Raman I Sujith

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.

The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibra-tional loads. Estimating the amplitude of the limit cycle oscillations (LCO) that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the LCO. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using 'spectral measures' which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.

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.

The role of non-normality and nonlinearity in thermoacoustic interaction in a Rijke tube is investigated in this paper. The heat release rate of the heating element is modeled by a modified form of King's law. This fluctuating heat release from the heating element is treated as a compact source in the one-dimensional linear model of the acoustic field. The temporal evolution of the acoustic perturbations is studied using the Galerkin technique. It is shown that any thermoacoustic system is non-normal. Non-normality can cause algebraic growth of oscillations for a short time even though 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 triggering, i.e., the thermoacoustic oscillations decay for some initial conditions whereas they grow for some other initial conditions. If a system is non-normal, then there can be large amplification of oscillations even if the excited frequency is far from the natural frequency of the system. The dependence of transient growth on time lag and heater positions are studied. Such amplifications (pseudoresonance) can be studied using pseudospectra, as eigenvalues alone are not sufficient to predict the behavior of the system. The geometry of pseudospectra can be used to obtain upper and lower bounds on the growth factor, which provide both necessary and sufficient conditions for the stability of a thermoacoustic system. © 2007 by K. Balasubramanian and R. 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.

In this study, we systematically analyze the effects of hydrogen enrichment in the well-known PRECCINSTA burner, a partially premixed swirl-stabilized methane/air combustor. Keeping the equivalence ratio and thermal power constant, we vary the hydrogen percentage in the fuel. Successive increments in hydrogen fuel fraction increase the adiabatic flame temperature and also shift the dominant frequencies of acoustic pressure fluctuations to higher values. Under hydrogen enrichment, we observe the emergence of periodicity in the combustor resulting from the interaction between acoustic modes. As a result of the interaction between these modes, the combustor exhibits a variety of dynamical states, including period-1 limit cycle oscillations (LCO), period-2 LCO, chaotic oscillations, and intermittency. The flame and flow behavior is found to be significantly different for each dynamical state. Analyzing the coupled behavior of the acoustic pressure and the heat release rate oscillations during the states of thermoacoustic instability, we report the occurrence of 2:1 frequency-locking during period-2 LCO, where two cycles of acoustic pressure lock with one cycle of the heat release rate. During period-1 LCO, we notice 1:1 frequency-locking, where both acoustic pressure and heat release rate repeat their behavior in every cycle.

This paper studies the effect of acoustic excitation on the heat release characteristics of a two dimensional premixed flame. Past researches have assumed the acoustic nearfleld and kinematics of the flame surface to be decoupled. However, recent studies by the authors have shown that the acoustic nearfleld is significantly affected by flame surface wrinkling and hence the coupling between flame surface kinematics and the acoustic field cannot be neglected. The acoustic velocity nearfleld of the flame surface is determined using a modified Boundary Integral Equation (BIE) to include the effects of flame front wrinkling on the acoustic field. A linearized G-equation is solved to obtain an expression for the flame surface wrinkling in terms of the acoustic velocity at the flame front. This equation is then solved simultaneously with the BIE using a Newton-Raphson scheme to obtain simultaneously, the flame surface shape and the acoustic velocity variation, for the case of a two-dimensional dump stabilized flame. The results show that the transfer function is controlled by two parameters, the flame Strouhal number and the half-angle at the apex of the flame (θ). The computed transfer function is compared with the transfer functions obtained assuming a one-dimensional axial velocity fluctuation and by neglecting kinematic coupling. The latter predicts transfer function magnitudes greater than unity. The inclusion of kinematic coupling however is observed to predict lower gain at low excitation Strouhal numbers when compared to the uncoupled case. The predicted magnitudes are seen to increase with decrease in θ. The predicted phase however, is observed to be insensitive to changes in θ.

Design of a linear controller for a thermoacoustic system taking the consequences of nonnormality into account is presented in this paper. The analysis is performed in the framework of the classical n-τ model of Crocco. The controllers based on classical stability analysis focuses on the stability of the individual eigenmodes of the system. However, the nonnormal nature of a thermoacoustic system which implies non-orthogonality of the eigenvectors causes redistribution of the acoustic energy between the eigenmodes even in the linear regime. Transient growth in a linearized system, even when the individual eigenvectors are decaying is an important characteristic of a nonnormal system. This short term growth amplifies the small disturbances present in the system. Traditional linear controllers based on classical linear stability analysis do not take transient growth into account. High enough amplitudes of the transient growth can cause the system to enter into the region where nonlinear effects are significant and linear controller designed would fail in this case. It is shown that, controlling the dominant mode in a nonnormal thermoacoustic system alone can cause the instability to occur at another frequency which was initially unexcited. This manifests as secondary peaks in the FFT of the evolution of the acoustic pressure and velocity. Hence, a controller based on the pole placement technique which is applicable to the transients as well as the asymptotic stability of the system designed, and its effectiveness is demonstrated with an example of a horizontal Rijke tube model. Copyright © 2008 by Kulkarni R.R. , K. Balasubramanian and R.I. Sujith.

This paper explores some fundamental issues involved in flame-acoustic interaction in the context of non-premixed flames. The combustion model considered is a two-dimensional co-flowing non-premixed flame. Both finite rate and infinite rate chemistry effects are examined. First, the velocity-coupled response of the flame to an externally imposed velocity fluctuation is studied at various frequencies of interest. The Damköhler number plays an important role in determining the amplitude and phase of the heat release fluctuations with respect to the velocity fluctuations. Second, the combustion model is coupled with the duct acoustics. The one-dimensional acoustic field is simulated in the time domain using the Galer kin method, taking the fluctuating heat release from the combustion zone as a compact acoustic source. The combustion oscillations are shown to cause exchange of acoustic energy between the different natural modes of the duct over several cycles of the acoustic oscillations.

This paper analyzes the near-field acoustic characteristics of premixed wrinkled, flame fronts subjected to acoustic excitation. The flame thickness is assumed to be very small compared to the length scale of the acoustic oscillations. Thus the flame is treated as a finite temperature discontinuity. The values of acoustic pressure and velocity on the wrinkled flame surface are transferred to a mean reference surface by means of a Taylor's expansion. A Boundary Integral Equation describing the expectation value of the coherent acoustic pressure field in the domain of interest is derived. The flame surface wrinkling is modeled by a Weierstrass-Mandelbrot fractal function. Numerical results for a dump combustor configuration using the Boundary Element Method(BEM) are presented. The acoustic pressure field is seen to be highly two-dimensional in the case of the wrinkled flame. The flame surface impedance is seen to decrease with increase in excitation frequency. The difference between the acoustic pressure on the flame surface and the wall is shown to be significant in the case of a wrinkled flame subjected to acoustic excitation from the downstream. The transmitted acoustic field characteristics due to upstream excitation are seen to have a weak dependence on wrinkling. The normalized flame surface acoustic impedance is found to vary monotonically from the base of the flame to the tip of the flame in the case of smooth flames (i.e flame front with no wrinkling). The wrinkled flame however, is seen to have a nearly constant impedance variation along its surface. © 2003 by Santosh H and R. I. Sujith.