1. The Role of Equivalence Ratio Oscillations in Driving Combustion Instabilities in Low NOx Gas Turbines*
Tim Lieuwen and Ben T. Zinn
Schools of Mechanical and Aerospace Engineering
Georgia Institute of Technology
Atlanta, GA 30332
27th International Symposium on Combustion
August 1998
University of Colorado at Boulder
____________________________________________________________________
* Research supported by U.S. Dept. of Energy

2. Combustion Instabilities in Low NOx Gas Turbines
Modern gas turbines operate in a lean, premixed mode of combustion to reduce NOx emissions
Key problem - occurrence of detrimental combustion instabilities
Need to understand mechanisms responsible for these instabilities

3. Dependence of Heat Release Rate on Equivalence Ratio
Chemical time increases rapidly as the equivalence ratio (f) decreases.
Quantitative Analysis - Fluctuation in reaction rate increases by 2 orders of magnitude as f decreased
Lieuwen, T., Neumeier, Y., Zinn, B.T., Comb. Sci. and Tech, Vol. 135, 1-6, 1998.
From Zukoski
Aerothermodynamics of Aircraft Gas Turbine Engines, 1978

4. A Mechanism for Combustion Instabilities due to f Oscillations
Flame Region
Heat Release Oscillations
Acoustic Oscillations in Inlet and Fuel Lines
Equivalence Ratio Fluctuations

5. Time evolution of disturbances responsible for the onset of instability
a. Pressure
a. Pressure
at flame
at flame t t t 1
b. Pressure
b. Pressure
at injector
at injector t t
c. Fuel Mass flow
modulation at
modulation at
injector
injector t t
d. Equiv. ratio
d. Equiv. ratio
fluct. at
fluct. at
injector
injector t t
e. Equiv. ratio
e. Equiv. ratio t
fluctuation
fluctuation
conv
at flame
at flame t t
f. Heat release
f. Heat release t
oscillation
oscillation
chem t t

6. Time evolution of disturbances responsible for the onset of instability (continued)
From Rayleigh's Criterion an instability can occur if
t1 + tconvect + tchem=T/2, 3T/2, ...
However:
If distance from injector to flame region is much shorter than a wavelength:
t1/T<<1
For low frequency instabilities:
tchem/T<<1
Thus, an approximate instability condition is:
tconvect /T= 1/2, 3/2, ...
Conclusion: tconvect /T is a key parameter in combustor stability

7. Combustor Model Linear Acoustics Model
1-D Wave solutions in fuel line and Regions i and iii:
Boundary Conditions:
Combustor Exit: compact choked nozzle
Upstream end of inlet duct: p'=0
Upstream end of fuel line: v'=0
Matching Conditions:
Flow through fuel orifice: mf = Kor(DP)1/2
Acoustic Oscillation in Regions i and iii matched by integrating across the flame region which was assumed to be acoustically compact
e.g. without mean flow or area discontinuities:

8. Combustor Model (continued)
Linear Heat Release Model:
Combustion process assumed to behave as a well stirred reactor (WSR)
An expression for the linearized response of a WSR to inlet f perturbations can be derived: Q' = z3f'
Linear f Oscillation Model:
f perturbation at fuel injector:
Mixture assumed to convect with the mean flow with unchanged composition: f'(x,t) = finj'exp(iw(t-x/u))
Solution determines the complex frequency w=wr+iwi

9. Model Results - Influence of Convective Time Delay on Combustor Stability
Parameter Ranges:
= 40, 60, 80 m/s
Laf = m
f =0.6-1
Choked fuel injector, p’=0 B.C. at inlet
Model Results are in good agreement with experimental data from DOE - FETC (Richards and Janus, ASME paper # 97-GT -244, Straub and Richards, ASME paper # 98-GT-492)

10. Incorporating Effects of Flame Structure
Spatial dependence of f ’
Spatial dependence of p’ M l /2
Lconvect
Lflame
Time lag between f‘ at flame base and Q’, teq:
Depends on structure of flame region and Stflame=fLflame/U:
Modifies instability criterion:
tconv,eff/T = (tconvect+teq)/T=Cn

11. Incorporating Effects of Flame Structure
1.5
Lflame= Lconvect
1.35
Corresponding Flame Shape
1.20
“ tconv,eff/T
1.05
Lconvect
0.90
Unstable Region
Lflame
tconvect/T
0.75
0.5 1
1.5 2
2.5 3
Flame Strouhal #
Conclusion: Structure of flame region may have significant effects on stability behavior!

12. Effects of Flame Structure on Stability Regions
Parameter Ranges:
= 40, 60, 80 m/s
Laf = m
f =0.6-1
Choked fuel injector, p’=0 B.C. at inlet
If assume conical flame where Lflame=Lconvect/2, Stflame<<1, predicted and measured regions agree almost perfectly

13. Incorporating Effects of Flame Structure
Not meaningful to correlate data with tconvect/T when significant changes in:
Structure of flame region
Flame Strouhal number
May explain recent data taken at DOE
(Richards, Straub, Yip, Woodruff, Proc AGTSR Combustion Workshop)

14. Summary and Conclusions
Combustion instabilities in LP combustors appear to be due to large heat release rate oscillations induced by f oscillations
In agreement with experiments at
U.Cal. - Berkeley (Mongia, Dibble and Lovett)
DOE - FETC (G. Richards)
Georgia Tech (to be reported at AIAA meeting, Jan. 1999, Reno, NV)
UTRC (T. Rosjford)

15. Recent Result from Georgia Tech Facility
Predicted Region

16. Summary and Conclusions
tconvect/T is a key parameter in describing combustor instability regions due to this mechanism
Determining “effective” tconvect/T can be more difficult for longer flame regions
Combustion instabilities could be suppressed by designing combustor parameters to be outside of instability ranges
e.g., as demonstrated by Solar Turbines
(Steele, Rob, Proc AGTSR Combustion Workshop)

17. Formation of Equivalence Ratio Oscillations
Significant f oscillations may form in inlet section
Acoustic oscillation of 1%, gives f oscillation of 20%!
(choked fuel flow, M=0.05)
Presence of f oscillations during instability recently confirmed by Mongia, Dibble, and Lovett
(“Measurement of Air-Fuel Ratio Fluctuations Caused by Combustor Driven Oscillations," ASME paper 98-GT-304).

18. Results of a well-stirred reactor (WSR) model
Unsteady WSR model subjected to perturbations in the inlet f.
Response of the unsteady rate of reaction increased as much as 200 times as f was decreased from stoichiometric to lean mixtures
Conclusion: f oscillations induce strong heat release oscillations that can drive combustion instabilities under lean conditions
From Lieuwen, T., Neumeier, Y., Zinn, B.T., Comb. Sci. and Tech, Vol. 135, 1-6, 1998.

19. Combustion Process Response Model
Using a global kinetic mechanism for propane and a WSR residence time of .1 ms.

20. Combustor Model
- A model was developed to predict the linear stability limits of the observed longitudinal combustion instabilities based on this mechanism

21. Fuel Line- Orifice Dynamics
Orifice Pressure drop = 2 atm., Combustor Pressure =10 atm., Fuel line Mach # = .05

22. Model Results- Effect of Fuel Injector Location on Combustor Stability
Mean flow velocity = 40 m/s m/s
tconvect/T3/2
tconvect/T1/2
tconvect/T1/2
Stable
Unstable

23. Model Results- Effect of Fuel Line Dynamics on Combustor Stability
Mean flow
velocity
Lfuel/l1/2
Lfuel/l1
= 40 m/s
Laf = 0.08 m
Stable
Unstable
Combustor stability altered when unstable wavelength matches the fuel line length • This suggests a variable length fuel line as a passive control approach