Raman I Sujith

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.

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.

The nonlinear steepening of finite amplitude magnetohydrodynamic (MHD) waves propagating perpendicular to the magnetic field is investigated. The nonlinear evolution of a planar fast magnetosonic wave in a homentropic flow field is understood well through simple waves. However, in situations where the wave is moving through a variable area duct or when the flow field is nonhomentropic, the concept of simple waves cannot be used. In the present paper, the quasi-one-dimensional MHD equations that include the effect of area variation and density gradients are solved using the wave front expansion technique. The analysis is performed for a perfectly conducting fluid and also for a weakly conducting fluid. Closed form solutions are obtained for the nonlinear evolution of the slope of the wave front in the limits of infinitely large and small conductivity. A general criterion for a compression wave to steepen into a shock is obtained. An analytical expression for the location of shock formation is derived. The effect of area variation and density gradient on shock formation is studied and examples highlighting the same are presented. © 2005 American Institute of Physics.

The effect of acoustic excitation on the heat-release characteristics of a two-dimensional premixed flame is studied. Past researchers have assumed that the acoustic nearfleld and kinematics of the flame surface are un-coupled. 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 nearfield of the flame surface is determined by using a boundary integral equation (BIE) modified 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 by 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 from two other models. The first model assumes a one-dimesional variation of acoustic velocity along the axial direction. The second model assumes a two-dimensional acoustic-velocity field while neglecting kinematic coupling. The inclusion of kinematic coupling leads to the prediction of a different value of the magnitude of the transfer function at low frequencies. This difference in predicted magnitudes depends on the excitation velocity amplitude. The predicted magnitudes increase with decrease in θ. The predicted phase is observed to be insensitive to changes in θ. Kinematic coupling also results in the reduction of the predicted spatial variation of the magnitude of the normalized acoustic velocity along the flame.

This paper presents the effect of axial acoustic fields on an air-atomized spray. In these experiments, a spray of ethanol is established in a transparent test section in which an acoustic field is set up using acoustic drivers. Visual observation shows that a high-amplitude acoustic field (160 dB) reduces the length of the spray. The spray velocity field was characterized by particle image velocimetry (PIV) measurements. The spray velocities are considerably reduced in the presence of the acoustic oscillations, indicating the presence of smaller droplets. The presence of acoustic oscillations increases the spray cone angle. The flow field in the near field of the spray was characterized. There is considerable entrainment of air into the spray in the presence of acoustic oscillations. It is seen that the acoustic velocity rather than the acoustic pressure primarily affects the spray. © Springer-Verlag 2005.

This work investigates the problem of finite amplitude longitudinal oscillations in a straight duct with an initially present temperature gradient. The one-dimensional gasdynamic equations with appropriate boundary conditions specified at both the ends are solved using Galerkin method. The formulation leads to a system of coupled nonlinear ordinary differential equations in time. These equations are solved numerically from the initial state till the limit cycle. An example of constant temperature gradient is considered. When the temperature is uniform in the duct, the limit cycle pressure waveform has a shock that decays over a sawtooth profile. The presence of non-zero temperature gradient in the duct reduces the shock strength and smoothens the sawtooth profile. At high values of temperature gradient, both the shock and sawtooth profile disappear. The shape of waveform becomes like an inverted U. In the presence of temperature gradient, the frequency response curve is skewed towards low frequency showing the softening behavior. The magnitude of softening increases with the increase in temperature gradient.

The present study investigates the flow field characteristics of a gas turbine swirler in a model combustion chamber, using particle image velocimetry. Detailed mean and RMS velocities, vorticity, Reynolds shear stress, and pseudoturbulent kinetic energy were obtained at various cross sections downstream of the swirler and in a plane along the inlet flow direction. The experiments were performed in a sudden expansion square geometry. A central toroidal recirculation zone and corner recirculation zone was observed and characterized. Another instability caused by swirl, called precessing vortex core, has been observed far downstream of the swirler, in the plane located at Z/D = 2.5 and 1.25 (D, diameter of the swirler) depending on the pressure drop across the swirler. High RMS velocity magnitudes are observed in several cross-sectional planes indicating high levels of turbulence generated by the swirling effect which promotes rapid mixing. The structure of the complex swirling flow field has been investigated both qualitatively and qualitatively. Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Most gas turbine engines in service use a prefilming airblast atomizer in combination with strong swirling flow. An experimental investigation of the characteristics of a hollow cone prefilming airblast atomizer in a strong swirling air flow Is presented in this paper. The measured quantities include the spray cone angle by planar imaging, patternation using planar laser-Induced fluorescence, planar droplet velocity field using two-component particle image velocimetry, and droplet size and velocity distributions using a phase Doppler particle-size analyzer and laser Doppler velocimetry. Patternation of the spray field showed regions of high droplet concentration and volume flux fluctuations in various cross-sectional planes. The investigation revealed the presence of droplets of narrow size range up to 25 μ around the axis of the atomizer in the central toroidal recirculation zone of the swirler. The presence of vortical structures entraining the droplets is observed from the instantaneous velocity vector fields. The velocity data shows entralnment of the droplets in the central toroidal recirculation zone. Examining the size and the velocity data reveals that the centrifugal action of the swirling air flowfleld from the atomizer carries the bigger droplets outward, toward the periphery of the spray.

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.