Raman I Sujith

Thermoacoustic instability has traditionally been investigated by linearizing the equations of combustion-acoustic interaction and testing for unstable eigenvalues of the linearized problem. However, it was observed that often the results of linear stability analysis agree poorly with experiments. Nevertheless, linear effects play a central role in combustion instability. The consequence of non-normality in the occurrence of subcritical transition to instability is illustrated in the context of a horizontal Rijke tube. It is shown that the coupled thermoacoustic system is non-normal as well as nonlinear. Non-normality can cause algebraic growth of oscillations for a short time even though all 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 subcritical transition to instability from initial states that have small energy. Measures to quantify transient growth are also discussed. Examples discussed include thermoacoustic instabilities in ducted premixed and diffusion flames and solid rocket motor. Copyright © 2004-06 by Asian Fluid Mechanics Committee.

We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.

Analysis of thermoacoustic instabilities were dominated by modal (eigenvalue) analysis for many decades. Recent progress in nonmodal stability analysis allows us to study the problem from a different perspective, by quantitatively describing the short-term behavior of disturbances. The short-term evolution has a bearing on subcritical transition to instability, known popularly as triggering instability in thermoacoustic parlance. We provide a review of the recent developments in the context of triggering instability. A tutorial for nonmodal stability analysis is provided. The applicability of the tools from nonmodal stability analysis are demonstrated with the help of a simple model of a Rjike tube. The article closes with a brief description of how to characterize bifurcations in thermoacoustic systems.

The presence of undesirable large-amplitude self-sustained oscillations in combustors resulting from thermoacoustic instability can lead to performance loss and structural damage to components of gas turbine and rocket engines. Traditional feedback controls to mitigate thermoacoustic instability possess electromechanical components, which are expensive to maintain regularly and unreliable in the harsh environments of combustors. In this study, we demonstrate the quenching of thermoacoustic instability through self-coupling—a method wherein a hollow tube is used to provide acoustic self-feedback to a thermoacoustic system. Through experiments and modeling, we identify the optimal coupling conditions for attaining amplitude death, i.e., complete suppression of thermoacoustic instabilities, in a horizontal Rijke tube. We examine the effect of both system and coupling parameters on the occurrence of amplitude death. We thereby show that the parametric regions of amplitude death occur when the coupling tube length is close to an odd multiple of the length of the Rijke tube. The optimal location to place the coupling tube for achieving amplitude death is near the antinode of the acoustic pressure standing wave in the Rijke tube. Furthermore, we find that self-coupling mitigates thermoacoustic instability in a Rijke tube more effectively than mutual coupling of two identical Rijke tubes. Thus, we believe that self-coupling can prove to be a simple, cost-effective solution for mitigating thermoacoustic instability in gas turbine and rocket combustors.

In this experimental study on a laboratory-scale turbulent annular combustor with sixteen swirl-stabilized burners, we study the flame-flame and flame-acoustic interactions during different dynamical states associated with the longitudinal mode of the combustor. We simultaneously measure the acoustic pressure and CH* chemiluminescence emission of the flame using a high-speed camera. Upon increasing the equivalence ratio, the combustor undergoes the following sequence of transition: combustion noise (CN) to low-amplitude longitudinal thermoacoustic instability (TAI) through the state of intermittency, and from low-amplitude to high-amplitude longitudinal TAI through a secondary bifurcation. We report the first evidence of secondary bifurcation from low-amplitude TAI to high-amplitude TAI for a turbulent thermoacoustic system which allows us to test the flame response at two different amplitude of perturbation in a natural setting. TAI arises at the first longitudinal mode of the combined burner tube and combustion chamber. The frequency of oscillations remain the same during the above transition. We find a significant difference in the dynamics of the flame interactions during the periodic part of intermittency and low- and high-amplitude TAI. Specifically, during the periodic part of intermittency, the phase difference between the local heat release rate (HRR) measured from various burners show significant phase slips in time. During low-amplitude TAI, there are fewer phase slips among the HRR response of the burners, which result in a state of weak synchronization among the flames. During high-amplitude TAI, we find that the flames are in perfect synchrony amongst themselves and with the pressure fluctuations. We then quantify the degree of temporal and spatial synchronization between different flames, and flames and pressure fluctuations using the Kuramoto order parameter and the phase-locking value. We show that synchronization theory can be conveniently used to characterize and quantify flame-acoustic interactions in an annular combustor.

This experimental study investigates the dynamical transition from stable operation to thermoacoustic instability in a turbulent bluff-body stabilised dump combustor. We conduct experiments to acquire acoustic pressure and local heat release rate fluctuations and use them to characterise this transition as we decrease the equivalence ratio towards a fuel-lean setting. More importantly, we observe a significant increase in local heat release rate fluctuations at critical locations well before thermoacoustic instability occurs. One of these critical locations is the stagnation zone in front of the bluff-body. By strategically positioning slots (perforations) on the bluff-body, we ensure the reduction of the growth of local heat release rate fluctuations at the stagnation zone near the bluff-body well before the onset of thermoacoustic instability. We show that this reduction in local heat release rate fluctuations inhibits the transition to thermoacoustic instability. We find that modified configurations of the bluff-body that do not quench the local heat release rate fluctuations at the stagnation zone result in the transition to thermoacoustic instability. We also reveal that an effective suppression strategy based on the growth of local heat release rate fluctuations requires an optimisation of the slots' area-ratio for a given bluff-body position. Further, the suppression strategy also depends on the spatial distribution of perforations on the bluff-body. Notably, an inappropriate distribution of the slots, which does not quench the local heat release rate fluctuations at the stagnation zone but creates new critical regions, may even result in a dramatic increase in the amplitudes of pressure oscillations.

In the present study, we investigate the effect of preheating of the reactants on the dynamics of a turbulent bluff-body-stabilized dump combustor during the onset of thermoacoustic instability. As we decrease the equivalence ratio towards a low fuel-lean value, we observe the dynamical transition of the combustor from the state of combustion noise to thermoacoustic instability via intermittency. Such an intermittency route to thermoacoustic instability is preserved for the range of preheat temperatures considered in this study. Further, we notice that an increase in the temperature of the reactants advances the point of the onset of thermoacoustic instability in the system. During the state of combustion noise, high temperature preheating of the reactants shifts the anchoring point of the flame from the shaft to the tip of the bluff-body and suppresses the oscillatory behavior of the global heat release rate in the system. We also observe a change in the multifractal characteristics of the heat release rate fluctuations such that the signal properties change from short-range to long-range correlations. On the other hand, preheating of the reactants to high temperatures during the state of thermoacoustic instability engenders a shift in the frequency of the acoustic field from the third unstable mode to the first unstable mode. Moreover, such preheating expanses the flame surface from one half of the combustor (lower) to both halves and, hence, increases the Pearson's correlation between the local heat release rate fluctuations measured on both halves of the combustor. Thus, we report that the preheating of the reactants significantly alters the dynamical characteristics of a turbulent combustor during the transition to thermoacoustic instability from that observed in the absence of preheating.

Abrupt transitions to the state of thermoacoustic instability (TAI) in gas turbine combustors are a significant challenge plaguing the development of next-generation low-emission aircraft and power generation engines. In this paper, we present the observation of abrupt transition in three disparate turbulent thermoacoustic systems: an annular combustor, a swirl-stabilized combustor, and a preheated bluff-body stabilized combustor. Using a low-order stochastic thermoacoustic model, we show that the reported abrupt transitions occur when an initially stable, supercritical limit cycle becomes unstable, leading to a secondary bifurcation to a large amplitude limit cycle solution. The states of combustion noise and intermittency observed in these turbulent combustors are well captured by the additive stochastic noise in the model. Through amplitude reduction, we analyze the underlying potential functions affecting the stability of the observed dynamical states. Finally, we make use of the Fokker–Planck equation, educing the effect of stochastic fluctuations on subcritical and secondary bifurcation. We conclude that a high enough intensity of stochastic fluctuations which transforms a subcritical bifurcation into an intermittency-facilitated continuous transition may have little effect on the abrupt nature of secondary bifurcation. Our findings imply the high likelihood of abrupt transitions in turbulent combustors possessing higher-order nonlinearities where turbulence intensities are disproportionate to the large amplitude limit cycle solution. Consequently, secondary bifurcations would be much more resilient to control, requiring improved control strategies.

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.

We develop a passive control strategy for suppressing thermoacoustic instability in a bluff-body stabilized premixed turbulent combustor. When the equivalence ratio is varied, there is a transition from combustion noise to thermoacoustic instability via intermittency in the combustor. We perform simultaneous acoustic pressure, 2D-PIV, and CH* chemiluminescence measurements to capture the pressure fluctuations, the velocity field, and the heat release rate (HRR) field during the transition. We measure the spatial distribution of the amplitude of turbulent velocity at the acoustic frequency, time-averaged vorticity, time-averaged HRR, and Rayleigh index and identify various regions of significance. We implement a passive control strategy by targeting these regions with a steady injection of secondary micro-jet of air to optimize the injection location and determine the critical region. Targeting the critical region with secondary air leads to greater than 20 dB suppression of the dominant thermoacoustic mode. We observe that the coherent structure forming from the shear layer following the dump plane gets suppressed, leading to an incoherent spatial distribution of HRR fluctuations. We find that the turbulent velocity amplitude correctly identifies the critical region for optimized passive control during thermoacoustic instability. In contrast, the Rayleigh index identifies the region of the most significant acoustic driving; however, it does not identify the region most sensitive to control. Finally, we extend our analysis by determining the spatial distribution of the Hurst exponent measured from the turbulent velocity field. We show that the Hurst exponent identifies the critical region during thermoacoustic instability and intermittency, unlike the other physical measures. Thus, we develop a smart passive control method by combining the need for finding critical regions in the combustor with the predictive capabilities of the Hurst exponent.