We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics. Periodic and chaotic behavior in combustion dynamics that can be observed as a result of combustion instabilities in fundamental and practical combustion systems are of importance to present-day combustion physics and nonlinear science research. In this paper, we experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. As the equivalence ratio / increases from 0.43 to 0.55, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. This is clearly demonstrated by a nonlinear time series analysis in combination with a surrogate data method, which has not been reported in details in previous fundamental combustion research. On the basis of the deterministic nature of the dynamic behavior extracted by the nonlinear time series analysis, a nonlinear forecasting method was performed to predict the time series of the pressure fluctuations. The short-term predicted pressure fluctuations obtained by updating the data library of the phase space coincide very closely with the measured pressure fluctuations, which shows that the nonlinear forecasting method we applied in this work has potential use for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor.

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