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Propulsion systems such as gas turbines are susceptible to combustion instability, when operated at lean equivalence ratio [1]. During combustion instability, there is a nonlinear interaction between combustion and acoustics leading to large amplitude acoustic oscillations. These large amplitude oscillations are detrimental to the stability of the combustor and can cause damages to the structural integrity of the combustor, flame flash back or blow off. The main source of nonlinearity is in the heat release rate caused due to the velocity perturbations at the flame holder [2]. The heat release rate fluctuations are due to the variation in the flame surface area. Hence there is a need to understand the flame dynamics that contributes to the heat release rate fluctuations. The present study aims in understanding the stability of a V - flame combustor by varying the flame location inside an acoustic resonator. By varying the flame location the instability regimes of the combustor are identified. At the flame locations where the system exhibits combustion instability, acoustic pressure oscillations are acquired simultaneously with high speed images of the flame front fluctuations so that a correlation can be made between them. Tools from dynamical systems theory are applied to the pressure signal to quantify different dynamical states of the system during combustion instability. Moreover the flame dynamics at each dynamical state are investigated. It is observed that combustion instability is characterized by interesting dynamical states such as frequency locked state, quasi-periodic oscillations, period 3 oscillations and chaotic oscillations. High speed imaging of the flame reveals different interesting patterns of flame behavior during combustion instability. Flame wrinkling, roll up of flame elements, separation as islands of the flame elements and mutual annihilation of flame elements were some of the interesting flame behavior observed. This study helps in understanding the role of nonlinear heat release rate mechanism in establishing different dynamical states during combustion instability. Copyright © 2014 by ASME.

GENERAL

Department of Aerospace Engineering

Department Of Chemical Engineering

ASME 2014 Gas Turbine India Conference, GTINDIA 2014

Investigation of flame dynamics in a v - Flame combustor during combustion instability

The influence of system parameters such as heater power, heater location and mass flow rate on the hysteresis characteristics of a horizontal Rijke tube is presented in this paper. It is observed that a hysteresis zone is present for all the mass flow rates considered in the present study. A power law relation is established between the non-dimensional hysteresis width and the Strouhal number, defined as the ratio between convective time scale and acoustic time scale. The transition to instability in a horizontal Rijke tube is found to be subcritical in all the experiments performed in this study. When heater location is chosen as the control parameter, period-2 oscillations are found for specific values of mass flow rate and heater power.

Fulltext

International Journal of Spray and Combustion Dynamics

Influence of system parameters on the hysteresis characteristics of a horizontal Rijke tube

The dynamic transition from combustion noise to combustion instability was investigated experimentally in two laboratory-scale turbulent combustors (namely, swirl-stabilized and bluff-body-stabilized backward-facing-step combustors) by systematically varying the flow Reynolds number. We observe that the onset of combustion-driven oscillations is always presaged by intermittent bursts of high-amplitude periodic oscillations that appear in a near-random fashion amidst regions of aperiodic low-amplitude fluctuations. These excursions to periodic oscillations last longer in time as operating conditions approach instability and finally the system transitions completely into periodic oscillations. A continuous measure to quantify this bifurcation in dynamics can be obtained by defining an order parameter as the probability of the signal amplitude exceeding a predefined threshold. A hysteresis zone was observed in the bluff-body-stabilized configuration that was absent in the swirl-stabilized configuration. The recurrence properties of the dynamics of intermittent burst oscillations were quantified using recurrence plots and the distribution of the aperiodic phases was examined. From the statistics of these aperiodic phases, robust early-warning signals of an impending combustion instability may be obtained. © 2014 Cambridge University Press.

Journal of Fluid Mechanics

Intermittency route to thermoacoustic instability in turbulent combustors

Thermoacoustic heat engine (TAHE) converts thermal power (heat) into acoustic power. TAHE has been gaining significant interest because of its non-fuel specific, low cost and high reliability (due to reduced moving parts) compared to conventional IC engines. The performance of TAHE depends upon the various parameters such as stack position, stack length and resonator length. Previously, we built a fixed TAHE which converts heat energy to electrical energy with an efficiency of 2 %. However, the performance of the fixed engine was not fully optimized. To investigate further, another novel tunable TAHE has been built with the goal of optimizing the efficiency by tuning three critical parameters, namely stack position, stack length and resonator length. This paper shows the influence of stack parameters (stack position and stack length) and resonator length on the performance of the thermoacoustic heat engine. The performance is measured in terms of the pressure amplitude generated inside the TAHE using air as the working fluid. It is observed that the stack's position considerably affects the performance. Further, from experiments, it is observed that the maximum acoustic power is generated when the stack is positioned closer to a pressure antinode. © 2014 IEEE.

2014 International Conference on Advances in Electrical Engineering, ICAEE 2014

Performance optimization of tunable standing wave thermoacoustic engine by varying the stack parameters and resonator length: An experimental study

The dynamic transitions preceding combustion instability and lean blowout were investigated experimentally in a laboratory scale turbulent combustor by systematically varying the flow Reynolds number. We observe that the onset of combustion-driven oscillations is always presaged by intermittent bursts of high-amplitude periodic oscillations that appear in a near random fashion amidst regions of aperiodic, low-amplitude fluctuations. The onset of high-amplitude, combustion-driven oscillations in turbulent combustors thus corresponds to a transition in dynamics from chaos to limit cycle oscillations through a state characterized as intermittency in dynamical systems theory. These excursions to periodic oscillations become last longer in time as operating conditions approach instability and finally the system transitions completely into periodic oscillations. Such intermittent oscillations emerge through the establishment of homoclinic orbits in the phase space of the global system which is composed of hydrodynamic and acoustic subsystems that operate over different time scales. Such intermittent burst oscillations are also observed in the combustor on increasing the Reynolds number further past conditions of combustion instability towards the lean blowout limit. Highspeed flame images reveal that the intermittent states observed prior to lean blowout correspond to aperiodic detachment of the flame from the bluff-body lip. These intermittent oscillations are thus of prognostic value and can be utilized to provide early warning signals to combustion instability as well as lean blowout. Copyright © 2014 by ASME.

World University root node

Proceedings of the ASME Turbo Expo

Intermittency in the dynamics of turbulent combustors

The present study aims at arming an operator of fielded turbulent combustors with a repertoire of mathematical measures for real-time monitoring to forewarn the onset of impending combustion instability. In turbulent combustors, the route to high-amplitude, periodic, combustion-driven oscillations from conditions of low-amplitude, chaotic, combustion noise happens through an intermediate regime in flow conditions where the measured pressure fluctuations display bursts of intermittent, high-amplitude, periodic oscillations that appear in a nearrandom manner amidst chaotic fluctuations. This loss of chaos from combustion noise to combustion instability can be quantified to serve as a precursor to impending instability. The recurrence properties of intermittent burst oscillations can be quantified using dynamical systems theory by tracking the distribution of the aperiodic segments in the measured signals. Several statistical measures may be constructed through such recurrence quantification that provide robust early warning signals to an impending instability. Further, the transition to combustion driven oscillations leads to a collapse of the number of relevant time scales involved in the problem. This collapse in time scales can be quantified using generalized Hurst exponents which serve as an additional measure that captures the onset of an impending combustion instability well in advance. The various patent pending measures illustrated in this paper serve as precursors due to the inevitable presence of an intermittent regime of burst oscillations in turbulent combustors. Copyright © 2014 by ASME.

Engineering precursors to forewarn the onset of an impending combustion instability

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.

Combustion and Flame

Novel perspectives on the dynamics of premixed flames

In this paper, we show how the phenomenon of intermittency observed in systems with turbulent flow-sound interaction is related to the formation of homoclinic orbits in the phase space. Such orbits that emerge via the intersection of the stable and unstable manifold of an equilibrium configuration result from interactions that happen at multiple spatial/temporal scales associated with turbulent convection and wave propagation. Through a quantification of the time spent by the dynamics in the aperiodic states using recurrence plots, we show how the presence of homoclinic orbits in the dynamics may be convincingly demonstrated, which is often not possible through a visual inspection of the phase space of the attractor. © 2013 AIP Publishing LLC.

Chaos

Identifying homoclinic orbits in the dynamics of intermittent signals through recurrence quantification

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.

Subcritical bifurcation and bistability in thermoacoustic systems

Analysing and quantifying parametric uncertainties numerically is a tedious task, even more so when the system exhibits subcritical bifurcations. Here a novel interpolation based approach is presented and applied to two simple models exhibiting subcritical Hopf bifurcation. It is seen that this integrated interpolation scheme is significantly faster than traditional Monte Carlo based simulations. The advantages of using this scheme and the reason for its success compared to other uncertainty quantification schemes like Polynomial Chaos Expansion (PCE) are highlighted. The paper also discusses advantages of using an equi-probable node distribution which is seen to improve the accuracy of the proposed scheme. The probabilities of failure (POF) are defined and plotted for various operating conditions. The possibilities of extending the above scheme to experiments are also discussed. © 2013 Elsevier Ltd.

Probabilistic Engineering Mechanics

Uncertainty quantification of subcritical bifurcations

The problem of combustion instabilities arising from the thermoacoustic interactions in a ducted premixed flame model is considered. Contrary to the conventionally used low-order models to describe such systems, a high dimensional model governed by a set of the acoustic equations coupled to the equations for flame dynamics is employed. The flame front is discretized into finite flame elements to assign internal degrees of freedom to the front and track its evolution. Model reduction schemes, namely proper orthogonal decomposition (POD) and balanced truncation, are used to reduce the size of this model. Compared to POD modes, balanced modes show superior input-output characteristics, in agreement with the full model. POD modes on the other hand capture the transient growth in the model while the balanced modes do not. Performance of POD modes is highly dependent on the snapshots used for their computation. A linear quadratic Gaussian (LQG) framework using the reduced-order model based on 16 balanced modes is formulated to control thermoacoustic instabilities in the linear model. The controllers thus obtained are then used on the nonlinear model. They successfully curtail limit cycle oscillations in the nonlinear plant and also avoid subcritical transition to instability. © 2013 Copyright Taylor and Francis Group, LLC.

Combustion Science and Technology

Thermoacoustic instabilities in a ducted premixed flame: Reduced-Order models and control

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

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.

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

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.

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

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

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

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.