Raman I Sujith

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.

Thermoacoustic oscillations occur due to the interaction between the acoustic field in the combustor and the unsteady heat release rate. This interaction gives rise to a wide variety of dynamical states. In our experiments on a ducted laminar premixed flame, a prototypical thermoacoustic system, we observed presence of type-II intermittency in addition to limit cycle oscillation and quasi-periodic oscillation. Each dynamical state of the system are investigated based on the analysis of the reconstructed phase space and recurrence plots. The intermittent state resulted from the bifurcation of a quasi-periodic state and further, was followed by flame blowout. The dynamical behavior of the flame during intermittency is also discussed through flame imaging. Copyright © 2012 by L. Kabiraj and R. I. Sujith.

Thermoacoustic systems with a turbulent reactive flow, prevalent in the fields of power and propulsion, are highly susceptible to oscillatory instabilities. Recent studies showed that such systems transition from combustion noise to thermoacoustic instability through a dynamical state known as intermittency, where bursts of large-amplitude periodic oscillations appear in a near-random fashion in between regions of low-amplitude aperiodic fluctuations. However, as these analyses were in the temporal domain, this transition remains still unexplored spatiotemporally. Here, we present the spatiotemporal dynamics during the transition from combustion noise to limit cycle oscillations in a turbulent bluff-body stabilized combustor. To that end, we acquire the pressure oscillations and the field of heat release rate oscillations through high-speed chemiluminescence images of the reaction zone. With a view to get an insight into this complex dynamics, we compute the instantaneous phases between acoustic pressure and local heat release rate oscillations. We observe that the aperiodic oscillations during combustion noise are phase asynchronous, while the large-amplitude periodic oscillations seen during thermoacoustic instability are phase synchronous. We find something interesting during intermittency: patches of synchronized periodic oscillations and desynchronized aperiodic oscillations coexist in the reaction zone. In other words, the emergence of order from disorder happens through a dynamical state wherein regions of order and disorder coexist, resembling a chimera state. Generally, mutually coupled chaotic oscillators synchronize but retain their dynamical nature; the same is true for coupled periodic oscillators. In contrast, during intermittency, we find that patches of desynchronized aperiodic oscillations turn into patches of synchronized periodic oscillations and vice versa. Therefore, the dynamics of local heat release rate oscillations change from aperiodic to periodic as they synchronize intermittently. The temporal variations in global synchrony, estimated through the Kuramoto order parameter, echoes the breathing nature of a chimera state.

The influence of system parameters such as the flame location, Peclet number and Damköhler number on the bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry is presented in this paper. In the bifurcation plot with flame location as the bifurcation parameter, subcritical Hopf bifurcation is found for lower values of flame location and supercritical Hopf bifurcation for higher values of flame location, for all the Damköhler numbers used in this study. The flame shapes are captured at eight different phases of a cycle of time series data of acoustic velocity at both the fold and Hopf points for bifurcation with flame location as the parameter. We find that the range of flame height variations at the Hopf point is more than the range of flame height variations obtained at the fold point. We also find that the flame oscillates in the same phase as pressure fluctuation but in a phase different from both velocity and heat release rate fluctuations in the region of hysteresis for bifurcation with flame location. The non-dimensional hysteresis width is plotted as a function of Damköhler number for variation of flame location in the subcritical region. An inverse power law relation is found between the non-dimensional hysteresis width and the Damköhler number. The bifurcation plot with Peclet number as parameter shows a subcritical Hopf bifurcation.

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.

The present study develops an alternative perspective on the response of premixed flames to flow perturbations. In particular, the linear response of laminar premixed flames to velocity perturbations is examined in the time domain, and the corresponding impulse response functions are determined analytically. Different flame types and shapes as well as different velocity perturbation models are considered. Two contributions to the flame response are identified: a convective displacement of the flame due to velocity perturbations, and a restoration mechanism, which is a consequence of the combined effects of flame propagation and flame anchoring. The impulse responses are used to identify the relevant time scales and to form non-dimensional frequencies. The link of the present results to previous studies formulated in the frequency domain is established. The time domain approach is found to facilitate analysis and interpretation of well-known properties of premixed flames such as excess gain, periodic cutoff and self-similar aspects of flame response. Characteristic time scales of response appear naturally and can be interpreted in a straightforward manner. © 2013 The Combustion Institute.

This paper proposes and compares two nonlinear time-domain models of self-excited thermoacoustic oscillations of laminar premixed flames. Both models are hybrid formulations, where the flame and its immediate vicinity are resolved with a reactive flow simulation, while the acoustic field is modeled with a low-order model that is coupled to the reactive flow simulation. Firstly, a flame model based on the fully compressible Navier-Stokes equations is investigated. In this case, the flame simulation is coupled to the low-order model via the characteristic wave amplitudes at the inlet boundary. Secondly, the flame is resolved with a low Mach number reactive flow simulation. In order to include two-way thermoacoustic feedback, this flame model is coupled with an acoustic network model via the global heat release rate and the fluctuation of the axial velocity at a reference position upstream of the flame. A bifurcation analysis using the plenum length as bifurcation parameter is conducted. Both models exhibit complex nonlinear oscillations and are in good agreement with each other. Therefore, we conclude that the coupling of a linear acoustic model and a nonlinear flame model via reference velocity and global heat release rate is sufficient to accurately capture thermoacoustic oscillations of the configuration investigated. This implies that the most important nonlinearities can be attributed to hydrodynamic effects and flame kinematics. Furthermore, the study corroborates that premixed flames respond predominantly to fluctuations of the upstream flow velocity.

Combustion instability is a nonlinear process with interaction between combustion and acoustics. The nonlinearity in the combustion process is observed in the flame dynamics. In our study of a ducted laminar premixed V-flame, we varied the distance between the flame anchor and the duct exit. We observed that the thermoacoustic system bifurcates from a stable state to a frequency locked state, followed by quasi-periodicity, period 3 oscillations, and finally chaotic oscillations. During the occurrence of these dynamical states, the role of flame dynamics is investigated using high speed imaging. We observed wrinkle formation, its propagation and growth along flame front, rollup of the flame, separation, and annihilation of flame elements during instability. From the present study it is found that each dynamical state is characterized by a particular sequence of flame behavior, highlighting the role of nonlinear flame dynamics in establishing the observed dynamical state.

An experimental investigation of the non-normal nature of thermoacoustic interactions in an electrically heated horizontal Rijke tube is performed. Since non-normality and the associated transient growth are linear phenomena, the experiments have to be confined to the linear regime. The bifurcation diagram for the subcritical Hopf bifurcation into a limit cycle behavior has been determined, after which the amplitude levels, for which the system acts linearly, have been identified for different power inputs to the heater. There are two main objectives for this experimental investigation. The first one deals with the extraction of the linear eigenmodes associated with the acoustic pressure from experimental data. This is accomplished by the Dynamic Mode Decomposition (DMD) technique applied in the linear regime. The non-orthogonality between the eigenmodes is determined for various values of heater power. The second objective is to identify evidence of transient perturbation growth in the system. The total acoustic energy in the duct has been monitored as the thermoacoustic system has been initialized by linear combinations of the two dominant eigenmodes. Transient growth, on the order of previous theoretical studies, has been found, and its parameter dependence on amplitude ratio and phase angle of the initial eigenmode components has been determined. This study represents the first experimental confirmation of non-normality in thermoacoustic systems. © 2011 by S. Mariappan, R. I. Sujith and P. J. Schmid.

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.