Interpretation of Intermittent Combustion Oscillations by a New Linearization Procedure

Abstract

The transition from the low-amplitude, aperiodic fluctuation to thermoacoustic instability is usually treated as a Hopf bifurcation, but the transition incorporates complex dynamical behaviors. Intermittent oscillations commonly occur in the transition process wherein chaotic states alternate with limit cycle oscillations and both the chaotic state and the limit cycle oscillation last with no fixed period. Intermittent oscillations that occur in the thermoacoustic system are demonstrated to be deterministic. A Koopman linearization procedure is implemented to model the intermittent combustion oscillations in the backward-facing step combustor. The nonlinear dynamics of intermittent combustion oscillations are approximated as a forced linear system in an orthogonal space, which is constructed by singular value decomposition of a delay coordinates matrix. The phase space of an intermittent combustion oscillation can be divided into linear and nonlinear regions by the magnitude of the nonlinear term in the forced linear system. As a result, intermittent combustion oscillations can be described as the transition between chaotic states and limit cycle oscillations, and the transition occurs when the nonlinear term is large.