IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

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.

IIT Madras

We revisit a simple reduced order model (Matveev, K. and Culick, F. E. C, (2003) "A Model for Combustion Instability Involving Vortex Shedding", Combust Sci. and Tech., 175, 1059-1083) and re-examine its implications in the light of the non-normal and nonlinear nature of combustion acoustic interactions. One-dimensional linear acoustics is used to model the acoustic field in an open-open duct. The Galerkin technique is used to expand the acoustic pressure and velocity fluctuations in terms of the natural acoustic modes. The coupled thermoacoustic system is shown to be non-normal and nonlinear. This leads to complicated, but interesting physics which were not examined in the earlier study. Examples showing triggering and bootstrapping in an initially decaying system are then presented. It is also shown that a vortex based combustor reaches different limit cycle amplitudes for the same system parameters, when subjected to different initial conditions. Further, the effect of damping on the non-normal behavior of the system is studied. Pseudospectra analysis reveals that for a lightly damped system, an increase in damping might lead to higher nonnormal interaction of modes.

Department of Aerospace Engineering

44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit

Revisiting a Model for Combustion Instability Involving Vortex Shedding

This article presents an investigation of the nonlinear response of a diffusion flame to unsteady velocity disturbances. The infinite rate chemistry flame model is employed to study unsteady two-dimensional co-flow non-premixed combustion. In this model, the flame geometry is given by the stoichiometric level surface, which is obtained by the equation for the Schvab-Zeldovich variable. In this article, this equation is solved using an integral equation approach. An approximate analytical expression is obtained for the flame length variation as a function of time. The heat release rate is obtained from thermodynamic calculations. The variation of the heat release rate with the velocity fluctuations is analyzed. It is seen that the flame response to a single frequency of excitation contains several frequencies even though the governing equation is linear. It is shown that the heat release rate has exponential dependence on the amplitude of velocity fluctuations. The nonlinear nature of flame response becomes significant at lower Fourier numbers (for mass transport). A nonlinear model for the transfer function to describe the response of the heat release rate to velocity perturbation has been constructed. Copyright © Taylor & Francis Group, LLC.

Combustion Science and Technology

Nonlinear response of diffusion flames to uniform velocity disturbances

A combustor with a divergent inlet passage and a coaxially movable bluff-body flame holder has been developed to enable self-excitation of high-amplitude acoustic oscillations, for the purpose of enhancing the rate of evaporation of water sprays. Commercially available liquid petroleum gas is used as fuel. The acoustic pressure levels and modal contents are controlled by varying the location of the bluff body along the axis of the combustor relative to its inlet. Locating the bluff body closer to the inlet yields higher acoustic pressure amplitudes over a wider range of fuel-air ratios. The excitation of high amplitudes is accompanied by a shift from the fundamental to the first harmonic at different fuel-air ratios for different air mass flow rates in the fuel-lean range. When high sound pressure levels are excited in the combustor, the heat transfer due to water cooling of the combustor walls and across the walls of the tailpipe increase considerably, up to 40% for an increase in sound pressure levels from 145 to 160 dB. Water-spray evaporation experiments are performed with low and high sound pressure levels of acoustic excitation for different water injection rates over a range of mass flow rates of fuel and air. For a given mass flow rate of air and fuel, it is found that the water evaporation rate increases significantly above a certain threshold acoustic pressure, up to 107 % for a sound pressure level of 156 dB, despite the considerable increase in heat loss due to the acoustic oscillations.

Journal of Propulsion and Power

Characterization of an acoustically self-excited combustor for spray evaporation

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.

GENERAL

46th AIAA Aerospace Sciences Meeting and Exhibit

The role of nonnormality in active control of combustion instability

Detection of vortices from PIV data has been a challenging task driving efforts in experimentation with various algorithms and physical criteria. In the present study, three algorithms are employed and are arranged in a predictor-corrector fashion to reduce computation time while maintaining accuracy and robustness. Two predictor methods, geometric gridding and streamlines method have been employed to ensure that there is redundancy in finding the regions of interest at the predictor stage. A redundancy in the predictor method also ensures generality and robustness in detection. The corrector method is a pattern matching algorithm using the Hamel-Oseen model for velocity which acts on the reduced domain obtained through the predictor algorithms. The performance of the proposed scheme is demonstrated by applying them to detect vortices from two component PIV data obtained from swirl flow measurements. Copyright © 2008 by Arun Manohar, A. V. Varun and R. I. Sujith.

An automated predictor-corrector method for vortex detection

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.

Characterization of a prefilming airblast atomizer in a strong swirl flowfield

This paper presents the effect of axial acoustic fields on evaporative sprays. Investigations were performed using ethanol as the spray liquid, inside a duct fitted with acoustic drivers. The spray field was characterized using phase Doppler particle size analyzer (PDPA) and three component laser Doppler velocimetry (3C-LDV) measurements. The spray velocity fields are altered with respect to the acoustic velocity oscillations in an acoustic cycle. Variation in phase averaged droplet diameter and their distribution in presence of acoustic velocity oscillations in an acoustic cycle is noticed. The variation of droplet velocity, diameter and their distribution in presence of acoustic velocity oscillations increases with increase in amplitude of the acoustic field. Maximum variation of 30% in phase averaged droplet diameter is observed in an acoustic cycle. The harmonics in the phase averaged droplet diameter are observed when there is reversal of droplet velocity. Smaller diameter droplets are entrained by the acoustic velocity oscillations.

An experimental investigation of evaporative sprays in axial acoustic fields

This paper presents the effect of axial acoustic fields on non-evaporative sprays. Investigations were performed using distilled water as the spray liquid, at the open end of a duct fitted with acoustic drivers. The spray field was characterized using particle image velocimetry (PIV), phase Doppler particle size analyzer (PDPA) and three component laser Doppler velocimetry (3C-LDV) measurements. The spray velocity fields are altered with respect to the acoustic velocity oscillations in an acoustic cycle. Length of the zone having high rms velocity magnitudes is shortened with increase in counter flowing acoustic velocity. Variation in phase averaged droplet diameter and their distribution in presence of acoustic velocity oscillations in an acoustic cycle is noticed. The variation of droplet velocity, diameter and their distribution in presence of acoustic velocity oscillations increases with increase in acoustic pressure amplitude. A maximum variation of 25% in phase averaged droplet diameter is observed in an acoustic cycle. The atomization and diameter distribution of the spray is altered in an acoustic cycle. Smaller diameter droplets are entrained by the acoustic velocity oscillations. Copyright © 2008 by R. Kumara Gurubaran and R. I. Sujith.

An experimental investigation of non-evaporative sprays in axial acoustic fields

There have been conflicting opinions in literature, about the consequences of ignoring the linear coupling terms in finite-dimensional thermoacoustic models. We try to clarify this issue in this paper. We study consequences of ignoring the linear coupling terms on the non-normal thermoacoustic interactions in a horizontal Rijke tube. In the Galerkin formulation, we use pseudospectra and Henrici index of non-normality to study the impact of linear coupling between the Galerkin modes on the non-normality and the ensuing transient growth. This linear coupling is important for the energy transfer between the eigenmodes of the system (which are not the same as the natural acoustic modes of the duct). Although ignoring this linear coupling results in negligible shift in the eigenfrequencies, it may have serious consequences on the non-normality of the thermoacoustic system and its dynamics. Nonlinear phenomena such as triggering, boot-strapping and limit cycle oscillations may be completely missed out when this linear coupling is ignored. Ignoring the linear coupling between the Galerkin modes is justified only when the non-normality and the nonlinear dynamics of the system are not altered significantly.

Impact of linear coupling on thermoacoustic instabilities

A vortex detection scheme using the wavelet transform of the discriminant of the eigenvalues of the velocity gradient matrix (d 2) is presented in this paper. The use of d 2 field results in better eduction capability over the previously used test fields such as enstrophy since it automatically distinguishes shear layers from vortices. Level sets are used to refine the shape of the vortex without causing a huge computational penalty. Further, the algorithm is easily automated to aid batch processing. The detection scheme was applied to swirl flow fields, successfully estimating the vortex location, the core radius and the vortex shape.

Experiments in Fluids

An automated vortex detection scheme using the wavelet transform of the d 2 field

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 in a uniform flow field, as in the Burke-Schumann geometry. 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 Galerkin 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.

Combustion Theory and Modelling

Unsteady combustion response of a ducted non-premixed flame and acoustic coupling

The objective of this paper is to derive an asymptotic solution to the one-dimensional Euler equations for isentropic flow through ducts with slowly varying area. The homogeneous (or constant-area) problem is generally handled using Riemann's method of characteristics. We solve the variable-area problem by an asymptotic expansion about this homogeneous solution. A length scale characterizing the area variation is introduced and an asymptotic power series in increasing powers of the inverse of the length scale s are constructed for the unknowns. The problem reduces to solving the homogeneous Euler equation, and coupled linear PDEs for successive correction terms in the asymptotic series. An integration methodology is also presented for simple wave regions. As an illustration, we obtain closed-form analytical expressions for the first order perturbation terms in the case of an exponential duct for a sample simple wave. Nonlinear distortion of the wavefront is captured accurately in the analytical solution, as verified by comparison with numerical results from CLAWPACK, a finite-volume simulation package for conservation laws. Other issues such as asymptoticness and convergence of the series are discussed.

Collection of Technical Papers - 37th AIAA Fluid Dynamics Conference

Asymptotic solution for the one dimensional Euler equations for isentropic flow in a variable area duct

The acoustic characteristics of a column are described when filled with different random packings of various shapes, sizes and void fractions. An experimental setup was developed to study the acoustic field in a packed-bed column. Eight different packings were used to fill the column, and for each packing the acoustic pressure amplitude and phase were measured along the length of the packed bed. The speed of sound and the attenuation coefficient were determined using a nonlinear regression technique. The speed of sound inside the column decreased when the column was filled with packings. The natural frequencies increased as the void fraction of a particular packing decreased. It is shown that the attenuation coefficient depends on a nondimensional frequency defined as ωd2/v, where v is the kinematic viscosity, ω is the angular frequency, and d is the effective diameter of the packing. © 2006 American Institute of Chemical Engineers.

AIChE Journal

Characteristics of acoustic standing waves in packed-bed columns

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.

Department Of Biotechnology

Collection of Technical Papers - 44th AIAA Aerospace Sciences Meeting

Oscillatory Response of a Ducted Non-Premixed Flame and Flame-Acoustic Interaction

An integral approach has been developed to model propagation of sound through the combustion zone for practical combustors based on the Green's function technique. Sample calculations done for typical gas turbine combustors indicate that models based on jump conditions across the flame can be quite inaccurate in predicting the acoustic mode shapes (pressure and velocity). There appears to be a strong dependency on the mean temperature profile inside the combustion zone on the final mode shapes of the acoustic quantities. The technique presented herein can be readily adapted to different models for heat release and various temperature profiles.

An integral approach to modeling sound propagation through a finite combustion zone

The goal of present work is to analytically investigate the process of nonlinear wave steepening, which leads to the shock formation, in a flow with heat addition or removal (Rayleigh line flow). The methodology used is the tracking of a propagating wave front in a hyperbolic system, whose evolution is governed by a first order nonlinear ordinary differential equation (Riccati's equation). The evolution equation can be exactly solved for the first derivative of an unsteady flow variable as function of Mach number of the base flow. This solution is used to develop the criteria of the shock formation in case of a compressive disturbance and quenching in case of an expansive disturbance. The expressions for the time and location of shock formation are derived In the Rayleigh line flow, two kinds of flow fields are identified: converging field and diverging field. According to the linear ray theory of wave propagation, the strength of the disturbance scales up in the converging field and scales down in the diverging field. The propagation of finite amplitude waves in the Rayleigh line flow exhibit many interesting behavior. In a diverging field, it is possible to prevent the steepening of a compression wave into shock. In a converging field, an expansion wave may quench or steepen into shock. However, these expansion shocks are unstable. Various regions are identified where shock formation is opposed or favored. It is found that there are regions in the base flow, where linear ray theory will predict the local amplification/attenuation of wave; however, shock formation in the flow may be opposed/favored.

World University root node

Nonlinear wave propagation in Rayleigh line base flow

There has been much debate in recent years as to the effectiveness of enhancing heat and mass transfer rates with resonant acoustic oscillations in industrial equipment such as boilers, dryers, calciners, gasifiers, and others. This article will briefly discuss the theoretical background of acoustic drying, the setup of the experimental apparatus used to investigate the feasibility of acoustically enhanced drying, the results of these experiments, and, finally, some conclusions drawn from this work. The theoretical discussion focuses on the use of the quasi-steady assumption to estimate the potential for enhancing the heat and mass transfer rate to and from the material using acoustic oscillations. The experimental work reported focuses on the successful application of acoustical oscillations to drying a cellulose sponge, which is a material that readily transports moisture to its surface where it can be effectively dried. Also reported is the unsuccessful application of acoustic oscillations to the drying of polyethylene terephthalate, which is a saturated, thermoplastic, polyester resin made by condensing ethylene glycol and terephthalic acid and is commonly used in the manufacture of plastic food and drink containers. Reasons for success and failure in each case are discussed along with the implications of these to the successful application of acoustic oscillations to future drying applications.

Drying Technology

The effect of resonant acoustic oscillations on heat and mass transfer rates in a convection air dryer

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.

Swirler flow field characteristics in a sudden expansion combustor geometry

Nearly all combustion systems are prone to exhibit self-excited oscillations. These oscillations are driven by means of acoustic interactions between the flame and it's acoustic near-field. This acoustic nearfield is sensitive to the shape of the flame surface. 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. 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 2-D dump and rod stabilized flame configurations 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 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 down-stream for the case of the dump stabilized flame. The same is observed under upstream excitation in the case of the rod stabilized flame. 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.

Acoustic nearfield characteristics of a wrinkled premixed flame

The nonlinear steepening of relativistic acoustic waves is investigated. The nonlinear evolution of a planar wave in a homentropic flow field is understood well through relativistic simple waves. However, in situations where the wave is nonplanar and the flow field is nonhomentropic, the concept of simple waves cannot be used. In the present paper, effect of entropy gradients on the nonlinear distortion of a spherical wave is analyzed using the wave front expansion technique. It is shown that the behavior of a relativistic wave in nonhomentropic environment is slightly different from the nonrelativistic wave. A closed form solution is obtained for the slope at the wave front. A general criterion for a compression wave to steepen into a shock is obtained. The distortion of compression and rarefaction waves is examined for some well known equations of state. However, the method used in this paper is general and can be easily extended to analyze shock formation in any fluid. Also, expressions for time and location of shock formation are obtained. The effects of gravity or self-gravity are not taken into account in this paper. © 2005 American Institute of Physics.