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

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

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

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

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

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

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:

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

Model Results - Influence of Convective Time Delay on Combustor Stability Parameter Ranges: = 40, 60, 80 m/s Laf = 0-0.15 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)

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

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!

Effects of Flame Structure on Stability Regions Parameter Ranges: = 40, 60, 80 m/s Laf = 0-0.15 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

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. 1998 AGTSR Combustion Workshop)

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)

Recent Result from Georgia Tech Facility Predicted Region

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. 1998 AGTSR Combustion Workshop)

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).

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.

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

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

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

Model Results- Effect of Fuel Injector Location on Combustor Stability Mean flow velocity = 40 m/s 80 m/s tconvect/T3/2 tconvect/T1/2 tconvect/T1/2 Stable Unstable

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