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 Outline A. Describe the role of linear and nonlinear processes in combustor’s dynamics B. Outline the current understanding of these processes in gas turbine combustors C. Present experimental data and discuss its implications D. 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 Pressure 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, 27 th Int’l Symposium on Combustion –Broda et al., 27 th 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

Examples of “u’/ u” Nonlinearities Reactive Mixture composition simplified for M<<1, choked injector Flame Front Response to Flow Perturbations Convective Time Modulation

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  = Combustor Pressure1-10 atm. Inlet Velocity10-60 m/s Inlet Length104 –164 cm Mass Flow Rate g/s

Correlation Between Combustor Inlet Velocity and Maximum Instability Amplitude

Scaling Implications Result shows that the limit cycle amplitude scales as: Assuming p’ and u’ are proportional, Suggests that important system nonlinearities are

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:

Relationship Between Instability Frequency and Inlet Velocity

Dependence of Instability Amplitude upon Frequency Linear ProcessesNonlinear Processes

Dependence of Instability Amplitude upon Frequency of Instability

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

Experimentally Observed Super- Critical Bifurcation

Experimentally Observed Sub- Critical Bifurcation

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

Another Example of a Spontaneously Occurring Instability

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) Time (Arb. Units) Normalized Pressure Amplitude (%) Combustion Region Pressure Sensor Premixed Reactants

Bifurcations

Example of Spontaneously Occurring Instability - Detail

Evolution of State Space Trajectories

Time Evolution of Pressure and Flame Structure - p’/ p = 0.02 (Flame visualized with CH radical chemiluminescence) Top half of picture - direct image of flame Bottom half of picture -Abel inverted image of flame Flow

Grassberger-Proccacia Dimension

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

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 Acoustic Oscillations in Inlet and Fuel Lines Equivalence Ratio Fluctuations

Dependence of Heat Release Rate on Equivalence Ratio Experimental data indicates that combustors are very sensitive to  oscillations under lean operating conditions Zukoski's Experimental Data