Samadhan A. Pawar

Intermittency Route to Combustion Instability in a Laboratory Spray Combustor

In the present study, we investigate the phenomenon of transition of a thermoacoustic system involving two-phase flow, from aperiodic oscillations to limit cycle oscillations. Experiments were performed in a laboratory scale model of a spray combustor. A needle spray injector is used to generate a droplet spray having one dimensional velocity field. This simplified design of the injector helps in keeping away the geometric complexities involved in the real spray atomizers. We investigate the stability of the spray combustor in response to the variation of the flame location inside the combustor. Equivalence ratio is maintained constant throughout the experiment. The dynamics of the system is captured by measuring the unsteady pressure fluctuations present in the system. As the flame location is gradually varied, self-excited high amplitude acoustic oscillations are observed in the combustor. We observe the transition of the system behaviour from low amplitude aperiodic oscillations to large amplitude limit cycle oscillations occurring through intermittency. This intermittent state mainly consists of a sequence of high-amplitude periodic bursts separated by low amplitude aperiodic regions. Moreover, the experimental results highlight that during intermittency, the maximum amplitude of bursts oscillations, near to the onset of intermittency, is as much as three times higher than the maximum amplitude of the limit cycle oscillations. These high amplitude intermittent loads can have stronger adverse effects on the structural properties of the engine than the low amplitude cyclic loading caused by the sustained limit cycle oscillations. Evolution of the three different dynamical states of the spray combustion system (viz. stable, intermittency and limit cycle) are studied in three-dimensional phase space by using a phase space reconstruction tool from the dynamical system theory. We report the first experimental observation of type-II intermittency in a spray combustion system. The statistical distributions of the length of aperiodic (turbulent) phase with respect to the control parameter, first return map and recurrence plot techniques are employed to confirm the type of intermittency.Copyright

Synchronous behaviour of two interacting oscillatory systems undergoing quasiperiodic route to chaos

Thermoacoustic instability, caused by a positive feedback between the unsteady heat release and the acoustic field in a combustor, is a major challenge faced in most practical combustors such as those used in rockets and gas turbines. We employ the synchronization theory for understanding the coupling between the unsteady heat release and the acoustic field of a thermoacoustic system. Interactions between coupled subsystems exhibiting different collective dynamics such as periodic, quasiperiodic, and chaotic oscillations are addressed. Even though synchronization studies have focused on different dynamical states separately, synchronous behaviour of two coupled systems exhibiting a quasiperiodic route to chaos has not been studied. In this study, we report the first experimental observation of different synchronous behaviours between two subsystems of a thermoacoustic system exhibiting such a transition as reported in Kabiraj et al. [Chaos 22, 023129 (2012)]. A rich variety of synchronous behaviours such as phase locking, intermittent phase locking, and phase drifting are observed as the dynamics of such subsystem change. The observed synchronization behaviour is further characterized using phase locking value, correlation coefficient, and relative mean frequency. These measures clearly reveal the boundaries between different states of synchronization.

Effect of time-delay and dissipative coupling on amplitude death in coupled thermoacoustic oscillators

We here systematically investigate amplitude death (AD) phenomenon in a thermoacoustic system using a mathematical model of coupled prototypical thermoacoustic oscillators, the horizontal Rijke tubes. AD has recently been identified as a relatively simple phenomenon, which can be exploited to stop the unwanted high amplitude pressure oscillations resulting from the occurrence of thermoacoustic instability. We examine the effect of time-delay and dissipative couplings on a system of two Rijke tubes when they are symmetrically and asymmetrically coupled. The regions where appropriate combinations of delay time, detuning, and the strengths of time-delay and dissipative coupling lead to AD are identified. The relative ease of attaining AD when both the couplings are applied simultaneously is inferred from the model. In the presence of strong enough coupling, AD is observed even when the oscillators of dissimilar amplitudes are coupled, while a significant reduction in the amplitudes of both the oscillators is observed when the coupling strength is not enough to attain AD.

Experimental Evidence of Amplitude Death and Phase-Flip Bifurcation between In-Phase and Anti-Phase Synchronization

Nonlinear phenomena emerging from the coupled behaviour of a pair of oscillators have attracted considerable research attention over the years, of which, amplitude death (AD) and phase-flip bifurcation (PFB) are two noteworthy examples. Although theoretical research has postulated the coexistence of AD and PFB upon variation of different control parameters, such an occurrence has not been reported in practical systems. Here, we provide the first experimental evidence of the coexistence of AD and PFB in a physical system, comprising of a coupled pair of candle-flame oscillators. As the strength of coupling between the oscillators is increased, we report a decrease in the span of AD region between the states of in-phase and anti-phase oscillations, leading up to a point of PFB. Understanding such a switching of phenomena between AD and PFB helps us to evade their undesirable occurrences such as AD in neuron and brain cells, oscillatory state in prey-predator systems, oscillatory spread of epidemics and so forth.

Intermittency: A State that Precedes Thermoacoustic Instability

Thermoacoustic instability is a plaguing problem in confined combustion systems, where self-sustained periodic oscillations of ruinous amplitudes that cause serious damage and performance loss to propulsive and power generating systems occur. In this chapter, we review the recent developments in understanding the transition route to thermoacoustic instability in gaseous combustion systems and describe a detailed methodology to detect this route in a two-phase flow combustion system. Until now, in these combustion systems, the transition to such instabilities has been reported as Hopf bifurcation, wherein the system dynamics change from a state of fixed point to limit cycle oscillations. However, a recent observation in turbulent gaseous combustion system has shown the presence of intermittency that precedes the onset of thermoacoustic instability. Intermittency is a dynamical state of combustion dynamics consisting of a sequence of high amplitude bursts of periodic oscillations amidst regions of relatively low amplitude aperiodic oscillations. Here, we discuss the process of transition to thermoacoustic instability in the two-phase flow system due to change in the control parameter, a location of flame inside the duct. As the flame location is varied, the system dynamics is observed to change from a region of low amplitude aperiodic oscillations to high amplitude self-sustained limit cycle oscillations through intermittency. The maximum amplitude of such intermittent oscillations witnessed during the onset of intermittency is much higher than that of limit cycle oscillations. We further describe the use of various tools from dynamical systems theory in identifying the type of intermittency in combustion systems.

Synchronization Transition in a Thermoacoustic System: Temporal and Spatiotemporal Analyses

The occurrence of thermoacoustic instability has been a major concern in the combustors used in power plants and propulsive systems such as gas turbine engines, rocket motors. A positive feedback between the inherent processes such as the acoustic field and the unsteady heat release rate of the combustor can result in the occurrence of large-amplitude, self-sustained pressure oscillations. Prior to the state of thermoacoustic instability, intermittent oscillations are observed in turbulent combustors. Such intermittent oscillations are characterized by an apparently random appearance of bursts of large-amplitude periodic oscillations interspersed between epochs of low-amplitude aperiodic oscillations. In most of the earlier studies, the pressure oscillations alone have been analyzed to explore the dynamical transition to thermoacoustic instability. The present chapter focuses on the instantaneous interaction between the acoustic field and the unsteady heat release rate observed during such a transition in a bluff-body-stabilized turbulent combustor. The instantaneous interaction of these oscillations will be discussed using the concepts of synchronization theory. First, we give a brief introduction to the synchronization theory so as to summarize the concepts of locking of phase and frequency of the oscillations. Then, the temporal and spatiotemporal aspects of the interaction will be presented in detail. We find that, during stable operation, aperiodic oscillations of the pressure and the heat release rate remain desynchronized, whereas synchronized periodic oscillations are noticed during the occurrence of thermoacoustic instability. Such a transition happens through intermittent phase-synchronized oscillations, wherein synchronization and desynchronization of the oscillators are observed during the periodic and the aperiodic epochs of the intermittent oscillations, respectively. Further, the spatiotemporal analysis reveals a very interesting pattern in the reaction zone. Phase asynchrony among the local heat release rate oscillators is observed during the stable operation, while they become phase-synchronized during the onset of thermoacoustic instability. Interestingly, the state of intermittent oscillations corresponds to a simultaneous existence of synchronized periodic and desynchronized aperiodic patterns in the reaction zone. Such a coexistence of synchrony and asynchrony in the reactive flow field mimics a chimera state.

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

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.

Characterization of forced response of density stratified reacting wake

The hydrodynamic stability of a reacting wake depends primarily on the density ratio [i.e., ratio of unburnt gas density (ρu) to burnt gas density (ρb)] of the flow across the wake. The variation of the density ratio from high to low value, keeping ρu/ρb>1, transitions dynamical characteristics of the reacting wake from a linearly globally stable (or convectively unstable) to a globally unstable mode. In this paper, we propose a framework to analyze the effect of harmonic forcing on the deterministic and synchronization characteristics of reacting wakes. Using the recurrence quantification analysis of the forced wake response, we show that the deterministic behaviour of the reacting wake increases as the amplitude of forcing is increased. Furthermore, for different density ratios, we found that the synchronization of the top and bottom branches of the wake with the forcing signal is dependent on whether the mean frequency of the natural oscillations of the wake (fn) is lesser or greater than the frequency of external forcing (ff). We notice that the response of both branches (top and bottom) of the reacting wake to the external forcing is asymmetric and symmetric for the low and high density ratios, respectively. Furthermore, we characterize the phase-locking behaviour between the top and bottom branches of the wake for different values of density ratios. We observe that an increase in the density ratio results in a gradual decrease in the relative phase angle between the top and bottom branches of the wake, which leads to a change in the vortex shedding pattern from a sinuous (anti-phase) to a varicose (in-phase) mode of the oscillations.