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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.

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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.

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Department of Aerospace Engineering

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International Journal of Spray and Combustion Dynamics

Loss of chaos in combustion noise as a precursor of impending combustion instability

Perturbations in a non-normal system can grow transiently even if the system is linearly stable. If this transient growth is sufficiently large, it can trigger self-sustained oscillations from small initial disturbances. This has important practical consequences for combustion-acoustic oscillations, which are a persistent problem in rocket and aircraft engines. Balasubramanian &amp; Sujith (J. Fluid Mech., vol. 594, 2008, pp. 29-57) modelled an infinite-rate chemistry diffusion flame in an acoustic duct and found that the transient growth in this system can amplify the initial energy by a factor, Gmax, of the order of 105 to 107. However, recent investigations by L. Magri and M. P. Juniper have brought to light certain errors in that paper. When the errors are corrected, Gmax is found to be of the order of 1 to 10, revealing that non-normality is not as influential as it was thought to be. © 2013 Cambridge University Press.

Journal of Fluid Mechanics

Non-normality in combustion-acoustic interaction in diffusion flames: A critical revision

We are now into the fifth year of publication of the International Journal of Spray and Combustion Dynamics. Last year, we were accredited by Web of Science (isiknowledge.com). Beginning with Volume 1, Issue 1, IJSCD will be indexed and abstracted in ï Science Citation Index Expanded (also known as SciSearch®) ï Journal Citation Reports/Science Edition ï Current Contents®/Engineering Computing and Technology&nbsp;

Editorial

Nonlinear self-excited thermoacoustic oscillations appear in systems involving confined combustion in the form of coupled acoustic pressure oscillations and unsteady heat release rate. In this paper, we investigate the nonlinear transition undergone by thermoacoustic oscillations to flame blowout via intermittency, in response to variation in the location of the combustion source with respect to the acoustic field of the confinement. A ducted laminar premixed conical flame, stabilized on a circular jet exit with a fully developed exit velocity profile, was investigated. Transition to limit cycle oscillations from a non-oscillatory state was observed to occur via a subcritical Hopf bifurcation. Limit cycle oscillations underwent a further bifurcation to quasi-periodic oscillations characterized by the repeated formation of elongated necks in the flame that pinch off as pockets of unburned fuel-air mixture. The quasi-periodic state loses stability, resulting in an intermittent state identified as type II through recurrence analysis of phase space trajectories reconstructed from the acoustic pressure time trace. In this state, the flame undergoes repeated lift-off and reattachment. Instantaneous flame images suggest that the intermittent flame behaviour is influenced by jet flow dynamics. © 2012 Cambridge University Press.

Nonlinear self-excited thermoacoustic oscillations: Intermittency and flame blowout

A linear mechanism for the emergence of acoustic waves from aperiodic vorticity disturbances is presented for a simple stagnation point flow. The non-modal approach, which made possible the discovery of a similar mechanism in unbounded shear flows, is employed. The phenomenon is shown to be closely related to the non-normal nature of the linearized operator governing the evolution of small perturbations about the mean flow. The vorticity disturbance acts as an acoustic source by interacting with the mean velocity gradient and drives the acoustic waves in a non-resonant manner. The physical mechanism by which the acoustic and vortical components of the disturbance exchange energy with the mean flow is presented. The proposed mechanism is relevant for numerous applications involving mass addition or removal, such as aeroacoustic instabilities in a solid rocket motor. Similar phenomena are expected to occur in accelerated flows, like the flow in a nozzle. Numerical simulations using a high order, dispersion relation preserving scheme is used to demonstrate how a localized vorticity disturbance of small amplitude generates sound waves when strained by the gradients in the base flow. The simulations reveal that the vorticity disturbance acts as a quadrupole source of sound, whose origin is explained using physical arguments. Linear simulations using a spectral code verify the results of the nonlinear simulations performed at small amplitude.

International Journal of Aeroacoustics

Sound production by vorticity fluctuations in a stagnation point flow

The question of which norm should be used to characterize the fluctuating disturbance energy in studies on thermoacoustic instabilities remains a topic of continued debate. In this paper we formulate a strategy for developing mathematically consistent norms that do not support spurious growth of disturbance energy in the absence of 'physical' sources of energy. A critical analysis of various disturbance energy norms existing in literature is conducted and important conclusions regarding positive definitiveness and susceptibility to exhibiting unphysical growth are drawn. It is shown that the energy norm proposed by Cantrell and Hart [Interaction between sound and flow in acoustic cavities: mass, momentum and energy considerations, Journal of Acoustical Society of America 36 (1964) 697706] and Myers first order disturbance energy norm [Transport of energy by disturbances in arbitrary steady flow, Journal of Fluid Mechanics 226 (1991) 383400] are positive definite if M0&lt;1 and M0&lt;1/γ, respectively, where M 0 is the magnitude of the local mean flow Mach number, γ is the ratio of specific heats at constant pressure and volume and the stipulated conditions should be met at every point in the flow domain. Our analysis shows that the disturbance energy norm proposed by Chu [On the energy transfer to small disturbances in fluid flow (part I), Acta Mechanica 1 (1965) 215234] does not exhibit unphysical growth. It is also shown that this property is not unique to Chus disturbance energy norm and there exists a family of norms which satisfy this requirement. The analysis also leads to an interesting interpretation of the acoustic energy conservation principle of Cantrell and Hart. The potential held by various disturbance energy norms for exhibiting fictitious growth is quantified using tools from nonmodal stability theory. It is concluded that if the mean flow Mach number is small, Myers norm is a suitable measure of the disturbance energy. © 2011 Elsevier Ltd. All rights reserved.

Journal of Sound and Vibration

Disturbance energy norms: A critical analysis

Lean flame blowout induced by thermoacoustic oscillations is a serious problem faced by the power and propulsion industry. We analyze a prototypical thermoacoustic system through systematic bifurcation analysis and find that starting from a steady state, this system exhibits successive bifurcations resulting in complex nonlinear oscillation states, eventually leading to flame blowout. To understand the observed bifurcations, we analyze the oscillation states using nonlinear time series analysis, particularly through the representation of pressure oscillations on a reconstructed phase space. Prior to flame blowout, a bursting phenomenon is observed in pressure oscillations. These burst oscillations are found to exhibit similarities with the phenomenon known as intermittency in the dynamical systems theory. This investigation based on nonlinear analysis of experimentally acquired data from a thermoacoustic system sheds light on how thermoacoustic oscillations lead to flame blowout. Copyright © 2012 by ASME.

Proceedings of the ASME Turbo Expo

Dynamics of thermoacoustic oscillations leading to lean flame blowout

The dynamics of combustion-driven thermoacoustic oscillations for a ducted laminar premixed flame has been investigated in lean equivalence ratio conditions. Combustion instability appears in the system as acoustic pressure and flame surface oscillations following a Hopf bifurcation. Further change in the control parameter leads to subsequent bifurcations, causing a rich dynamical behavior such as quasi-periodic and intermittent burst oscillations to appear in the system. During the burst oscillation phase, the system dynamics resembles the flame blowout phenomenon, which is of interest in practical combustion applications. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Fluid Dynamics Research

Investigating the dynamics of combustion-driven oscillations leading to lean blowout

Bifurcation analysis is performed on experimental data obtained from a simple setup comprising ducted laminar premixed conical flames in order to investigate the features of nonlinear thermoacoustic oscillations. It is observed that as the bifurcation parameter is varied, the system undergoes a series of bifurcations leading to characteristically different nonlinear oscillations. Through the application of nonlinear time series analysis to pressure and flame (CH chemiluminescence) intensity time traces, these oscillations are characterized as periodic, aperiodic, or chaotic oscillations, and subsequently the nature of the obtained bifurcations is explained based on dynamical systems theory. Nonlinear interaction between the flames and the acoustic modes of the duct is clearly reflected in the high speed flame images acquired simultaneously with pressure time series. © 2012 by ASME.

Journal of Engineering for Gas Turbines and Power

Bifurcations of self-excited ducted laminar premixed flames

I am very pleased to inform you that International Journal of Spray and Combustion Dynamics has been selected for coverage in the Web of Science (Thomson Reuter’s products and services). Beginning with Volume 1, Issue 1, IJSCD will be indexed and abstracted in • Science Citation Index Expanded (also known as SciSearch®) • Journal Citation Reports/Science Edition • Current Contents®/Engineering Computing and Technology&nbsp;

Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario. © 2012 American Institute of Physics.

Chaos

Route to chaos for combustion instability in ducted laminar premixed flames

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.

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

Bifurcation analysis and observation of intermittency in combustion-driven thermoacoustic oscillations

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.

47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit 2011

Non-normality of thermoacoustic interactions: An experimental investigation

Non-normality can cause transient growth of perturbations in thermoacoustic systems with stable eigenvalues. This can cause low-amplitude perturbations to grow to amplitudes high enough to make nonlinear effects significant, and the system can become nonlinearly unstable, even though it is stable under classical linear stability. In this paper, we have demonstrated that this feature can lead to the failure of the traditional controllers that were designed on the basis of classical linear stability analysis. We have also shown in a simple model that it is possible to prevent 'nonlinear driving' by controlling transient growth, using linear controllers. The analysis is performed in the context of a horizontal Rijke tube. © 2011 Cambridge University Press.

Non-normality and its consequences in active control of thermoacoustic instabilities

Bifurcation analysis is conducted on experimental data obtained from a simple setup comprising of ducted, laminar premixed conical flames to investigate the features of nonlinear thermoacoustic oscillations. It is observed that as the bifurcation parameter is varied, the system undergoes series of bifurcations leading to characteristically different nonlinear oscillations. Through the application of nonlinear time series analysis on pressure and flame (CH* chemiluminescence ) intensity time traces, these oscillations are characterised as periodic, aperiodic or chaotic oscillations and subsequently the nature of the obtained bifurcations is explained based on dynamical systems theory. Nonlinear interaction between the flames and the acoustic modes of the duct is clearly reflected in the high speed flame images acquired simultaneously with pressure and flame intensity measurements. Copyright © 2011 by ASME.

Experimental studies of bifurcations leading to chaos in a laboratory scale thermoacoustic system

An experimental investigation of the bistable region of instability in a thermoacoustic system comprising of ducted, premixed laminar flames has been performed. The stability diagram of the system is obtained and the bistable region for a range of flame locations at different fuel-air mixture equivalence ratios is identified. Subsequently, threshold amplitudes for triggering instability in the system using sinusoidal acoustic forcing, introduced externally, is obtained. It is observed that depending on how close the system is to the Hopf point and the nature of oscillations at the Hopf point, the triggered oscillations can exhibit different dynamical behavior. Copyright © 2011 by ASME.

Investigation of subcritical instability in ducted premixed flames

This paper investigates the non-normal nature of premixed flame-acoustic interaction. The thermoacoustic system is modelled using the acoustic equations for momentum and energy, together with the equation for the evolution of the flame front obtained from the kinematic G-equation. As the unsteady heat addition acts as a volumetric source, the flame front is modelled as a distribution of monopole sources. Evolutions of the system are characterized with a measure of energy due to fluctuations. In addition to the acoustic energy, the energy due to fluctuations considered in the present paper accounts for the energy of the monopole sources. The linearized operator for this thermoacoustic system is non-normal, leading to non-orthogonality of its eigenvectors. Non-orthogonal eigenvectors can cause transient growth even when all the eigenvectors are decaying. Therefore, classical linear stability theory cannot predict the finite-time transient growth observed in non-normal systems. In the present model, the state space variables include the monopole source strengths in addition to the acoustic variables. Inclusion of these variables in the state space is essential to account for the transient growth due to non-normality. A parametric study of the variation in transient growth due to change in parameters such as flame location and flame angle is performed. In addition to projections along the acoustic variables of velocity and pressure, the optimal initial condition for the self-evolving system has significant projections along the strength of the monopole distribution. Comparison of linear and corresponding nonlinear evolutions highlights the role of transient growth in subcritical transition to instability. The notion of phase between acoustic pressure and heat release rate as an indicator of stability is examined. © 2011 Cambridge University Press.

Non-normality and internal flame dynamics in premixed flame-acoustic interaction

An analysis of thermoacoustic instability is performed for a horizontal Rijke tube with an electrical resistance heater as the heat source. The governing equations for this fluid flow become stiff and are difficult to solve by the computational fluid dynamics (CFD) technique, as the Mach number of the steady flow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore, an asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stiffness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic field and the other for the unsteady flow field in the hydrodynamic zone around the heater. In this analysis, the coupling between the acoustic field and the unsteady heat release rate from the heater appears from the asymptotic analysis. Furthermore, a non-trivial additional term, referred to as the global-acceleration term, appears in the momentum equation of the hydrodynamic zone, which has serious consequences for the stability of the system. This term can be interpreted as a pressure gradient applied from the acoustic onto the hydrodynamic zone. The asymptotic stability of the system with the variation of system parameters is presented using the bifurcation diagram. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD techniques for the hydrodynamic zone. The results confirm the importance of the global-acceleration term. Bifurcation diagrams obtained from the simulations with and without the above term are different. Acoustic streaming is shown to occur during the limit cycle and its effect on the unsteady heat release rate is discussed. © 2011 Cambridge University Press.

Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube

A systematic approach for non-modal stability analysis of thermoacoustic systems with a localized heat source is proposed. The response of the heat source to flow perturbations is obtained from unsteady computational fluid dynamics combined with correlation-based linear system identification. A model for the complete thermoacoustic system is formulated with a Galerkin expansion technique, where the heat source is included as an acoustically compact element. The eigenvalues of the resulting system are obtained from discretization of the solution operator, the maximum growth factor is estimated from the pseudospectra using Kreiss' theorem. The approach is illustrated with a simple Rijke tube configuration. Results obtained with a simple "baseline" model for the heat source dynamics based on King's law - widely used in hot wire anemometry - are compared against the more advanced treatment developed here. Analysis of pseudospectra diagrams shows that the choice of the heat source model does influence the sensitivity of eigenvalues to perturbations and hence the non-normal behavior. The maximum growth factor for the system with the heat source model based on King's law is more sensitive to changes in the heat source location than the CFD-based heat source model. © 2010 Elsevier Inc. All rights reserved.

Applied Mathematics and Computation

Identification of heat transfer dynamics for non-modal analysis of thermoacoustic stability

Chu [On the energy transfer to small disturbances in fluid flow (part I), Acta Mechanica 1 (1965) 215234] proposed a positive definite energy norm for characterizing the level of fluctuation in a disturbance. In the absence of heat transfer at the boundaries, work done by boundary or body forces, heat and material sources of energy, this norm is a monotone, non-increasing function of time. In this paper, we show that Chus disturbance energy defines an inner product, with respect to which the conservation equations of fluid motion linearized about a uniform base flow are self-adjoint. This ensures that the eigenvectors of the linearized operator are orthogonal to each other, and the property that the energy norm is a non-increasing function of time in the absence of physical sources of energy follows as an immediate consequence. Examples from numerical simulations of Euler equations are presented to highlight the importance of choosing an energy norm that is consistent with the underlying physics. We demonstrate that the disturbance energy as measured by Chus norm does not exhibit spurious transient growth in the absence of physical sources of energy and hence is suitable for analyzing thermoacoustic instability. © 2011 Elsevier Ltd.