We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation. © 2016 American Physical Society.

R. I. Sujith

Department of Aerospace Engineering

J. Tony

E. Sreelekha

Bifurcation (mathematics)

FOKKER PLANCK EQUATION

Stochastic systems

AMPLITUDE DISTRIBUTIONS

BI-STABLE OSCILLATORS

EFFECT OF NOISE

HIGH-INTENSITY NOISE

Parameter regimes

STOCHASTIC BIFURCATION

THERMOACOUSTIC SYSTEMS

Unsteady pressures

Thermoacoustics

Fulltext

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IIT Madras

Physical Review E

An experimental study on a turbulent, swirl-stabilized backward facing step combustor is conducted to understand the spatiotemporal dynamics during the transition from combustion noise to thermoacoustic instability. By using a turbulence generator, we investigate the change in the spatiotemporal dynamics during this transition for added turbulence intensities. High-speed CH* images of the flame (representative of the field of local heat release rate fluctuations ((Formula presented.) (x,y,t))) and simultaneous unsteady pressure fluctuations (p'(t)) are acquired for different equivalence ratios. In the study, without the turbulence generator, as the equivalence ratio is reduced from near stoichiometric values, we observe an emergence of coherence in the spatial dynamics during the occurrence of intermittency, enroute to thermoacoustic instability. As the turbulence intensity is increased using the turbulence generator, we find that there is an advanced onset of thermoacoustic instability. Spatial statistics and the instantaneous fields of (Formula presented.) show that during the transition from combustion noise to thermoacoustic instability, the emergence of coherent spatial structures in the instantaneous fields of (Formula presented.) for the experiments with higher turbulence intensities is advanced. However, as the equivalence ratio is reduced further, we notice that higher turbulence intensities result in the reduction of the strength of the pressure oscillations during the state of thermoacoustic instability. We find that, at these low equivalence ratios, there is a decrease in the coherence due to the dispersal of (Formula presented.), which explains the reduction in the strength of the pressure oscillations. © The Author(s) 2017.

International Journal of Spray and Combustion Dynamics

Spatiotemporal dynamics during the transition to thermoacoustic instability: Effect of varying turbulence intensities

We present a systematic investigation of the effect of external noise on the dynamics of a system of two coupled prototypical thermoacoustic oscillators, horizontal Rijke tubes, using a mathematical model. We focus on the possibility of amplitude death (AD), which is observed in the deterministic model of coupled thermoacoustic oscillators as studied by Thomas et al. [Chaos 28, 033119 (2018)], in the presence of noise. Although a complete cessation of oscillations or AD is not possible in the stochastic case, we observe a significant reduction in the amplitude of coupled limit cycle oscillations (LCOs) with the application of strong coupling. Furthermore, as we increase the noise intensity, a sudden drop in the amplitude of pressure oscillations at the transition from LCO to AD, observed in the noise free case, is no longer discernible because of the amplification of noise in AD state. During this transition from LCO to AD, we notice a qualitative change in the distribution of the pressure amplitude from bimodal to unimodal. Furthermore, in order to demarcate the boundary of the transition from LCO and AD in the noisy case, we use 80 % suppression in the amplitude of LCO, which generally occurs in the parameter range over which this qualitative change in the pressure distribution happens, as a threshold. With the help of bifurcation diagrams, we show a qualitative change as well as a reduction in the size of amplitude suppression zones that happen due to the increase in noise intensity. We also observe the relative ease of suppressing the amplitude of LCO with time-delay coupling when detuning and dissipative couplings are introduced between the two thermoacoustic oscillators in the presence of noise. © 2018 Author(s).

Chaos

Effect of noise amplification during the transition to amplitude death in coupled thermoacoustic oscillators

Abstract This paper analyses subcritical transition to instability, also known as triggering in thermoacoustic systems, with an example of a Rijke tube model with an explicit time delay. Linear stability analysis of the thermoacoustic system is performed to identify parameter values at the onset of linear instability via a Hopf bifurcation. We then use the method of multiple scales to recast the model of a general thermoacoustic system near the Hopf point into the Stuart-Landau equation. From the Stuart-Landau equation, the relation between the nonlinearity in the model and the criticality of the ensuing bifurcation is derived. The specific example of a model for a horizontal Rijke tube is shown to lose stability through a subcritical Hopf bifurcation as a consequence of the nonlinearity in the model for the unsteady heat release rate. Analytical estimates are obtained for the triggering amplitudes close to the critical values of the bifurcation parameter corresponding to loss of linear stability. The unstable limit cycles born from the subcritical Hopf bifurcation undergo a fold bifurcation to become stable and create a region of bistability or hysteresis. Estimates are obtained for the region of bistability by locating the fold points from a fully nonlinear analysis using the method of harmonic balance. These analytical estimates help to identify parameter regions where triggering is possible. Results obtained from analytical methods compare reasonably well with results obtained from both experiments and numerical continuation. © Cambridge University Press 2013.

Journal of Fluid Mechanics

Subcritical bifurcation and bistability in thermoacoustic systems

We experimentally investigate the effect of noise on the stability of a thermoacoustic system operating in a bistable region. The thermoacoustic system chosen for investigation is a ducted non-premixed flame. The system is excited by random fuel flow rate fluctuations which affects the system dynamics as parametric noise. Under the influence of noise, the system undergoes transition from stable to oscillatory state. In particular, transition is observed even when the amplitude of the noise is significantly less than the triggering amplitude of the corresponding deterministic system. While triggering from noise of low amplitudes, phase portraits reveal that the system evolves transiently towards an unstable periodic orbit, before eventually growing to a stable periodic orbit. A stochastic stability map is constructed to represent the probability of the system to undergo transition. It is also observed that the amplitude of the oscillatory state is affected by the noise level. © 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Proceedings of the Combustion Institute

Experimental investigation of noise induced triggering in thermoacoustic systems

The role of non-normality and nonlinearity in thermoacoustic interaction in a Rijke tube is investigated in this paper. The heat release rate of the heating element is modeled by a modified form of King's law. This fluctuating heat release from the heating element is treated as a compact source in the one-dimensional linear model of the acoustic field. The temporal evolution of the acoustic perturbations is studied using the Galerkin technique. It is shown that any thermoacoustic system is non-normal. Non-normality can cause algebraic growth of oscillations for a short time even though the eigenvectors of the system could be decaying exponentially with time. This feature of non-normality combined with the effect of nonlinearity causes the occurrence of triggering, i.e., the thermoacoustic oscillations decay for some initial conditions whereas they grow for some other initial conditions. If a system is non-normal, then there can be large amplification of oscillations even if the excited frequency is far from the natural frequency of the system. The dependence of transient growth on time lag and heater positions is studied. Such amplifications (pseudoresonance) can be studied using pseudospectra, as eigenvalues alone are not sufficient to predict the behavior of the system. The geometry of pseudospectra can be used to obtain upper and lower bounds on the growth factor, which provide both necessary and sufficient conditions for the stability of a thermoacoustic system. © 2008 American Institute of Physics.

Physics of Fluids

Thermoacoustic instability in a Rijke tube: Non-normality and nonlinearity

Coherence resonance in a thermoacoustic system

Stochastic bifurcations caused by multiplicative noise in systems with hard excitement of auto-oscillations

Stochastic bifurcations in a prototypical thermoacoustic system

Journal	Data powered by TypesetPhysical Review E
Publisher	Data powered by TypesetAmerican Physical Society
ISSN	24700045
Open Access	No