The dynamic transition from combustion noise to combustion instability was investigated experimentally in two laboratory-scale turbulent combustors (namely, swirl-stabilized and bluff-body-stabilized backward-facing-step combustors) by systematically varying the flow Reynolds number. We observe that the onset of combustion-driven oscillations is always presaged by intermittent bursts of highamplitude periodic oscillations that appear in a near-random fashion amidst regions of aperiodic low-amplitude fluctuations. These excursions to periodic oscillations last longer in time as operating conditions approach instability and finally the system transitions completely into periodic oscillations. A continuous measure to quantify this bifurcation in dynamics can be obtained by defining an order parameter as the probability of the signal amplitude exceeding a predefined threshold. A hysteresis zone was observed in the bluff-body-stabilized configuration that was absent in the swirlstabilized configuration. The recurrence properties of the dynamics of intermittent burst oscillations were quantified using recurrence plots and the distribution of the aperiodic phases was examined. From the statistics of these aperiodic phases, robust early-warning signals of an impending combustion instability may be obtained.

The transition in dynamics from low-amplitude, aperiodic, combustion noise to high-amplitude, periodic, combustion instability in confined, combustion environments was studied experimentally in a laboratory-scale combustor with two different flameholding devices in a turbulent flow field. We show that the low-amplitude, irregular pressure fluctuations acquired during stable regimes, termed ‘combustion noise’, display scale invariance and have a multifractal signature that disappears at the onset of combustion instability. Traditional analysis often treats combustion noise and combustion instability as acoustic problems wherein the irregular fluctuations observed in experiments are often considered as a stochastic background to the dynamics. We demonstrate that the irregular fluctuations contain useful information of prognostic value by defining representative measures such as Hurst exponents that can act as early warning signals to impending instability in fielded combustors.

Combustion noise has been traditionally thought of as stochastic fluctuations present in the background of the dynamics in combustors amongst the flow, heat release and the chamber acoustics. Through a series of determinism tests, we show that these aperiodic fluctuations are in fact chaotic of moderately high dimensions (d 0 ≅ 8-10). These chaotic fluctuations then transition to high amplitude combustion instability when the operating conditions are varied towards leaner equivalence ratios. Precursors to such a transition from chaos to dynamics dominated by periodic oscillations are of interest to designers and operators of combustors in estimating the boundaries of operability. We introduce a test for chaos, known as 0-1 test for chaos in the literature, as a measure of the proximity of the combustor to an impending instability. The measure is robust and shows a smooth transition for variation in flow conditions towards instability enabling thresholds to be set for operational boundaries. NOMENCLATURE Re-flow Reynolds number φ -equivalence ratio m · -mass flow rate D 1 -characteristic dimension for the computations of Reynolds number D 0 -diameter of the burner p(t) -unsteady pressure measurement µ -dynamic viscosity

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