Bifurcation Analysis of Thermoacoustic Instability in a Horizontal Rijke Tube

Subramanian, Priya; Mariappan, Sathesh; Sujith, R. I.; Wahi, Pankaj

doi:10.1260/1756-8277.2.4.325

Cited by 111 publications

(113 citation statements)

References 32 publications

(44 reference statements)

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“…On the other hand, for the horizontal configuration, pulsating behaviour is observed at all equivalence ratios (even for fuel-lean mixtures) and the phase plot shows a lobed structure. Such a lobed structure is also reported for quasiperiodic orbits by Subramanian et al [20].…”

Section: Dynamic Characterization Of Laboratory-scale Combustorsupporting

confidence: 80%

Non-linear dynamics in pulse combustor: A review

2015

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The state of the art of non-linear dynamics applied to pulse combustor theoretically and experimentally is reviewed. Pulse combustors are a class of air-breathing engines in which pulsations in combustion are utilized to improve the performance. As no analytical solution can be obtained for most of the nonlinear systems, the whole set of solutions can be investigated with the help of dynamical system theory. Many studies have been carried out on pulse combustors whose dynamics include limit cycle behaviour, Hopf bifurcation and period-doubling bifurcation. The dynamic signature has also been used for early prediction of extinction.

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Section: Dynamic Characterization Of Laboratory-scale Combustorsupporting

confidence: 80%

Non-linear dynamics in pulse combustor: A review

2015

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“…Fig. 9 shows a good agreement with the [62,74]. When the heat release coefficient β is larger than the values of the Hopf points, an infinitesimal perturbation would result in a large-amplitude limit cycle, defined globally to be unstable.…”

Section: Effect Of Bi-parameterssupporting

confidence: 60%

“…Using different measurement for the limit cycles, they display the same tendency and the critical points are the same in both figures. Figure 6 presents a subcritical Hopf bifurcation and is similar to the bifurcation diagrams reported in [33,62,72]. The stability of each periodic solution was determined by Floquet multipliers, as discussed in Section 3.2.…”

Section: Effect Of Heat Releasementioning

confidence: 59%

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Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system

Yang

Turan

Lei³

2017

Communications in Nonlinear Science and Numerical Simulation

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In this paper, of primary concern is a time-delayed thermoacoustic system, viz. a horizontal Rijke tube. A continuation approach is employed to capture the nonlinear behavior inherent to the system. Unlike the conventional approach by the Galerkin method, a dynamic system is naturally built up by discretizing the acoustic momentum and energy equations incorporating appropriate boundary conditions using a finite difference method. In addition, the interaction of Rijke tube velocity with oscillatory heat release is modeled using a modified form of King's law. A comparison of the numerical results with experimental data and the calculations reported reveals that the current approach can yield very good predictions. Moreover, subcritical Hopf bifurcations and fold bifurcations are captured with the evolution of dimensionless heat release coefficient, generic damping coefficient and time delay.Linear stability boundary, nonlinear stability boundary, bistable region and limit cycles are thus determined to gain an understanding of the intrinsic nonlinear behaviors.

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“…This is the case for the horizontal Rijke tube, which has been investigated with a Galerkin approach by various researchers. For example, Balasubramanian & Sujith (2008) have studied the transient growth and triggering that can result from the combined effect of nonlinearity and non-normality; Subramanian et al (2010) have calculated bifurcation plots for various system parameters (heater power, heater location, damping) and observed interesting dynamical behaviours. However, for many combustor geometries, the eigenmodes have a slightly different profile.…”

Section: Green's Function Approach To Predicting Instabilities In Commentioning

confidence: 99%

A Green’s function approach to the rapid prediction of thermoacoustic instabilities in combustors

Bigongiari

Heckl

2016

J. Fluid Mech.

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The prediction of thermoacoustic instabilities is fundamental for combustion systems such as domestic burners and industrial gas turbine engines. High-amplitude pressure oscillations cause thermal and mechanical stress to the equipment, leading to premature wear or even critical damage. In this paper we present a new approach to produce nonlinear (i.e. amplitude-dependent) stability maps of a combustion system as a function of various parameters. Our approach is based on the tailored Green's function of the combustion system, which we calculate analytically. To this end, we assume that the combustor is one-dimensional, and we describe its boundary conditions through reflection coefficients. The heat release is modelled by a generalised nτ law. This includes a direct-feedback term in addition to the usual time-lag term; moreover, its parameters (time lag, coupling coefficients) depend on the oscillation amplitude. The model provides new insight into the physical mechanism of the feedback between heat release rate and acoustic perturbations. It predicts the key nonlinear features of the thermoacoustic feedback, such as limit cycles, bistability and hysteresis. It also explains the frequency shift in the acoustic modes.

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Bifurcation Analysis of Thermoacoustic Instability in a Horizontal Rijke Tube

Cited by 111 publications

References 32 publications

Non-linear dynamics in pulse combustor: A review

Non-linear dynamics in pulse combustor: A review

Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system

A Green’s function approach to the rapid prediction of thermoacoustic instabilities in combustors

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