in equivalence ratio has a larger effect on flame

speed at lower equivalence ratios, so reducing the main flame equivalence ratio should

produce a stronger effect on flame structure at low equivalence ratios.

However, for all operating conditions, the change in flame length is less than 6%,

and for all but the lowest equivalence ratio and highest velocity case, the change in flame

length is under 4%. Flame length affects flame response primarily through the convective

time for a disturbance to reach the center of heat release. For a constant inlet velocity, the

104

percent difference in convective time is equivalent to the percent difference in the flame

length. A difference of less than 4% is small and unlikely to affect the flame response.

Figure 5.3: Percent change in flame length (change in flame length divided flame length with 0%

pilot) for all operating conditions, Tin = 250C

Figure 5.4 shows the difference in flame angle between the unpiloted and piloted

cases for all operating conditions. Again, the pilot only makes a very slight difference.

For all cases, the difference is less than 6 degrees, which is not a significant difference.

For all but the lowest equivalence ratio and highest inlet velocity tested, the difference is

less than 4 degrees.

Based on the results of Kim et al. [79], flames with similar flame length and flame

structure should behave the same. However, experimental results from this study have

shown that the pilot flame affects the combustor stability despite similar stable flame

structure defined by flame length and flame angle. A different mechanism must be

responsible for the observed effects of pilot flame.

25 30 35 40 45 500

2

4

6

8

10

Uin [m/s]

L

f/Lf,0%

[%

]

overall

= 0.525

overall

= 0.55

overall

= 0.60

overall

= 0.65

25 30 35 40 45 500

2

4

6

8

10

Uin [m/s]

L

f/Lf,0%

[%

]

105

Figure 5.4: Change in flame angle for all operating conditions, Tin = 250C

5.3 Effect of pilot flame on flame width

In addition to flame length and flame angle, both Peluso [75] and Bunce [76]

noted the importance of flame width Wf as an additional parameter to define flame

structure. They both observed that as flame length increases, flame width increases as

well. A unit change in flame length typically corresponds to a proportinally larger change

in flame width. Figure 5.5 shows the flame width plotted against flame length for the

operating conditions in this study. For both the unpiloted and piloted cases, the flame

width is linearly related to the flame length. This is similar to Peluso’s experimental

results which were performed in the same test facility. In both studies, the flame interacts

with combustor wall in all cases. Bunce noted a nonlinear relationship between flame

length and flame width in cases where the flame did not interact with the combustor wall,

but there were no observed cases in this study in which the flame did not interact with the

combustor wall.

25 30 35 40 45 500

1

2

3

4

5

Uin [m/s]

f [deg]

overall

= 0.525

overall

= 0.55

overall

= 0.60

overall

= 0.65

25 30 35 40 45 500

1

2

3

4

5

Uin [m/s]

f [deg]

106

Figure 5.5: Stable flame width (Wf) versus flame length (Lf)

0% pilot cases: ϕoverall = 0.525, ϕoverall = 0.55, ϕoverall = 0.60, ϕoverall = 0.65

6.5% pilot cases: ϕoverall = 0.525, ϕoverall = 0.55, ϕoverall = 0.60, ϕoverall = 0.65

Lines of best fit: --- 0% pilot; ---- 6.5% pilot

The best fit lines showing the linear relationship between flame length and flame

width are also plotted in Figure 5.5. The pilot flame changes the slope of the line relating

the flame length to the flame width from 2.4 to 3.5. The effect of the pilot flame on flame

width is most noticeble for low equivalence ratios and high velocities, as shown in Figure

5.6 which plots the percent change in flame width for the operating conditions tested in

this study. Peluso found that that an increased flame width could lead to more interaction

of the flame with the outer recirculation zone, which in turn would create a more complex

3 4 5 60

1

2

3

4

5

6

Lf [in]

Wf [

in]

3 4 5 60

1

2

3

4

5

6

Lf [in]

Wf [

in]

107

local flame response in that region. However, the majority of the operating conditions

tested in this study fall into a region around where these two lines intersect and the effect

of the pilot flame on flame width is relatively weak. Flame blow off occurred for leaner

conditions where the pilot flame had a stronger effect on flame width, so this

phenomenon could not be studied in detail. Therefore, for most cases investigated in this

study, the effect of pilot flame on flame width is small and unlikely to have a strong

effect on the response of the main flame.

Figure 5.6: Percent change in flame width (change in flame width divided flame width with 0%

pilot) for all operating conditions, Tin = 250C

5.4 Effect of pilot flame on flame base location

5.4.1 Definition of flame base distance

In addition to the flame metrics discussed in the previous sections, the pilot flame

also changes the overall shape of the stable flame structures shown in Figure 5.1. Flame

contours are useful for quantifying these changes in flame shape. Chemiluminescence

intensity has been shown to be proportional to fuel flow rate, and therefore heat release,

25 30 35 40 45 500

10

20

30

40

50

Uin [m/s]

W

f/Wf,0%

[%

]

ov erall

= 0.525

ov erall

= 0.55

ov erall

= 0.60

ov erall

= 0.65

25 30 35 40 45 500

10

20

30

40

50

Uin [m/s]

W

f/Wf,0%

[%

]

108

at a constant equivalence ratio [133]. In the stable flame images discussed in this section,

the flame is stable so there are no significant oscillations in flow rate or equivalence ratio,

and the chemiluminescence in these images is then proportional to heat release. CH*

flame images provide information on the presence and strength of the combustion process

in specific regions of the combustor [117]. For a given stable operating condition, the

chemiluminescence emissions from the flame are related directly to the concentration of

excited species. Both an increase in chemical reactions as well as higher flame

temperatures will increase the chemiluminescence intensity [133]. Both increased

combustion and higher flame temperatures indicate improved flame anchoring [2, 36–

38].

An example of a contour of the flame is shown in Figure 5.7. In this figure, a

contour of 5% of the maximum image intensity is plotted on top of the original

chemiluminescence intensity image. These contours allow important features of the flame

to be identified and compared between unpiloted and piloted cases.

Figure 5.7: Stable flame CH* chemiluminescence intensity image with contour of 5% maximum

image intensity; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525, 0% pilot

One important feature of the flame is the location of the flame base. The flame

base is the region near the exit of the injector where the flame anchors to the centerbody.

The flame base distance Lfb is defined as the shortest distance from the edge of the

centerbody to the base region of the flame. This metric is used to quantify how well the

109

flame anchors to the centerbody. A similar metric was used by Arndt et al. to define the

lift off height of a flame transitioning between a lifted flame structure and a flame

anchored to the burner nozzle [134]. Similar to the flame base distance, this flame lift off

height characterized how well their flame anchored to the burner nozzle. They chose a

threshold value in their OH PLIF images and then defined the lift-off height as the

minimum distance between the nozzle and the location at which OH within that threshold

value first occurred.

Several factors affect the distance from the centerbody to the flame base. At

higher equivalence ratios, the flame speed is higher, and the flame will be able to

propagate further upstream into the higher velocity region near the exit of the injector.

Similarly, as the inlet velocity decreases, the flame will stabilize further upstream

because the inlet velocity is closer to the flame speed. Both high temperatures and

radicals from combustion products carried upstream by the inner recirculation zone

promote combustion of incoming products in this region. Introducing a pilot flame

increases the temperature and the concentration of radicals recirculated to the flame base,

thereby promoting combustion and improving flame anchoring.

When more reactants burn near the flame base, heat release in this region

increases, and the chemiluminescence intensity in the flame images is greater. The higher

chemiluminescence intensity in the flame base region causes the flame base identified by

the flame contour to extend upstream closer to the centerbody. Characterizing flame

anchoring is important in the investigation of a pilot flame because several studies (see

Section 1.4.2) have suggested that hot products produced by a pilot flame promote

combustion in the main flame base and increase flame stability by improved flame

110

anchoring. Stronger flame anchoring prevents flame blowoff and oscillations in flame

anchoring location that can drive instabilities.

5.4.2 Example of flame base contours without and with a pilot flame

Contours of 5% of the maximum stable flame intensity without pilot and with

6.5% pilot are shown in Figure 5.8, and the flame base location for each flame is

indicated by an ‘x’. In this example, the flame base location is clearly closer to the

centerbody in the 6.5% pilot case. The equivalence ratio of the main flame in the 6.5%

pilot case is reduced compared to the unpiloted case in order to maintain a constant

overall equivalence ratio. In unpiloted cases, reducing the main flame equivalence ratio

causes the flame base to anchor further from the centerbody. The fact that the main flame

in the 6.5% pilot case anchors further upstream despite the reduced main flame

equivalence ratio shows that the presence of the pilot flame does affect the base region of

the main flame.

Figure 5.8: Comparison of 5% maximum intensity contours without a pilot flame and with 6.5%

pilot flame; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525

5.4.3 Choice of flame contour value

It is common to use a flame contour to define the boundary of the flame brush.

However, the value chosen for the contour is often selected somewhat arbitrarily. For

example, Venkataraman et al. example, used a 5% contour [135], while Bunce used 10%

contours [76]. There is typically very little justification to explain why these values were

111

chosen. In the previous section, the flame shape was characterized by a contour of 5% of

the maximum flame intensity, and the analysis in the following section use 5% contours

to calculate the flame base location for a variety of operating conditions. While contours

of 5% of the maximum intensity were chosen for this study, the value of the contour does

not have a strong effect on the comparison of flame base distance, Lfb, between the

unpiloted and piloted cases. The independent nature of the flame contour is demonstrated

in this section before further analyzing the flame base location.

Figure 5.9a and Figure 5.9b show several stable flame contours for a typical

operating condition with no pilot flame and with a 6.5% pilot flame, respectively. The

contours vary from 3% to 15% of the maximum image intensity at 2% increments. The

intensity at the flame base is relatively low compared to the maximum flame intensity,

and the intensity decreases closer to the centerbody. Therefore, flame base location

calculated from a 3% contour will be closest to the centerbody, and as the contour value

increases, the flame base location identified by the flame contour moves further

downstream. This can be observed by inspecting the flame base regions in Figure 5.9.

a)

Increasing % max

intensity contour

112

b)

Figure 5.9: Varying flame contour values for stable flames a) without and b) with 6.5% pilot

flame; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525

The flame base locations for each of these curves for both the unpiloted and 6.5%

pilot cases were calculated and are plotted in Figure 5.10a. This plot shows that as the

percent of the maximum intensity selected for the flame contour increases, the flame base

distance Lfb increases because the location of the flame base moves further from the

centerbody. However, regardless of the contour chosen, the unpiloted case is always

located further from the centerbody than the 6.5% pilot case. If this difference in flame

base distance is approximately constant, then the choice of contour will not affect the

comparison of the flame base distance. Figure 5.10b shows the percent difference

between the unpiloted and 6.5% pilot flame base locations for all contours considered.

For all cases, the percent difference is between 50% and 55%. This shows that any of

these contours may be used to compare the flame base location without and with 6.5%

pilot. 5% of the maximum image intensity was chosen to compare the flame base location

for a variety of operating conditions.

Increasing % max

intensity contour

113

a) b)

Figure 5.10: Effect of flame contour value on a) Calculated main flame base distance and b)

relative difference in main flame base distance between unpiloted and 6.5% pilot cases;

Tin = 250C, Uin = 45 m/s, ϕoverall = 0.525

5.4.4 Effect of pilot flame on flame base location for all operating conditions

Flame base distances Lfb without a pilot flame and with a 6.5% pilot are plotted in

Figure 5.11 for all operating conditions. The percent change in flame base distance

relative to the flame base distance with 0% pilot (∆𝐿𝑓𝑏 𝐿𝑓𝑏,0%⁄ ) is plotted in Figure 5.12.

For all cases, the pilot flame extends the flame base anchoring location closer to the

centerbody. The difference flame length caused by the pilot flame tends to decrease with

increasing equivalence ratio. As equivalence ratio increases, the unpiloted flame base

extends upstream, closer to the centerbody. In the piloted case, the flame base also

extends slightly further upstream as equivalence ratio increases, but the effect of

equivalence ratio is not as great as in the unpiloted case. Because the equivalence ratio

has a greater effect on the unpiloted flame base location than the piloted flame base

location, the difference between the piloted and unpiloted cases decreases as equivalence

ratio increases.

Of the operating conditions tested, the smallest change in flame base location

occurs for Uin = 30m/s and ϕoverall = 0.60. At this operating condition, a dramatic change

1 3 5 7 9 11 13 150

1

2

3

Percent Max Intensity

LF

B [

in.]

1 3 5 7 9 11 13 150

1

2

3


LF

B [

in.]

0%

6.5%

1 3 5 7 9 11 13 150

10

20

30

40

50

60


L

FB [

%]

1 3 5 7 9 11 13 150

10

20

30

40

50

60


L

FB [

%]

114

in the unpiloted flame structure occurs between Uin = 30m/s and Uin = 35m/s. When Uin =

30m/s, the flame base extends relatively far upstream without the addition of the pilot

flame. At 35 m/s, the unpiloted flame base location moves further downstream. As the

velocity increases further, the flame base location exhibits much less variation, and the

effect of the pilot on the flame base location remains relatively constant as velocity

increases. There is likely a critical inlet velocity below which the flame speed is close

enough to the flow velocity that the flame base can propagate upstream and anchor near

the centerbody. Above the critical velocity, the flame base stabilizes further downstream.

The lowest equivalence ratio case, ϕoverall = 0.525, has the opposite relationship to

velocity. In this low equivalence ratio case, the difference in flame base distance

decreases as inlet velocity increases. As the overall equivalence ratio decreases, the

equivalence ratio of the pilot flame also decreases. The weaker pilot does not produce as

high a concentration of hot products and the product temperature is not as high as for a

stronger pilot in higher equivalence ratio cases. The weaker pilot cannot anchor the main

flame as effectively at higher inlet velocities where the difference between the local

velocity and the flame speed is greater than in lower velocity cases, and in which increase

strain in the flame base region is high. The piloted main flame then anchors further

downstream, and the difference between the piloted and unpiloted flame base location is

smaller for high velocity and low equivalence ratio cases.

115

Figure 5.11: Flame base distance for all operating conditions, Tin = 250C

Figure 5.12: Percent change in flame base distance (change in flame base distance divided flame

base distance with 0% pilot) for all operating conditions, Tin = 250C

The results of the flame base distance study show that the pilot flame has a strong

effect on the stable flame base location. The pilot flame reduces the flame base distance

by 35% to 42% of the original, unpiloted flame base distance. The attachment of the

flame base is likely to play some role in reducing the magnitude of self-excited

25 30 35 40 45 500.0

0.5

1.0

1.5

2.0

Uin

[m/s]

Lfb

[in

]

overall = 0.525, 0%

overall

= 0.55, 0%

overall

= 0.60, 0%

overall

= 0.65, 0%

overall

= 0.525, 6.5%

overall

= 0.55, 6.5%

overall

= 0.60, 6.5%

overall

= 0.65, 6.5%

25 30 35 40 45 500.0

0.5

1.0

1.5

2.0

Uin

[m/s]

Lfb

[in

]

25 30 35 40 45 500

10

20

30

40

50

Uin [m/s]

L

fb/L

fb,0

% [%

]

overall

= 0.525

overall

= 0.55

overall

= 0.60

overall

= 0.65

25 30 35 40 45 500

10

20

30

40

50

Uin [m/s]

L

fb/L

fb,0

% [%

]

no pilot

6.5% pilot

116

combustion instabilities. However, while the results in this section show that the pilot

flame improves flame anchoring for all operating conditions, self-excited data presented

in Sections 4.2 and 4.3 showed that the effectiveness of the pilot flame varies depending

on the operating condition. For example, the results presented in Figure 4.3 showed a

large change in the effect of the pilot flame when the inlet velocity was increased from 35

m/s to 40 m/s while keeping the overall equivalence ratio at ϕoverall = 0.55. The flame base

location of the piloted flame, on the other hand, shows no significant variation with inlet

velocity at this equivalence ratio.

In addition to operating condition, the effectiveness of the pilot flame is also

affected by the frequency of the instability. For the same operating condition, and

therefore the same stable flame shape, the pilot may eliminate certain instabilities, but not

others, as shown in Figure 4.8. These results suggest that while improved flame

anchoring caused by the hot products from the pilot flame may contribute to a more

stable flame, this explanation alone is not sufficient to determine when a pilot flame will

or will not reduce or eliminate a self-excited instability. Phase averaged flame images of

unstable flames are necessary to identify instability mechanisms and determine how the

pilot flame affects these mechanisms. Phase averaged results are discussed in Chapter 6.

5.5 Conclusions

Many studies have shown that stable flame structure, defined by the flame length,

angle, width, and shape, plays an important role in determining the response of a pre-

mixed flame. However, the results of this study of stable flame structure showed that the

pilot flame does not have a strong influence on flame length, angle, or width. The pilot

does transition the flame shape from an M-flame to a V-flame, but contrary to the

117

findings of previous studies, the V-flame structure produced by the pilot flame is more

stable than the unpiloted M-flame.

Stable flame results show the pilot flame decreases the distance between the main

flame base and the centerbody, indicating that stronger anchoring of the stable flame to

the injector centerbody. This finding agrees with the commonly accepted explanation for

the pilot flame effect. However, static stability does not guarantee dynamic stability, and

improved flame anchoring alone does not explain why the pilot flame eliminates

instabilities more successfully for certain operating conditions and instability modes. The

effectiveness of the pilot flame varies depending on the operating condition. Furthermore,

for the same operating condition, the effect of the pilot varies depending on the

combustor length and corresponding instability frequency. The pilot effect is more

complicated than simply improving flame anchoring.

The behavior of the unstable flame and interactions between the main and piloted

flames must be better understood to determine how the pilot eliminates instabilities in

some cases but not others. The study of unstable flames is left to the next chapter.

118

Chapter 6

Interaction of the main and pilot flames under unstable conditions

The results presented in Chapter 5 showed that stable flame structure did not fully

explain the effects of the pilot flame. This chapter uses phase averaged flame images to

investigate unstable flame structure. Phase averaged CH* chemiluminescence flame

images of unstable, technically pre-mixed, swirl stabilized flames are presented. Section

6.1 provides background on various instability mechanisms that affect unstable,

technically pre-mixed flames. Section 6.2, presents phase averaged images for unstable

flame from this study. The mechanisms driving the instabilities are identified from the

phase averaged flame images without a pilot flame, and the effects of the pilot flame on

these mechanisms are discussed. The pilot flame itself is shown to oscillate in cases

where the pilot flame does not have a strong effect on the instability. In Section 6.3, the

effect of equivalence ratio oscillations on the unstable pilot flame is investigated by

varying the location where the pilot fuel is injected. The effect of inlet velocity

oscillations on the pilot flame is investigated in Section 6.4 by studying the forced flame

response at various forcing amplitudes.

6.1 Instability mechanisms

In technically pre-mixed flames, combustor pressure fluctuations produce both

velocity and equivalence ratio oscillations which then cause heat release fluctuations in

the flame. Inlet velocity oscillations may lead to bulk movement of the flame, causing the

flame to oscillate back and forth in the axial direction of the combustor. Large amplitude

inlet velocity oscillations can also lead to the shedding of coherent vortex structures.

Velocity oscillation mechanisms cause heat release oscillations through distortion of the

119

flame area. Equivalence ratio oscillations on the other hand, cause fluctuations in heat

release through variations in either heat of reaction or laminar flame speed. Very lean

conditions caused by equivalence ratio fluctuations can lead to local flame extinction.

Instability mechanisms are explained in greater detail in Section 1.3. Evidence of these

instability mechanisms can be found in phase averaged flame images under unstable

operating conditions. Unstable flame images are presented in the next section.

6.2 Unstable flame images

In the self-excited study of technically pre-mixed flames discussed in Chapter 4,

the pilot flame was shown to have a strong effect for certain operating conditions but a

weak effect for others. The pilot is considered to have a strong effect if it eliminates an

instability that occurred when the pilot flame was not present. The pilot effect is

considered weak if the instability persists after adding the pilot flame. This section first

discusses phase averaged flame images for an operating condition where the pilot flame

has a strong effect. Images are compared for the unpiloted and 6.5% pilot cases. The

behavior of the flame over a period of instability is discussed and instability mechanisms

are identified. Possible effects of pilot flame on these mechanisms are also discussed.

Results from a case with a weak pilot flame effect are then presented, and reasons for the

weak pilot flame effect are discussed.

6.2.1 Phase averaged flame images for a strong pilot effect case

6.2.1.1 Instability mechanisms in the unpiloted case

Figure 6.1 shows a series of phase averaged CH* chemiluminescence intensity

flame images of an unstable flame with no pilot. The images show a period of a self-

excited instability at phase angle increments of Δ = 30. Each image is labeled with the

120

corresponding phase angle. The images are scaled to the overall maximum intensity

which occurs at a phase angle of = 90. Contours of 5% of the maximum intensity of

each image are plotted over the flame image to show the edge of the flame and highlight

the flame structure. A black ‘+’ symbol marks the center of heat release in each flame

image.




conditions: Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55, Lcomb = 25 in., 0% pilot

These phase averaged images show evidence of bulk motion of the flame caused

by the fluctuating inlet velocity. The inlet velocity, measured at the two microphone

location in the injector, reaches a maximum at = 0. The center of heat release of the

flame moves downstream from = 0 to = 150. After = 150, the center of heat

release moves back upstream. There is a phase difference of approximately 60 between

the inlet velocity oscillation and the motion of the center of heat release. This delay may

be due to an equivalence ratio oscillation. When a high equivalence ratio disturbance is

convected to the flame, it will burn after some time delay, causing the center of heat

0 30 60

90 120 150

180 210 240

270 300 330

121

release to occur further downstream than would be predicted by considering the velocity

oscillation alone. A direct measurement of equivalence ratio fluctuations is necessary to

confirm the presence of the mechanism, but this measurement technique was not

available in this study. There is also a time delay for the velocity oscillation measured at

the two microphone location to convect downstream to the flame, which would also

contribute to a time delay.

The base of the flame is observed to oscillate during a period of instability. At a

phase angle of = 0, the base appears to be strongly anchored to the centerbody because

of high intensity in the flame base region. As the flame oscillates downstream, the

attachment point of the flame base also moves further downstream, leading to weaker

flame anchoring. From = 180 - 270 low intensity near the flame base indicates the

flame base detaches from its anchoring location at the centerbody. At = 300, intensity

in the flame base region increases, suggesting the base of the flame reignites and the

flame again becomes anchored to the centerbody. This periodic detachment of the flame

base contributes to the instability of the flame.

Phase averaged images in Figure 6.1 also show that the flame shape distorts as the

flame fluctuates downstream and upstream. This distortion of the flame can be observed

from = 0 - 210. As the flame moves downstream, it expands towards the center of the

combustor, causing an increase in the flame area. This behavior is associated with large

amplitude velocity oscillations. Distortion of the flame area leads to fluctuations in heat

release. Kim [136] observed similar movement of a flame towards the center of the

combustor in a fully pre-mixed, forced flame experiment. As the forcing amplitude

increased and the behavior of the flame became non-linear, the flame was observed to

122

oscillate towards the center of the combustor. This movement of the flame will cause

fluctuations in flame area that will lead heat release fluctuations.

6.2.1.2 Effect of 6.5% pilot flame on instability mechanisms

Adding a 6.5% intensity pilot flame at the operating condition discussed in the

previous section eliminated the self-excited instability. Phase averaged flame images of

this strong pilot effect case are shown in Figure 6.2. The piloted case is clearly more

stable than the unpiloted case shown in Figure 6.1. Neither the main nor pilot flames

show significant variation in location or flame shape over the instability period. The

center of heat release of the main flame remains approximately constant. The base of the

flame remains well anchored to the centerbody for all phase angles. The flame structure

of the main flame with a 6.5% pilot flame is distinctly different from the flame structure

in the absence of the pilot flame. With 6.5% pilot, the main flame brush indicated by the

5% intensity contour is located further from the center recirculation zone than when there

is no pilot flame present. The stretching of the flame and increase in flame area that was

seen from = 0 – 210 in Figure 6.1 is not present in the 6.5% pilot case shown in

Figure 6.2. Stable flame structure without and with a pilot flame compared in order to

demonstrate that the observed reduction in main flame oscillations towards the center of

the combustor occurs due to a suppression of unstable flame dynamics rather than a

fundamental change in flame structure. The stable flame structure for the unpiloted and a

piloted flame are compared in Figure 6.3.

123

Figure 6.2: Phase averaged CH* chemiluminescence images at a frequency of 167 Hz. Images are



= 0.55, Lcomb = 25 in., 6.5% pilot

Figure 6.3a shows the mean flame position of the stable main flames without and

with a pilot flame, indicated by blue and black lines, respectively. The mean flame

position is calculated by finding the local maximum intensity in each column. The mean

flame position indicates the location in the flame brush where the flame is most likely to

reside. The mean flame location does not change when the pilot flame is added. There is

no inherent tendency for the flame to move closer to the centerline of the combustor

when the flame is stable.

Figure 6.3b shows the contour of 5% of the maximum intensity of the flame. This

contour indicates the approximate boundary of the flame brush. The inner edge of the

main flame located closest to the center of the combustor approximately coincides for the

unpiloted and piloted flames. The unpiloted flame does not tend to reside closer to the

inner recirculation zone. The stable flame images show that the main flame is not pushed

in the radial direction by the pilot flame when the flame is stable. In the unstable flame

0 30 60

90 120 150

180 210 240

270 300 330

124

images, the bulging of the main flame towards the center of the combustor is most likely

due to the bulk motion of the flame caused by the velocity oscillation, and not by an

inherent tendency for the unpiloted main flame to stabilize closer to the center of the

combustor. This result supports the hypothesis that the pilot flame helps to suppress

unstable oscillations of the main flame to promote stability.

a)

b)

Figure 6.3: Comparison of the stable flame structure characterized by (a) mean flame position and

(b) flame shape defined by contours 5% of the maximum image intensity. Operating conditions:

Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55; Blue: 0% pilot; Black: 6.5% pilot

Self-excited combustion instabilities in technically pre-mixed flames are a

complicated phenomenon with multiple coupled mechanisms, each contributing to the

instability. The pilot flame may affect multiple instability mechanisms simultaneously,

and if one instability mechanism is reduced by the presence of the pilot flame, other

mechanisms may be reduced as well. Therefore the effect of the pilot flame cannot be

attributed solely to one mechanism such as improved flame anchoring. For example, the

hot products produced by the pilot flame are convected to the base of the main flame

where they promote combustion in the base region and improve flame anchoring. When

the flame is well anchored to the centerbody, it is less likely to be disturbed by

oscillations due to velocity fluctuations. If the flame does not experience large bulk

oscillations, local extinction due to stretching of the flame as well as stretching of the

125

flame towards the center of the combustor will not occur, further improving the stability

of the flame.

In addition to improved flame base anchoring, the pilot flame can also act to

confine the flame main flame by producing a high pressure and temperature region along

the centerline of the combustor. The presence of the pilot flame prevents the main flame

from moving inwards towards the centerline of the combustor. Several studies have

shown that the confinement of a flame has a strong effect on flame response in both

laminar and turbulent flames [42, 137, 138]. Typically confinement is studied by varying

the diameter of the combustor section around the outside of the main flame. However, it

is possible for the main flame to be confined in the inner region by the pilot flame.

Cuquel et al. speculated that confinement effects could be caused by the hot gases of

neighboring flames [138]. Confining the main flame prevents fluctuations in flame area

which lead to heat release fluctuations. Smaller heat release oscillations leads to reduced

energy added to the acoustic disturbance, and an overall reduction in the magnitude of the

self-excited instability. Lower velocity oscillations will result in smaller bulk oscillations

in the flame main flame, as well as weaker fluctuations in the flame anchoring location,

which in turn will further reduce the instability.

The pilot flame was shown to be an effective strategy for eliminating self-excited

instabilities for certain operating conditions but not others. For the instability presented in

this section, the pilot was shown to successfully interfere with the instability mechanisms

driving the self-excited instability. However, in certain cases, the pilot flame does not

successfully interfere with the instability mechanisms to produce a stable condition. A

126

case where the pilot flame does not successfully eliminate a self-excited instability is

investigated in the following section.

6.2.2 Phase averaged flame images for a weak pilot effect case

6.2.2.1 Phase averaged images with no pilot flame

The pilot was shown to be very successful at eliminating self-excited instabilities

at certain operating conditions, but for other conditions the pilot caused little to no

reduction in instability magnitude. Figure 6.4 shows a series of phase averaged images

for an unpiloted case where the addition of a pilot flame does not eliminate the self-

excited instability. In this weak effect case, the behavior of the flame and instability

mechanisms in the unpiloted case appears to be similar to the strong effect case shown in

Figure 6.1.

The flame in Figure 6.4 oscillates due to inlet velocity oscillations. This motion of

the flame causes periodic weakness in the attachment of the flame to the centerbody. The

flame motion also causes flame to move towards the center of the combustor, resulting in

increased flame area that leads to a heat release fluctuation. Despite the similarities in

unstable flame behavior between the cases presented in Figure 6.1 and Figure 6.4, the

addition of a pilot flame does not have the same stabilizing effect. In the case presented

in Figure 6.1, the addition of a 6.5% pilot flame reduced the combustor pressure

oscillations magnitude from 1.30% to 0.14%. In the present case, the pilot only reduces

combustor pressure oscillations from 1.13% to 0.85%. The similarities in the unstable

flame behavior between these two cases show the difference in the pilot effect is not

caused the mechanisms driving the unpiloted instability. Instead, the difference in pilot

flame effect must be caused by the pilot flame itself and how it responds to the instability

127

at this condition. The unstable behavior of the pilot flame for this operating condition is

discussed in the next section.




conditions: Tin = 250C, Uin = 35 m/s, ϕoverall = 0.55, Lcomb = 27 in., 0% pilot

6.2.2.2 Phase averaged images an unstable flame with a 6.5% pilot flame

Figure 6.5 shows a series of phase averaged images for the same operating

condition discussed in the previous section but with a 6.5% pilot flame. Unlike the strong

pilot effect case shown in Figure 6.2, the case shown in Figure 6.5 is clearly not stable

despite the presence of the pilot flame. The images in Figure 6.5 show that both the main

and pilot flames oscillate with the mean velocity oscillations.

The unstable behavior of the main flame is similar to the unpiloted case shown in

Figure 6.4. As in the unpiloted case, the main flame base oscillates and becomes detached

from the centerbody. Velocity oscillations also lead to bulging of the main flame towards

the center of the combustor. The pilot flame does not effectively inhibit the main flame

motion to prevent distortion of the flame area, nor does it improve anchoring of the flame

base to the centerbody.

0 30 60

90 120 150

180 210 240

270 300 330

128

In this case, oscillations are observed in the pilot flame itself. Starting at = 0,

when the inlet velocity is highest, the pilot flame moves downstream. From = 0 - 120,

both the pilot flame and main flame move downstream. The pilot flame is located

upstream of the main flame, allowing room for the main flame to move towards the

center of the combustor and increase the flame area as it oscillates. Additionally, the pilot

flame intensity decreases as the pilot flame oscillates upstream. The low intensity of the

pilot flame further allows the main flame to expand towards the centerline of the

combustor, despite the presence of the pilot flame. Without the high pressure created by

the pilot to prevent the main flame moving towards the center of the combustor, the main

flame is free to oscillate and the flame area fluctuates leading to heat release oscillations.

The pilot flame oscillations also affect the ability of the pilot to improve

anchoring of the main flame base. As the pilot flame moves downstream, the production

of hot products occurs further from the flame base. The products have a larger distance to

travel upstream to sustain the flame base. Depending on the velocity of the inner

recirculation zone, the movement of the pilot flame downstream could prevent the hot

products from reaching the flame base in time to prevent destabilization from the

anchoring location at the centerbody.

Oscillations in pilot flame intensity also prevent the generation of hot products to

support the flame base. If the pilot flame intensity is low when the main flame base

intensity is low (i.e. if the main flame base and pilot flame oscillate in phase), then the

hot products produced by the pilot flame may be insufficient to keep the main flame

anchored to the centerbody.

129




conditions: Tin = 250C, Uin = 35 m/s, ϕoverall = 0.55, Lcomb = 27 in., 6.5% pilot

While the pilot flame did not result in a stable operating condition for this case,

the magnitude of the self-excited combustor pressure fluctuations was reduced from

1.13% to 0.85%. In comparison with the unpiloted flame at this operating condition, the

main flame in the piloted case does not distort as much. The oscillating pilot flame

prevents it from having a strong effect on the self-excited instability, but it is still able to

provide some hot products to support the flame base. For example, comparing the flame

base in = 210 - 300 between Figure 6.4 and Figure 6.5 shows slightly higher flame

base intensity indicating improved anchoring in the case with a pilot flame. In addition,

the pilot provides some confinement to inhibit the distortion of the main flame. The small

effect of the pilot flame on the oscillations main flame corresponds to the small effect of

the pilot flame on reducing the magnitude of the self-excited instability.

0 30 60

90 120 150

180 210 240

270 300 330

130

6.2.2.3 Effect of the phase of pilot flame oscillations

The phase of the pilot flame oscillations were investigated in further detail by

comparing the total CH* chemiluminescence intensity of the pilot flame with the total

intensity of the main flame. The chemiluminescence intensity of the pilot flame and main

flame can be separated by dividing the flame image into a main and pilot region and

summing the total intensity of each region. The main flame can be divided further to

examine only the base region where the main flame attaches to the centerbody. The flame

base region was chosen to represent the region near where the flame base anchors to the

centerbody. Therefore the region between the centerbody and the dump plane was

selected to represent this region. The axial limit of this region did not affect the calculated

phase of the base angle oscillations. The division of these main, pilot, and main base

regions is demonstrated in an example flame image in Figure 6.6.

Figure 6.6: Example of a CH* chemiluminescence intensity flame image with the flame base

region indicated with a white box and the main flame and pilot flame region divided by a pink

line.

A plot of the total CH* chemiluminescence intensity for the pilot flame and main

flame base regions over the instability period is shown in Figure 6.7. These values of CH*

intensity were obtained from the phase averaged images in Figure 6.5 and the flame

regions shown in Figure 6.6. The base of the main flame and the pilot flame oscillate in

phase with a phase difference of Δθ = 45°. In phase oscillation means that the pilot flame

produces the lowest concentration of hot products when the main flame base is weakest.

131

Without a high concentration of hot products to sustain the flame base, the main flame

can detach from its anchoring location, leading to an unstable flame.

Figure 6.7: Normalized CH* intensity oscillations from the main flame base and the pilot flame

over a period of instability; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55; 6.5% pilot

In phase oscillations of the main flame base relative to the pilot flame was found

to be a common feature in all cases where the pilot flame had a weak effect. The phase

differences between CH* chemiluminescence intensity oscillations in the main flame

base and the pilot are plotted in Figure 6.8 for all operating conditions at which an

instability occurred with a pilot flame and for which high speed flame images were

acquired. These operating conditions are summarized in Table 6.1. From this plot, it is

clear that for all of these conditions, the pilot flame oscillates in phase with the main

flame base. These results demonstrate the importance to the hot products supplied to the

flame base by the pilot flame. If the production of these hot products is not properly

phased with the flame base oscillations, the pilot flame will not have a strong effect on

the reduction of self-excited combustion oscillations.

0 50 100 150 200 250 3000.0

0.5

1.0

1.5

2.0

Phase [deg]

CH

* /C

H* m

ean

0 50 100 150 200 250 3000.0

0.5

1.0

1.5

2.0

Phase [deg]

CH

* /C

H* m

ean

Main base

Pilot flame

132

Figure 6.8: Phase difference between flame base and pilot flame CH* chemiluminescence

intensity oscillations for operating conditions where the pilot flame did not eliminate a self-

excited instability

Table 6.1: List of operating conditions in from Figure 6.8

Operating

Condition

Uin

(m/s) φoverall Frequency

(Hz)

1 30 0.60 165

2 35 0.55 162

3 40 0.60 454

5 45 0.55 226

6.3 Effect of pilot fuel injection location on pilot flame oscillations

The influence of the phase of pilot flame oscillations was discussed in the

previous section. In a practical gas turbine system, the most straightforward way to

control the phase of an instability is to adjust the fuel injection location. The pilot fuel

injection system in this study was modified to test whether varying the fuel injection

location could increase the effectiveness of the pilot flame under certain operating

conditions.

Operating Condition

base -

pilo

t

133

6.3.1 Details of pilot injector modifications

A schematic of the pilot fuel injection system is shown in Figure 6.9. The pilot

fuel injection system is located within the centerbody of the injector. Approximately 5%

of the total inlet air enters the outer passage of the pilot injection system. Some of that air

enters the inner passage through a hole connecting the two pathways. The pilot fuel is

injected through a nozzle into the inner passage. The fuel and fraction of air in the inner

passage mix over the distance between fuel injection location and the entrance of the

combustor. The remainder of the air mixes with the fuel and air mixture just before

entering the combustion chamber.

Figure 6.9: Redesigned pilot fuel injector indicating Lpilot, the distance from the edge of the pilot

fuel nozzle to the exit of the injector

A convective time, τconv,pilot, controls the time required for an equivalence ratio

disturbance to travel from the pilot fuel injection location to the center of heat release of

the pilot flame. The convective time is defined as:

𝜏𝑐𝑜𝑛𝑣,𝑝𝑖𝑙𝑜𝑡 =

𝐿𝑖𝑛𝑗,𝑝𝑖𝑙𝑜𝑡 + 𝐿𝑓,𝑝𝑖𝑙𝑜𝑡

𝑈𝑝𝑖𝑙𝑜𝑡

(6.1)

where Linj,pilot is the distance from the pilot fuel nozzle exit to the pilot injector exit.

Linj,pilot is illustrated in Figure 6.9. Lf,pilot is the pilot flame length from the pilot injector

exit to the center of the release of the pilot flame. Upilot is the velocity of the jet exiting the

Linj,pilot

134

pilot passage into the combustor. Upilot was calculated from the flowrates pilot air and

fuel and the geometry of the pilot passage. If an equivalence ratio oscillation dominates

the oscillations in the pilot flame, then changing the convective time should change the

phase of the flame oscillations. In this study, the length of the pilot fuel injector, Lpilot,

was varied to change τconv,pilot.

The degree to which Linj,pilot could be varied was limited by the injector geometry.

The modified fuel injection location is 1.38 in. upstream of the original location. This

location was as far upstream as the injection location could be moved while still keeping

all pilot components within the centerbody. The pilot was moved upstream rather than

downstream of the original location because moving fuel injection downstream would

decrease the distance for the pilot fuel and air to mix which could lead to inadequate

mixing of the pilot fuel and air.

Moving the fuel injection location upstream also moves the center of heat release

location upstream by 0.36 in. The modified pilot fuel injector leads to an overall increase

of 1.02 in. for an equivalence ratio disturbance to travel before reaching the pilot flame.

This change in convective distance corresponds to a change in convective time of

𝜏𝑐𝑜𝑛𝑣,𝑝𝑖𝑙𝑜𝑡 = 0.536 ms.

6.3.2 Effect of pilot injection modification on combustor pressure oscillations

The magnitudes of the combustor pressure oscillations before and after the pilot

fuel injection modification were investigated. Pressure oscillation magnitudes for a

typical operating condition are shown in Figure 6.10 for the original and modified pilot

fuel injection locations. The solid lines and filled circles indicate the original injection

location. The dashed lines and open circles indicate the modified injection location. There

135

is no significant change in the unpiloted pressure oscillations, which is expected because

modifying the pilot fuel injection location should not change the combustor stability

characteristics if there is no pilot flame present.

The change in convective time caused by the modification of the pilot fuel

injection location also has a negligible effect on the magnitude of the self-excited

instability when the pilot flame is present. The change in convective time was ineffective

regardless of instability frequency, indicating that the lack of change was not due to

simply changing the injection location to an integer multiple related to the period of the

instability. A larger change in Lpilot may produce a more significant change in the stability

characteristics of the pilot flame. However, moving the pilot fuel injection further

upstream would place pilot passage components outside of the centerbody, while moving

the injection location further downstream would decrease the mixing time for the pilot

fuel and air. Modifying the fuel injection location within the constraints of the current

injector geometry is not a practical solution for improving the pilot flame effect in this

injector design.

136

Figure 6.10: Effect of the pilot fuel injection location on the magnitude of combustor pressure

oscillations; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55

6.4 Forced flame response

The frequency and magnitude of self-excited instabilities depend on the acoustics

of the system and cannot be directly controlled. The random nature of a self-excited

instability makes a direct comparison of the piloted and unpiloted flames impossible

because the instability amplitude and frequencies are never exactly the same. In order to

directly compare the flame response without and with a pilot flame under equivalent

disturbances, a forced experiment was conducted.

In particular, the forced flame response study was used to determine the effect of

inlet velocity oscillation amplitude on the pilot flame. The motivation for this study

comes from self-excited results (discussed in detail in Chapter 4) which showed that for a

given operating condition, the pilot flame effect on the magnitude of self-excited pressure

oscillations varied depending on the mode of the instability. For example, for the

operating condition presented in Figure 6.11a, increasing the pilot flame up to 8%

25 30 35 40 45 50 55 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


p/

pm

ean [

%]

Original 0%

Original 6.5%

Modified 0%

Modified 6.5%

25 30 35 40 45 50 55 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


p/

pm

ean [

%]

137

eliminates the first three peaks in pressure oscillation magnitude. However, the fourth

peak is not affected by the presence of the pilot flame.

The corresponding inlet velocity oscillations shown in Figure 6.11b show that

although the 0% pilot pressure oscillation magnitude is largest for the second peak, the

inlet velocity oscillations are largest for the fourth peak, which corresponds to the

instability that is not affected by the presence of the pilot flame. These results suggest

that the magnitude of the inlet velocity oscillations will influence the effect of the pilot

flame on the instability.

Under large amplitude longitudinal inlet forcing, the vortex breakdown bubble

may lock on to the forcing frequency [53], and the inner recirculation zone may oscillate

and change shape [55–57]. The pilot flame appears to stabilize along the central axis of

the combustor in the inner recirculation zone. As the inner recirculation zone oscillates,

the pilot flame likely oscillates as well. As the inlet velocity oscillation amplitude

increases, the pilot flame may lock onto the instability frequency and become unstable. In

order to isolate the effect of forcing amplitude, a forced flame response experiment was

conducted in which the forcing amplitude was incrementally increased for a fixed

operating condition and forcing frequency.

138

a)

b)

Figure 6.11: a) Peak combustor pressure fluctuations and b) corresponding inlet velocity

oscillation magnitude; Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60; 0% pilot, 4% pilot, 6.5%

pilot, 8%

In forced response studies, the siren system discussed in Section 2.1.2 and shown

in Figure 2.2 imposes an inlet velocity perturbation. A forcing frequency of 170 Hz was

produced by adjusting the speed of the motor driving the siren. This relatively low

frequency also allowed higher amplitude forcing than could be achieved for higher

25 30 35 40 45 50 55 600.0

1.0

2.0

3.0

4.0

5.0


p/

pm

ean [

%]

25 30 35 40 45 50 55 600.0

1.0

2.0

3.0

4.0

5.0


p/

pm

ean [

%]

0%

4%

6.5%

8%

25 30 35 40 45 50 55 600.0

10.0

20.0

30.0

40.0

50.0


U/

Um

ean [

%]

25 30 35 40 45 50 55 600.0

10.0

20.0

30.0

40.0

50.0


U/

Um

ean [

%]

0%

4%

6.5%

8%

I

II

III

IV

I

II

III

IV

139

forcing frequencies. The forcing amplitude was varied from 5% to 50% of the mean inlet

velocity by increasing the fraction of the total flow diverted through the siren.

6.4.1 Comparison of PMT and high speed camera flame transfer function gain

The response of the flame to inlet velocity forcing is determined by measuring

CH* chemiluminescence fluctuations from the flame. Due to the technically pre-mixed

nature of the flame, chemiluminescence intensity is not directly proportional to the heat

release rate, but a qualitative comparison between piloted and unpiloted flames can still

be made. The significance of chemiluminescence intensity in a technically pre-mixed

flame is discussed in greater detail in 1.3.2.

Two methods can be used to measure total CH* chemiluminescence intensity of a

flame. A photomultiplier tube (PMT) measures the global CH* intensity from the entire

flame. Alternatively, a high speed ICCD camera takes images of the flame where each

image pixel captures the local CH* intensity. The global intensity can be calculated by

taking the sum of the intensity of all pixels in the image. An example of the normalized

chemiluminescence intensity oscillations calculated from both methods is shown in

Figure 6.12 for a forcing frequency of 170 Hz and a range of forcing amplitudes. There is

good agreement between these two methods, demonstrating that both methods are valid

ways of measuring global CH* chemiluminescence intensity.

140

Figure 6.12: Comparison of flame transfer function measured by a PMT () and high speed

camera images ()

When a pilot flame is present, the global CH* intensity captures a combination of

the main and pilot flame responses. In order to directly compare flame response for cases

without and with a pilot flame, the flame response of the main flame must be separated

from the flame response of the pilot flame. In this study of flame response, the flame

transfer function will be calculated using CH* measurements from high speed flame

images. The procedure for dividing the main and pilot flame intensity is explained in the

next section.

6.4.2 Separation of the main flame response and the pilot flame response

Measurements of total CH* intensity are typically used in calculating a flame

transfer function. However, when both a main and pilot flames are present, this total

measurement can be misleading because the flame responses of the main and pilot flames

are combined into one total flame response measurement. The goal of the flame transfer

function study is to compare the response of the main flame without and with a pilot

flame present. In order to compare cases without and with a pilot flame, the flame

response of the main flame must be isolated in the cases where a pilot flame is present.

0 10 20 30 40 50 600

20

40

60

80

100

U/Umean

[%]

CH

* /C

H* m

ean [

%]

PMT

Image

141

The main flame response is isolated by dividing the flame image into pilot flame

and main flame regions. The main and pilot flame regions were separated by finding the

local intensity minimum in the region between the two flames. An example of the

division of the main and pilot flame regions is shown in Figure 6.13. The pink line

divides the main flame region from the pilot flame region. The intensity of each region

can then summed to find the total CH* intensity of each region. In the following section,

the reported flame response gain is for the main flame region only.

Figure 6.13: Example of a flame image with a dashed line dividing the main flame region from

the pilot flame region

6.4.3 Main flame transfer function with varying pilot flame intensity and forcing amplitude

Figure 6.14 shows the main flame CH* intensity based gain (𝐶𝐻∗′ 𝐶𝐻∗̅̅ ̅̅ ̅⁄ ) (𝑢′ �̅�⁄ )⁄

versus the forcing amplitude (𝑢′ �̅�⁄ ) for a typical operating conditions. Two pilot

intensities, 4% and 6.5%, were tested in addition to a 0% pilot case. For low forcing

amplitudes, the magnitude of the flame response decreases with increasing pilot flame

intensity. For example, at a forcing amplitude of 5%, the flame transfer function gain

decreases from 3.26 to 2.44 as the pilot flame intensity increases from 0% to 6.5%. This

result shows that for low forcing amplitudes, the amplification of a disturbance by the

main flame is lower when a pilot flame is added. This lower flame response could lead to

an overall decrease in the magnitude of a self-excited instability.

Pilot Flame

Main Flame

142

As the forcing amplitude increases, the effect of the pilot flame decreases. For a

forcing amplitude of 50%, the largest forcing amplitude tested, the pilot flame does not

have a significant effect on magnitude of the chemiluminescence intensity oscillations.

The results of this forced response study show that as the velocity oscillation amplitude

increases, the effect of the pilot flame weakens. The effect of forcing amplitude on the

pilot flame is investigated in the next section to determine why the pilot is not effective

for large forcing amplitudes.

Figure 6.14: CH* intensity based flame transfer function gain at various forcing amplitude for

three levels of pilot flame; Operating conditions: Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60,

Frequency = 170 Hz

6.4.4 Effect of pilot flame on forced instabilities at low forcing amplitudes

Figure 6.15 and Figure 6.16 show phase averaged images for 5% forcing amplitude

with no pilot and with 6.5% pilot, respectively. The behavior of the unpiloted flame is

similar to that of self-excited case discussed in Section 6.2. The center of heat release is

observed to oscillate with fluctuations in the mean velocity. Examination of the flame

base, particularly for phase angles from θ = 60° – 150°, shows evidence that the flame

0 5 10 15 20 25 30 35 40 45 50 55 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

U/Umean

[%]

Gain

CH

*

0%

4%

6.5%

0 5 10 15 20 25 30 35 40 45 50 55 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

U/Umean

[%]

Gain

CH

*

143

base periodically attaches and detaches from its anchoring location at the centerbody.

There is also evidence from the flame contours between = 60° – 240° that the flame

oscillates towards the center of the combustor.

The observed pilot flame mechanisms also appear to be the same as those

observed in the self-excited case presented in Section 6.2. The forced flame response case

with a pilot flame shown in Figure 6.16 shows evidence of improved flame anchoring and

reduced bulging of the main flame towards the center of the combustor. Reducing the

oscillations of the main flame leads to a decrease in chemiluminescence intensity

fluctuations which accounts for the decreased flame transfer function gain observed in

Figure 6.14.




= 0.60, Forcing Frequency = 170 Hz, Amplitude = 5%, 0% pilot

0 30 60

90 120 150

180 210 240

270 300 330

144




= 0.60, Forcing Frequency = 170 Hz, Amplitude = 5%, 6.5% pilot

6.4.5 Effect of pilot flame on forced instabilities at high forcing amplitudes

As the forcing amplitude increases, the effect of the pilot flame on the flame

transfer function gain decreases. For the largest forcing amplitudes studied, 40% - 50% of

the mean inlet velocity, the pilot flame has a negligible effect on the flame transfer

function gain. Phase averaged images without a pilot and with a 6.5% pilot flame under

50% amplitude inlet velocity forcing are compared in Figure 6.17 and Figure 6.18,

respectively. These figures give insight to why the pilot flame is not effective for large

forcing amplitudes.

Figure 6.17 shows the oscillations of the flame for the unpiloted case. Similar to

previously described unstable flame images, bulk oscillations of the main flame as well

as periodic detachment of the flame base from its attachment point at the centerbody are

evident in these figures. Previous cases have indicated that the pilot flame is able to

counteract these mechanisms. However, in the case of high amplitude inlet velocity

forcing, the pilot is shown to be unsuccessful.

0 30 60

90 120 150

180 210 240

270 300 330

145




= 0.60, Forcing Frequency = 170 Hz, Amplitude = 50%, 0% pilot

Figure 6.18 shows the same operating condition as Figure 6.17 but with a 6.5%

pilot flame. The main flame behavior suggests similar instability mechanisms are

responsible for the flame response as the unpiloted case shown in Figure 6.17. This series

of phase averaged flame images also reveals large amplitude oscillations of the pilot

flame when the flame is forced with 50% forcing amplitude. Increased forcing amplitude

likely leads to a more unstable pilot flame because as the forcing amplitude increases,

oscillations of the flow field in the combustor become stronger and the pilot flame is

more likely to become unstable.

Oscillations of the pilot flame explain why the pilot flame does not affect the

flame transfer function at high forcing conditions. Similar oscillations of the pilot flame

were observed in the self-excited case presented in Section 6.2.2. Pilot flame oscillations

under various forcing amplitudes are discussed in greater detail in the next section.

0 30 60

90 120 150

180 210 240

270 300 330

146




= 0.60, Forcing Frequency = 170 Hz, Amplitude = 50%, 6.5% pilot

6.4.6 Effect forcing amplitude on pilot flame stability

Oscillations of the pilot flame location can be observed in the forced flame

images. The amplitude of the oscillations increases as forcing amplitude increases. These

oscillations in pilot flame location are quantified by determining the fluctuations in the

pilot flame center of heat release location.

The pilot flame’s center of heat release location is shown in Figure 6.19 for

selected forcing amplitudes. These amplitudes were selected to represent low, middle,

and high amplitude forcing. For the lowest forcing amplitude case, 𝑢′ 𝑢𝑚𝑒𝑎𝑛⁄ = 5%, the

x-location of the pilot flame varies by approximately 6% from its mean value. As the

forcing amplitude increases, the axial movement of the pilot flame increases. For the

maximum forcing amplitude, case, 𝑢′ 𝑢𝑚𝑒𝑎𝑛⁄ = 50%, the variation of the center of heat

release location increases to as much as 50% of the mean value.

0 30 60

90 120 150

180 210 240

270 300 330

147

Figure 6.19: Axial location of the pilot flame center of heat release for three forcing amplitudes;

Operating conditions: Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60, Forcing Frequency = 170 Hz;

= 5% forcing amplitude; = 25% forcing amplitude; = 50% forcing amplitude

Oscillations in the pilot flame center of heat release are accompanied by

fluctuations in the pilot flame intensity. The CH* intensity fluctuations of the pilot flame

are shown in Figure 6.20. With 5% forcing amplitude, the pilot flame is relatively stable

and does not show large variations in CH* intensity. As the forcing amplitude increases,

pilot flame oscillations become more intense. In high forcing amplitude cases,

fluctuations can reach over 50% of the mean value.

0 50 100 150 200 250 300 3501

2

3

4

5

Phase Angle [Deg]

pilo

t x

CoH

R [in

.]

5%

25%

50%

148

Figure 6.20: CH* intensity fluctuations in the pilot flame region for three forcing amplitudes;

Operating conditions: Tin = 250C, Uin = 40 m/s, ϕoverall = 0.60, Forcing Frequency = 170 Hz;

= 5% forcing amplitude; = 25% forcing amplitude; = 50% forcing amplitude

Oscillations of the pilot flame, both in location and intensity, demonstrate why the

pilot flame reduces the main flame response for low forcing amplitudes but not high

forcing amplitudes. When the forcing amplitude is low, the pilot flame oscillations are

small and the pilot is always able to provide stability to the main flame through the

mechanisms explained in Section 6.2.1.2. When the forcing amplitude increases, the large

fluctuations in the pilot flame location and intensity inhibit the ability of the pilot to

stabilize the main flame.

For example, for 50% forcing amplitude, the pilot flame is located furthest

upstream at a phase angle of θ = 120°. This phase angle also corresponds to the lowest

pilot flame intensity. When θ = 120° in the phase averaged images for 50% forcing

amplitude with a pilot flame shown in Figure 6.18, the main flame expands towards the

center of the combustor. This fluctuation in the main flame can occur despite the

presence of the pilot flame because the pilot is located far upstream and it is not

0 50 100 150 200 250 300 350-100

-50

0

50

100

Phase Angle [Deg]

(I/I m

ea

n) p

ilo

t [%

]

0 50 100 150 200 250 300 350-100

-50

0

50

100

Phase Angle [Deg]

(I/I m

ea

n) p

ilo

t [%

]

5%

25%

50%

149

producing hot gases to confine the main flame. Examination of the main flame base in

Figure 6.18 also shows weak flame attachment for phase angles θ = 120° - 150°. The low

intensity of the pilot flame at this at these phase angles suggests the pilot is not producing

a sufficient concentration of hot products to maintain strong flame anchoring.

Results from this section suggest that in addition to operating condition and

instability frequency, the amplitude of the instability may also influence whether the pilot

flame has an effect.

6.5 Conclusions

Phase averaged flame images were used to investigate the behavior of self-excited

instabilities without and with a 6.5% pilot flame. Under certain conditions, the pilot flame

appeared to interfere with various instability mechanisms to produce a stable flame, but at other

conditions the pilot flame was shown to be unsuccessful and a self-excited instability persisted

despite the presence of the pilot flame. In cases where the pilot flame did not the eliminate

instabilities, the pilot flame was found to oscillate in phase with the base of the pilot flame. Cases

where the pilot flame was unsuccessful were related to both the operating condition and

instability frequency.

A forced flame response study showed that as the amplitude of inlet velocity oscillations

increases, the pilot flame effect on the flame transfer function gain decreases. At high forcing

amplitudes (greater than 40% of the mean inlet velocity) the pilot flame does not affect the gain.

Flame images showed that as the forcing amplitude increases, the pilot flame oscillations

increase. Oscillations in the pilot flame produce fluctuations in the pilot flame location and the

intensity of the pilot fluctuates. When the pilot flame oscillates, it cannot prevent interfere with

the mechanisms driving the flame response. The forced response results suggest that instability

amplitude may influence the pilot flame effect.

150

Chapter 7

Summary and future work

This dissertation presented the results of an experimental study of technically pre-

mixed, self-excited combustion instabilities. The main focus of this investigation was the

study effect of a partially pre-mixed plot flame on self-excited combustion instabilities.

All experiments were performed using a lean-pre-mixed, single nozzle, atmospheric,

industrial gas turbine research facility with a variable length combustor capability. The

results of this dissertation provide increased understanding of the interactions between a

main and pilot flame and help explain how pilot flames suppress combustion instabilities

under certain conditions and why it does not suppress instabilities under other condtiions.

This chapter summarizes the results of this experimental study and suggests possible

future work to further the understanding of the effect of pilot flames on combustion

instabilities.

7.1 Summary

The topic of combustion instabilities is introduced in Chapter 1. The feedback

loop that sustains an instability was discussed, and a summary of combustion instability

mechanisms was provided. Both fully pre-mixed and technically pre-mixed flame

response studies were discussed. The majority of combustion instability studies have

focused on fully pre-mixed flames which do not include equivalence ratio oscillations.

This literature review highlighted the need for more studies involving technically pre-

mixed flames. The problem of combustion instabilities in the operation of gas turbines

motivated the need for a method of controlling these instabilities. A review of pilot flame

151

studies showed that although pilot flames are a common method for controlling

combustion instabilities in industry, further research is needed to understand how they

interact with the main flame and suppress instabilities.

The experimental test facility and a summary of important features of the facility

were presented in Chapter 2. All experiments were performed using a single nozzle,

atmospheric, industrial gas turbine test facility. A variable length combustor allowed the

acoustics of the system to be tuned to either excite or damp combustion instabilities.

Experimental measurements including pressure measurements, velocity measurements,

and chemiluminescence intensity measurements as well as data processing techniques

were discussed. Flame imaging techniques for both stable, time averaged images and

unstable, phase averaged images were also discussed.

Chapter 3 discussed the general stability characteristics of the test facility without

the pilot flame. This section was used to explain how combustor stability is characterized

through combustor pressure oscillation measurements. The stability of the combustor was

shown to vary with combustor length, both in amplitude and frequency. For certain

combustor lengths, abrupt jumps in instability frequency were observed, indicating a

switch in the resonant mode of the combustor. An acoustic model was used to determine

the resonant modes of the test facility. The various instability frequencies observed in

experiments were shown to correspond to the various resonant modes predicted by the

acoustic model. The results of this section demonstrate conditions where large

instabilities occur. The effect of the pilot flame on these regions of large instabilities was

investigated in later chapters.

152

The effect of the pilot flame on self-excited, technically pre-mixed combustion

instabilities was demonstrated in Chapter 4. Various operating conditions were tested

over the operating range of the test facility. The combustor length was varied from 25 in.

to 59 in. to excite a variety of resonant modes. The effect of the pilot flame on the

magnitude of self-excited instabilities was found to vary with both the operating

condition and the combustor length, and the corresponding instability frequency. The

results presented in this chapter demonstrated that a pilot flame could be a useful method

for eliminating instabilities. However, these results also showed that the pilot was not

successful in all cases. The variability of the pilot flame effect required further

investigation using flame images in order to understand the mechanisms responsible for

the pilot flame effect and why the pilot is only successful in certain cases.

Both stable and unstable flame images were investigated. First, stable flame

images were investigated in Chapter 5 using time averaged, CH* chemiluminescence

intensity flame images. These stable, time averaged flame images allowed investigation

of the stable flame structure without a pilot and with a pilot flame. The presence of the

plot flame was shown to have a negligible effect on common stable flame metrics such as

flame length, flame angle, and flame width. These metrics have been shown in past

studies to have a strong effect on flame response, but the negligible effect of the pilot

flame suggests a change in stable flame structure is not responsible for the pilot effects

observed in Chapter 4. The pilot flame was shown to improve anchoring of the main

flame base to the centerbody under stable conditions. However, this does not fully

account for the effect of the pilot flame because for a given operating condition, the effect

of the pilot flame varies with the frequency of the instability.

153

Instability mechanisms affected by the pilot flame and unstable pilot flame

conditions were investigated in further detail in Chapter 6 using phase averaged flame

images. Several instability mechanisms were identified from phase averaged images of

unstable flames with a pilot. These mechanisms include periodic extinction of the main

flame base and flame area fluctuations caused by periodic oscillations of the main flame

towards the center of the combustor. The pilot flame may interfere with the first

mechanism by producing hot products that are recirculated to the flame base to promote

combustion and improve flame anchoring to the centerbody. The second mechanism is

suppressed by the pilot because the pilot flame produces a region of high temperatures

which would lead to higher pressures. This high temperature and pressure region in the

center of the combustor confines the main flame and prevents flame area oscillations.

In cases where the pilot flame does not improve stability, the pilot was found to

lock on to the instability and oscillate both in its axial location and intensity. When the

pilot oscillates, is not able to interfere with certain instability mechanisms. The main

flame is free to oscillate towards the center of the combustor when the pilot flame

intensity is low. If the pilot oscillates in phase with the main flame base, the pilot does

not produce enough hot products to sustain anchoring of the main flame to the

centerbody. The main flame base and pilot flame base were shown to oscillate in phase

for all conditions where the pilot flame did not affect the instability. Investigation of the

forced flame response for various forcing amplitudes suggested that as the amplitude of

inlet velocity oscillations increase, the pilot flame oscillations increase and the effect of

the pilot flame decreases.

154

7.2 Recommendations for future work

The research presented in this dissertation investigates the effect of a pilot flame

located along the central axis of a single nozzle combustion test facility on self-excited,

technically pre-mixed combustion instabilities. Flame structure and unstable flame

dynamics were investigated using CH* chemiluminescence flame images. While these

images are very useful for understanding interactions between the main and pilot flames,

additional diagnostics would help further improve understanding of the effect of the pilot

flame. For example, inserting a pilot flame into the inner recirculation zone likely has a

strong effect on the flow field, as discussed in Section 1.3.1.4. The inner recirculation

zone is also likely to influence the dynamics of the main flame, as discussed in Section

6.4. Flow field would be useful for understanding the influence of the pilot flame on the

combustor flow field.

The geometry of the pilot fuel injection system is complicated and the air and fuel

mixing of the pilot flame is not well understood. The degree of air and fuel mixing will

affect the pilot flame. For example, the pilot will behave differently if it is a pre-mixed,

or a diffusion flame, or if there are rich and lean regions in the flame. The mixing of the

pilot flame may be further complicated when the pilot flame oscillates. A measurement

technique such as PLIF (planar laser-induced fluorescence) techniques could be useful in

understanding the spatial distribution of the fuel-air mixture.

The injector configuration used in this study was selected because it was of

particular interest to industry. However, an overall understanding of pilot flame behavior

would benefit from tests conducted using a simplified injector geometry where various

parameters may be varied independently. For example, in the injector configuration used

155

in this study, the air flow into the pilot is diverted from the main air supply. The pilot air

flow cannot be uncoupled from the main flow. Fu et al. demonstrated that an instability

mode of a pilot flame may dominate a self-excited instability [124], demonstrating the

importance of studying the stability characteristics of the pilot flame in the absence of the

main flame. However, in the current system, the pilot flame will blow out at the high

velocity operating conditions tested in this study. Separate air and fuel flow paths would

eliminate this problem.

Furthermore, an injector with completely separate flow paths for pilot air would

be useful because the pilot would not be affected by oscillations in main inlet air. The

pilot flame was also shown to be ineffective when oscillating in phase with the main

flame base. This effect could be investigated in further detail if the pilot flame could be

forced independently of the main flame. The pilot and main flame could be forced in and

out of phase to determine the effect of the phase of pilot flame oscillations.

The main flow sent through the pilot line also functions as cooling air for the face

of the centerbody exposed to the combustor. In the fully pre-mixed case, this flow is fully

pre-mixed air/fuel mixture that produces a secondary flame regardless of whether pilot

fuel is added. This set up makes testing the effect of a pilot on fully pre-mixed flames

impossible on this injector configuration. Separating the main and pilot flow and cooling

the centerbody with air supplied independently from the main flow would prevent this

secondary flame in the fully pre-mixed case. Running fully pre-mixed uncouples the

effect of velocity and equivalence ratio oscillations. Although technically pre-mixed

flames reflect how actual gas turbines operate, fully pre-mixed studies are important for

understanding how velocity oscillations alone affect instabilities. Fully pre-mixed studies

156

would allow for a better understanding of how the pilot flame interacts with velocity

oscillation mechanisms only.

For technically pre-mixed experiments, a direct measurement of equivalence ratio

oscillations using an IR (infrared) absorption technique would be useful in understanding

the interaction of velocity and equivalence ratio oscillations. This type of measurement

could show whether velocity or equivalence ratio oscillations dominated during a

particular frequency and whether the pilot flame is more effective for controlling either

velocity or equivalence ratio driven instabilities.

157

Appendix A

Uncertainty and repeatability of self-excited results

Data was acquired at a sampling rate of fs = 8192 samples per second and a

sampling time of t = 8 seconds. The data was then divided into eight sets, each 1 second

long, and the mean and standard deviation was calculated. Figure A.1 shows an example

of normalized combustor pressure oscillation magnitude without and with a 6.5% pilot

flame versus combustor length. The figure includes error bars representing two standard

deviations of the mean value. The standard deviation reflects variations in the instability

magnitude during the 8 second time period in which the data was recorded. The error bars

are relatively small. There is no overlap in the error bars between the 0% and 6.5% pilot

cases, indicating the observed differences in pressure oscillation magnitude without and

with a pilot flame are due to an actual effect caused by the pilot, and not variations that

occur during the recording of the data.

Figure A.1: Peak combustor pressure fluctuations with error bars indicating two standard

deviations of the mean; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55; 0% pilot, 6.5% pilot

25 30 35 40 45 50 55 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5


p/

pm

ean [

%]

25 30 35 40 45 50 55 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5


p/

pm

ean [

%]

0% pilot

6.5% pilot

158

The combustor pressure fluctuation frequencies presented in this study are the

mode of all eight sets. Figure A.2 shows the frequencies for all eight sets for a typical

operating condition. For most combustor lengths, there is only a small variation in

frequency between sets, typically less than 10 Hz, so the data points overlap on the

figure. For combustor lengths where peaks in combustor fluctuations occur, the

frequency only varies by 1 Hz between sets. There is a large jump between sets for 29 in.

< Lcomb < 30 in. During these combustor lengths, the frequency periodically switches

between resonant modes before finally settling on the higher frequency mode at Lcomb =

31 in. Large jumps in instability frequency also occur for Lcomb = 51 in. This is also a

combustor length where a switch in the instability mode occurs. Further, this oscillation

magnitude is very low at this combustor length. There are several small peaks with

similar magnitudes at different instability frequencies. For very low amplitude

oscillations there is not a strong coherent instability, so one frequency with a strong peak

is not expected.

Figure A.2: Frequency of peak combustor pressure fluctuation for all eight data sets; Tin = 250C,

Uin = 45 m/s, ϕoverall = 0.55; 0% pilot

25 30 35 40 45 50 55 600

200

400

600

800

1000


Fre

quency [

Hz]

25 30 35 40 45 50 55 600

200

400

600

800

1000


Fre

quency [

Hz]

159

In self-excited experiments, instabilities occur due to a complicated feedback loop

between the system acoustics, unsteady heat release, and unsteady flow. It is important to

make sure experimental results are repeatable because small variations in test conditions

could potentially affect this feedback loop and change experimental results. Figure A.3

compares the results presented in Figure A.1 to results obtained at the same operating

conditions on a different day. The results are repeatable. Some variation in the pressure

oscillation magnitude exists for the 0% pilot case for combustor lengths 31 in. < Lcomb <

35 in. However, the trend of a strong peak at Lcomb = 31 in. and a steady decrease in

instability magnitude from 32 in. < Lcomb < 35 in. is consistent. On both days, the effect

of the pilot flame on pressure oscillation magnitude remained consistent. Repeatability of

experimental results confirms that the observed effect of pilot flame is a real effect, and

not simply due to a random variation in the self-excited response.

Figure A.3: : Peak combustor pressure fluctuations with error bars indicating two standard

deviations of the mean taken on two different days; Tin = 250C, Uin = 45 m/s, ϕoverall = 0.55;

0% pilot, Day 1; 6.5% pilot, Day 1; 0% pilot, Day 2; 6.5% pilot, Day 2;

25 30 35 40 45 50 55 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5


p/

pm

ean [

%]

25 30 35 40 45 50 55 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5


p/

pm

ean [

%]

0% pilot, Day 1

6.5% pilot, Day 1

0% pilot, Day 2

6.5% pilot, Day 2

160

Appendix B

Effect of a perforated plate on self-excited instabilities

The focus of this study has been on the effect of a secondary pilot flame on self-

excited combustion instabilities. However, there are other methods for passively

addressing self-excited combustion instabilities. This appendix investigates the effect of

an area restriction produced by a perforated plate on the magnitude of self-excited

combustion instabilities. The plate is located in the injector inlet, upstream of the swirler.

Understanding the effect of this plate is important for several reasons. First, modification

to this plate could provide a simple method for tuning this injector in industry. Second,

understanding the effect of an upstream boundary condition is necessary for

understanding self-excited combustion instabilities, in particular for modeling efforts.

B.1 Technically pre-mixed study perforated plate study

The injector used in this study includes a perforated plate located upstream of the

swirler to even out the air flow into the injector. It was proposed that in addition to its

original purpose, this plate could be modified to reduce the magnitude of combustion

instabilities. This section focuses on the effect of this perforated plate on self-excited,

technically pre-mixed instabilities. The effect of plate location and plate open area were

tested for a range inlet velocities, equivalence ratios, plate locations, and plate open areas.

Two plates of different open area were tested: the original 55% open area plate and a

modified plate with 35% open area. The area reduction was achieved by reducing the

diameter of the holes in the perforated plate. For each of these plates, three plate locations

were studied:

161

Location 1: the original location of the plate

Location 2: 1 inch upstream of the original location

Location 3: 2 inches upstream of the original location

For each operating condition, the combustor length was varied from 25 inches to

59 inches at 1 inch increments to vary the acoustics of the combustor and excite various

unstable modes. At each combustor length, the stability of the combustor was

characterized by measuring combustor pressure oscillations, velocity oscillations near the

exit of the injector, and chemiluminescence intensity oscillations of the flame.

B.1.1 Effect of original plate location

Figure B.1 shows a plot of the normalized combustor pressure fluctuations and

corresponding frequency for all operating conditions tested with the original perforated

plate. Locations 1, 2, and 3 are indicated by blue circles, red squares, and black triangles,

respectively. There are four frequency ranges that tend to become unstable in the

combustion test rig used for this study. The lowest frequency instabilities, from 150 Hz to

175Hz, occur when the combustor length is shortest. As the combustor length increases,

some operating conditions exhibit an instability between 430 Hz and 485 Hz. This jump

to a higher frequency suggests a switch in the unstable mode of the combustor. At even

longer combustor lengths, some operating conditions have a 310 Hz to 390 Hz instability.

Finally, at the longest combustor lengths tested, the instability frequency ranges from

210Hz to 240Hz.

162

Figure B.1: Magnitude and frequency of self-excited, technically pre-mixed combustor pressure

fluctuations for all operating conditions with the original perforated plate.

Plate Locations: Location1, Location 2, Location 3

The location of the plate had a very little effect on magnitude and frequencies of

these self-excited instabilities. The instabilities occur in the same frequency ranges,

indicating there is no change in the unstable mode of the combustor. The magnitudes of

the instabilities also do not show any significant change when the plate location is varied.

To more clearly illustrate the effect of the perforated plate location, the stability map for a

typical operating condition with the original plate is shown in Figure B.2.

Normalized combustor pressure oscillations and the corresponding instability

frequencies are plotted against combustor length for the three plate locations. There are

three regions where the combustor was clearly unstable, regardless of plate location. The

160 Hz (Lcomb < 33in.) and 220 Hz (Lcomb > 54in.) instabilities were unaffected by plate

location. The magnitude of the 355 Hz instability (37in. < Lcomb < 51in.) was reduced

slightly by moving the plate upstream. A reduced area plate was proposed as a possible

way of amplifying this effect.

163

Figure B.2: Stability map showing the effect of perforated plate location on self-excited,


technically pre-mixed, original plate. Plate Location: Location1, Location 2, Location 3

The open area of the plate was reduced to create a boundary that was less

acoustically transparent than the original plate. Before considering the effect of plate

location with the reduced area plate, the two plates are compared. The plate is positioned

in the original location (Location 1) for this comparison.

B.1.2 Effect of plate open area

Figure B.3 shows a comparison of the original (55% open area) and reduced area

(35% open area) plates. Reducing the open area tended to reduce the magnitude of all of

the self-excited instabilities observed at this operating condition. Differences between the

two plates in the instability frequency were small (less than 10 Hz). The 160 Hz

instability (Lcomb < 33in.) was eliminated with the reduced area plate. The 355 Hz

instability (37in. < Lcomb < 51in.) was reduced from a maximum magnitude of 2.95%

164

with the original plate to 1.91% with the reduced area plate. The 220 Hz instability (Lcomb

> 54in.) was also reduced from a maximum magnitude of 2.89% to 2.16%. This

reduction in the instability magnitude is likely due to increased damping with the reduced

area plate. Acoustic impedance is frequency dependent, which may explain why 160 Hz

instability is eliminated while the other instabilities are just reduced. An impedance tube

test experiment would be useful for determining the acoustic properties of these plates.

Acoustic characterization of the perforated plates is left for future work.

Figure B.3: Stability map showing the effect of perforated plate open area on self-excited,


technically pre-mixed, Location 1 (original location). Plates: Original, Reduced area

B.1.3 Effect of reduced area plate location

The effect of plate location with the reduced area plate is shown in Figure B.4.

The 220 Hz instability (Lcomb > 54in.) was not affected by plate location. However, the

reduced area plate had a larger effect than the original plate on the 360 Hz instability

(37in. < Lcomb < 51in.). When the plate was moved upstream, the magnitude of the

165

instability was reduced from 1.91% to 0.55%. Although moving the plate one inch

upstream from Location 1 to Location 2 had a strong effect on reducing the instability,

moving the plate upstream from Location 2 to Location 3 did not affect the instability.

This suggests there is a specific quality about the original plate location that makes the

instability worse. Possible effects of the plate on the acoustics of the system and the flow

of air entering into the combustor will be discussed later in the next section.

Figure B.4: Stability map showing the effect of plate location self-excited, technically pre-mixed

instabilities with the reduced area plate. Operating condition: Tin = 250°C, u = 40 m/s, φ = 0.55,

technically pre-mixed, reduced area plate. Plate Locations: Location1, Location 2,

Location 3

Although moving the plate upstream successfully reduced the magnitude the 360

Hz instability for the previous operating condition, examples were found in which

moving the plate upstream made the instability worse. The stability map for a higher

equivalence ratio case is shown in Figure B.5. At this operating condition, an instability

occurred at 450 Hz (30in. < Lcomb < 34in.), while the 360 Hz instability observed in the

166

previous operating condition was not excited. For this higher frequency instability,

moving the plate upstream increased the magnitude of the instability.

Figure B.5: Stability map for a case where moving the perforated plate upstream increases the

magnitude of a self-excited, technically pre-mixed instability. Operating condition: Tin = 250°C,

u = 40 m/s, φ = 0.60, technically pre-mixed, reduced area plate. Plate Locations: Location1,

Location 2, Location 3

B.1.4 Acoustic explanation for the effect of plate location

The acoustic model explained in Section 3.4 was used to predict the mode shapes

for the instabilities discussed in the previous section. Studying the acoustics of the test rig

offers insight into why the moving the plate upstream reduces the instability in one case

but increases it in another. A simple acoustic model of the test rig predicted natural

frequencies close to the frequencies observed in experiments. The mode shape plotted in

Figure B.6 corresponds to the predicted natural frequency for the φ = 0.55, Uin = 40 m/s,

with a combustor length of Lcomb = 41 in. At this condition, the magnitude of the

instability was reduced by moving plate upstream. Based on this plot of mode shape,

167

moving the plate upstream moves the plate towards a local pressure maximum, which

would increase the damping effect of the perforated plate.

Figure B.6: Natural frequency mode shape predicted for Tin = 250°C, u = 40 m/s, φ = 0.55, Lcomb

= 41in.

Figure B.7 shows the mode shape corresponding to the natural frequency

predicted for the φ = 0.60, Uin = 40 m/s, with a combustor length of Lcomb = 32 in. At this

condition, moving the plate upstream increased the magnitude of the instability. The

mode shape for this combustor length and frequency is quite different from the previous

case. Moving the plate upstream of its original location brings the plate to a location

where the pressure oscillation amplitude is lower, which would reduce the damping effect

of the plate and increase the magnitude of the combustion instability

Figure B.7: Natural frequency mode shape predicted for Tin = 250°C, Uin = 40 m/s, φ = 0.60,

Lcomb = 32in.

Original Plate

Location

Original

Plate

Location

168

B.2 Fully pre-mixed study perforated plate study

Technically pre-mixed flames were initially tested because this most closely

resembles how fuel and air are mixed in actual gas turbine operation. However, there is

some ambiguity in studying the technically pre-mixed case due to the presence of both

velocity and equivalence ratio oscillations. It is possible that the plate location effect not

be a purely acoustic effect. For example, the plate location may influence the phase of the

velocity oscillations, or the relationship between the velocity and equivalence ratio

oscillations. To eliminate the ambiguity that occurs in the presence of the equivalence

ratio oscillations, fully pre-mixed operating conditions were tested in addition to

technically pre-mixed conditions. All fully pre-mixed experiments were performed using

the reduced are (35% open area) perforated plate.

B.2.1 Effect of perforated plate location on fully pre-mixed combustion instabilities

If the plate location affects stability for fully pre-mixed flames, then the primary

mechanism causing the plate effect is not a change in the relationship between velocity

and equivalence ratio oscillations. Figure B.8 shows a typical fully pre-mixed condition

with the reduced area plate. In this case with no equivalence ratio oscillations, the plate

location still reduces the magnitude of the self-excited instability.

169

Figure B.8 Stability map showing the effect of plate location self-excited, fully pre-mixed

instabilities with the reduced area plate. Operating condition: Tin = 250°C, Uin = 35 m/s, φ = 0.60,

fully pre-mixed, reduced area plate. Plate Locations: Location1, Location 2, Location 3

A range of fully pre-mixed operating conditions were tested with the reduced area

plate. The magnitude of the normalized combustor pressure oscillations are plotted in

Figure B.9 against the corresponding instability frequency. In all cases tested, an

instability occurred with a frequency of approximately 350Hz when the plate was in the

original location. When the plate was moved upstream, the magnitude of the instability

was reduced for all cases tested. These results show that the effect of the plate is not due

to a mechanism involving equivalence ratio oscillations.

170

Figure B.9: Magnitude and frequency of self-excited, fully pre-mixed combustor pressure

fluctuations for all operating conditions with the reduced area perforated plate. Plate Locations:

Location1, Location 2, Location 3

B.2.2 Effect of plate location velocity oscillation phase

The effect of the plate on velocity oscillation phase was investigated at the

operating condition shown in Figure B.10 to confirm that the plate location does not

affect phase. Figure B.10a shows the phase difference between heat release rate and

velocity over the range of unstable combustor lengths. Similar plots for the phase

difference between velocity and pressure, and pressure and heat release are shown in

Figure B.10b and Figure B.10c, respectively. These phase measurements are not affected

in the range of combustor lengths where the plate location had a strong effect on the

instability. These results show that the plate effect is not caused by a change in the phase

of the inlet velocity oscillations.

171

Figure B.10: Effect of perforated plate location on the phasing. a) Phase difference between heat

release rate and velocity fluctuations; b) Phase difference between velocity and pressure

fluctuations; c) Phase difference between pressure and heat release rate fluctuations. Operating

condition: Tin = 250°C, Uin = 35 m/s, φ = 0.60, fully pre-mixed, reduced area plate. Plate

Locations: Location1, Location 2, Location 3

B.3 Conclusions

This section demonstrates the importance of understanding the upstream

boundary conditions in an injector. When the upstream boundary condition is a

perforated plate, as in this study, the percent open area as well as the plate location affects

the magnitude of self-excited combustion instabilities. The effect of the plate was shown

to be caused by an acoustic effect rather than a change in the phase of the velocity

oscillations. These results demonstrate the importance of characterizing the acoustics of

boundary conditions.

a) b)

c)

172

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Vita Bridget C. O’Meara

Bridget O’Meara graduated from The Cooper Union for the Advancement of Science and

Art with a bachelor’s degree in Mechanical Engineering in 2011. She began graduate school at

the Pennsylvania State University in the Fall 2011 semester. She was a teaching assistant for ME

320 – Fluid Flow during her first semester of graduate school. In the Spring 2012 semester she

joined the Turbulent Combustion Lab to research combustion dynamics in lean-pre-mixed gas

turbines. In the summer of 2014 she had an internship with Solar Turbines as part of the UTSR

Gas Turbine Industrial Fellowship.

an experimental study of the effect of a pilot flame …

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