Nonlinear oscillations lie at the heart of numerous complex systems. Impulsive forcing arises naturally in many scenarios, and we endeavour to study nonlinear oscillators subject to such forcing. We model these kicked oscillatory systems as a piecewise smooth dynamical system, whereby their dynamics can be investigated. We investigate the problem of pattern formation in a turbulent combustion system and apply this formalism with the aim of explaining the observed dynamics. We identify that the transition of this system from low amplitude chaotic oscillations to large amplitude periodic oscillations is the result of a discontinuity induced bifurcation. Further, we provide an explanation for the occurrence of intermittent oscillations in the system.

R. I. Sujith

Department of Aerospace Engineering

Akshay T. Seshadri

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

A bifurcation giving birth to order in an impulsively driven complex system.

Chaos

Recently, there has been a growing interest in understanding and characterising intermittent burst oscillations that presage the onset of combustion instability. We construct a deterministic model to capture this intermittency route to instability in a bluff-body stabilised combustor by coupling the equations governing vortex shedding and the acoustic wave propagation in a confinement. A feedback mechanism is developed wherein the sound generated due to unsteady combustion affects the vortex shedding. This feedback leads to a variation in the time of impingement of the vortices with the bluff body causing the system to exhibit chaos, intermittency, and limit cycle oscillations. Experimental validation of the model is provided using various precursor measures that quantify the observed intermittent states. © 2016 Informa UK Limited, trading as Taylor & Francis Group.

Combustion Theory and Modelling

A reduced-order deterministic model describing an intermittency route to combustion instability

Identifying nonlinear structures in a time series, acquired from real-world systems, is essential to characterize the dynamics of the system under study. A single time series alone might be available in most experimental situations. In addition to this, conventional techniques such as power spectral analysis might not be sufficient to characterize a time series if it is acquired from a complex system such as a thermoacoustic system. In this study, we analyze the unsteady pressure signal acquired from a turbulent combustor with bluff-body and swirler as flame holding devices. The fractal features in the unsteady pressure signal are identified using the singularity spectrum. Further, we employ surrogate methods, with translational error and permutation entropy as discriminating statistics, to test for determinism visible in the observed time series. In addition to this, permutation spectrum test could prove to be a robust technique to characterize the dynamical nature of the pressure time series acquired from experiments. Further, measures such as correlation dimension and correlation entropy are adopted to qualitatively detect noise contamination in the pressure measurements acquired during the state of combustion noise. These ensemble of measures is necessary to identify the features of a time series acquired from a system as complex as a turbulent combustor. Using these measures, we show that the pressure fluctuations during combustion noise has the features of a high-dimensional chaotic data contaminated with white and colored noise. © 2015 American Physical Society.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Detecting deterministic nature of pressure measurements from a turbulent combustor

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 high-amplitude 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 swirl-stabilized 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. © 2014 Cambridge University Press.

Journal of Fluid Mechanics

Intermittency route to thermoacoustic instability in turbulent 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 (d0 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.

Journal	Data powered by TypesetChaos
Publisher	Data powered by TypesetAmerican Institute of Physics Inc.
ISSN	10541500
Open Access	No