Experimental investigation on critical slowing down of premixed combustion in a backward-facing step combustor

Critical slowing down phenomena occur during the transition process of various dynamical states, such as bifurcations. The eigenvalues of dynamical systems can be regarded as an indicator of critical slowing down of impending bifurcation. Adaptive, locally linear models can extract local eigenvalues of the nonlinear dynamical system by segmenting a full-time series into multi-windows, and eigenvalue spectrum analysis is based on the eigenvalues. The state transition between different combustion states occurs through bifurcation processes. In this paper, we investigate critical slowing down in the bifurcation process of backward-facing step combustor. We performed a series of experiments by fixing the air mass flow and varying the fuel mass flow from the lean blowout condition to a thermoacoustic instability condition with a quasi-steady change, and the combustion state varying versus the change of the operation conditions exhibit a quasi-Hopf bifurcation process. The measured pressure fluctuations were treated by the local linear model to analyse the eigenvalue spectrum. The real parts of the eigenvalues approximate zero gradually when the equivalence ratio increases, and this tendency corresponds to the critical slowing down. Furthermore, the commonly used early warning signals were also used to support the analysis results of the eigenvalue spectrum.