Experimental Investigation of Limit Cycle Oscillations in an

Unstable Gas Turbine Combustor*

Timothy C. Lieuwen^ and Ben T. Zinn#

School of Aerospace Engineering

Georgia Institute of Technology

Atlanta, GA

*Research supported by AGTSR^Assistant Professor#Regents’ Professor

Background

• Objective of Study – Characterize limit cycle data from unstable gas turbine combustor in

order to improve understanding of nonlinear processes in these combustors

• Presentation OutlineA. Describe the role of linear and nonlinear processes in combustor’s

dynamicsB. Outline the current understanding of these processes in gas turbine

combustorsC. Present experimental data and discuss its implicationsD. Conclusions and recommendations for future work

Background• Combustion instabilities continue to hinder the development

of lean, premixed gas turbine combustors

• Need to understand the processes controlling the linear and nonlinear characteristics of these combustors

time

Pre

ssur

e

Measured time dependence of Combustor Pressure in GT facility

Overview

• A number of experimental and theoretical investigations have investigated the mechanisms of instability – Anderson and Morford, ASME 98-GT-568, – Straub and Richards, ASME Paper # 98-GT-492 – Lieuwen and Zinn, 27th Int’l Symposium on Combustion– Broda et al., 27th Int’l Symposium on Combustion

• Processes controlling nonlinear characteristics have received less attention– Some theoretical work reported– No good empirical correlations of amplitude data

Important Nonlinear Processes in Gas Turbine Combustors

• Theoretical investigations suggest that combustion process nonlinearities control nonlinear dynamics of these combustors– Dowling, J. Fluid Mech., 1997

– Peracchio and Proscia, ASME Paper # 98-GT-269

– Lieuwen, Ph.D. Thesis, 1999

• Nonlinear processes become significant when )u(O~'u

Examples of “u’/ u” Nonlinearities

• Reactive Mixture composition • simplified for M<<1, choked injector

• Flame Front Response to Flow Perturbations• Convective Time Modulation

u/'u1

u/'u'

Approaches taken in this Study

• Characterized time series data– Advantage - Lots of information obtained from each test– Disadvantage – Difficult to distinguish between

nonlinearity and noise

• Studied the dependence of instability amplitude upon operating conditions

Schematic of Facility

Air

Combustor Section-Front View

Studied Parameter Space

• Equivalence Ratio =0.65-1

• Combustor Pressure 1-10 atm.

• Inlet Velocity 10-60 m/s

• Inlet Length 104 –164 cm

• Mass Flow Rate 6.1-21.1 g/s

Correlation Between Combustor Inlet Velocity and Maximum Instability

Amplitude

0.01

0.02

0.03

0.04

0 10 20 30 40 50 60Mean Inlet Velocity (m/s)

Max

imum

Pre

ssur

e (p

'/p)

up

'pmax

g/s 1.211.6m

cm 164104L

m/s 60-10 u

atm 101p

165.0

inlet

Scaling Implications

• Result shows that the limit cycle amplitude scales as:

• Assuming p’ and u’ are proportional,

• Suggests that important system nonlinearities are

,...)geometry , ,p ,u(f x u'p cycle itlim

)u/'u(f

,...)geometry , ,p ,u(f x u'u cycle itlim

Typical Instability Amplitudes Consistent with Expected Results

from these Nonlinearities

• Typical Instability Amplitudes on the order of 1-4%– nonlinear processes effective at saturating instability at very low amplitudes

(significantly smaller than those observed in rockets or ramjets)

– suggests that gas dynamic nonlinearities do not play an important role in limit cycle oscillations

• For low Mach number flows, “ ” -type nonlinearities become significant at low pressure amplitudes.– For example, assuming M=0.05, and =0.04:

u/'u

)1(O~8.0c

'u

M

1

u

'u

c/'u

Relationship Between Instability Frequency and Inlet Velocity

0

10

20

30

40

50

60

0 100 200 300 400 500 600 700 800

Frequency (Hz)

Inle

t Vel

ocity

(m

/s) Slope corresponds toconvect/T=1.14

f ,T u as constT

u/L

Tconvect

g/s 1.211.6m

cm 164104L

m/s 60-10 u

atm 101p

165.0

inlet

Dependence of Instability Amplitude upon Frequency

maxp

'puf

Linear Processes Nonlinear Processes

Dependence of Instability Amplitude upon Frequency of Instability

0

0.01

0.02

0.03

0.04

0 200 400 600 800Frequency (Hz)

Pre

ssur

e A

mpl

itud

e (p

'/p)

g/s 1.211.6m

cm 164104L

m/s 60-10 u

atm 101p

165.0

inlet

System Nonlinearities

• Good correlation of amplitude data over entire studied parameter space suggests important role of “ ” nonlinearities

• Results suggest, however, that there are qualitative differences in system nonlinearities at different operating conditions

u/'u

Experimentally Observed Super-Critical Bifurcation

0

0.005

0.01

0.015

0.02

18 21 24 27 30Mean Inlet Velocity (m/s)

Nor

mal

ized

Pre

ssur

e (

p'/p

)

g/s 8.11m

atm 2.32p

89.0

Experimentally Observed Sub-Critical Bifurcation

0

0.0025

0.005

0.0075

0.01

0.0125

0.015

13 13.5 14 14.5 15 15.5Mean Inlet Velocity (m/s)

Nor

mal

ized

Pre

ssur

e (p

'/p)

g/s 6.15m

atm 9.69.5p

86.0

Experimentally Observed Bifurcations

• Results suggest that there are qualitative differences in system nonlinearities at different operating conditions

• However, over the majority of conditions only supercritical bifurcations were observed

Example of Spontaneously Occurring Instability

-1.5

-1

-0.5

0

0.5

1

1.5

0 500 1000 1500 2000 2500

Number of Cycles

Pres

sure

(ps

i)

Another Example of a Spontaneously Occurring Instability

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 1000 2000 3000 4000 5000 6000Number of Cycles

Nor

mal

ized

Pre

ssur

e(p'

/p)

Conclusions and Recommendations for Future

Work• Data suggests that mean velocity has a strong

influence on the amplitude of instabilities– Future Work: Take simultaneous fluctuating velocity

data

• Results consistent with prior theoretical predictions

• Results suggest a complex coupling between linear, nonlinear and stochastic processes near combustor stability boundaries– Future Work: Perform system identification study

Time Evolution of Pressure and Flame Structure - p’/ p = 0.01

(Flame visualized with CH radical chemiluminescence)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25

Time (Arb. Units)

Nor

mal

ized

Pre

ssur

e A

mpl

itud

e (%

) CombustionRegion

Pressure Sensor

PremixedReactants

Bifurcations

-1 -0.5 0 0.5 1

Am

pli

tud

e

Stable Unstable

Supercritical

-1 -0.5 0 0.5 1System Parameter

Am

pli

tud

e

Subcritical

Example of Spontaneously Occurring Instability - Detail

-1

-0.5

0

0.5

1

1800 1900 2000 2100 2200 2300

Number of Cycles

Pres

sure

(ps

i)

Example of Spontaneously Occurring Instability - Detail

-1

-0.5

0

0.5

1

1825 1875 1925

Number of Cycles

Pres

sure

(ps

i)

Evolution of State Space Trajectories

-5-4-3-2-1012345

-5 -3 -1 1 3 5

p'(t) [ KPa]

p'(t

+.3

2T)

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -3 -1 1 3 5

p(t) [ KPa]

p(t+

.32T

)

-5

-3

-1

1

3

5

-5 -3 -1 1 3 5

p'(t) [ KPa]

p'(t

+.3

2T)

-5

-3

-1

1

3

5

-5 -3 -1 1 3 5

p'(t) [ KPa]

p'(t

+.3

2T)

Time Evolution of Pressure and Flame Structure - p’/ p = 0.02 (Flame visualized with CH radical chemiluminescence)

PremixedFuel + Air

• Top half of picture - direct image of flame

• Bottom half of picture -Abel inverted image of flame

Flow

Grassberger-Proccacia Dimension

0

1

2

3

4

5

6

-2 -1.5 -1 -0.5 0Log10 (R/rmax)

Poin

twis

e D

imen

sion

Six out of first Seven Longitudinal Modes of Combustor Excited During Tests

0

100

200

300

400

500

600

0 200 400 600 800 1000

Frequency (Hz)

PS

D

0

100

200

300

400

500

600

700

800

900

0 200 400 600 800 1000

Frequency (Hz)

PS

D

0

50

100

150

200

250

300

350

400

450

500

0 200 400 600 800 1000

Frequency (Hz)

PS

D

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000

Frequency (Hz)

PS

D

Combustion Instability Mechanism

• Data showing that instability behavior is controlled by convective processes suggests that instabilities arise from a feedback loop between pressure oscillations, equivalence ratio ( oscillations, and fluctuating heat release

Heat Release Oscillations

AcousticOscillationsin Inlet andFuel Lines

Equivalence Ratio

Fluctuations

Dependence of Heat Release Rate on Equivalence Ratio

Release heatof Rate• Experimental data indicates that combustors are very sensitive to oscillations under lean operating conditions

Zukoski's Experimental Data

chem1/ Rate

Reaction

Release

Heat

of Rate

0

0.0005

0.001

0.0015

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9Equivalence Ratio

Cha

ract

eris

tic Ig

nitio

n Ti

me,

ms