Journal ArticleDOI
Thermoacoustic instability in a solid rocket motor: non-normality and nonlinear instabilities
Sathesh Mariappan,R. I. Sujith +1 more
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In this paper, an analytical framework is developed to understand and predict the thermoacoustic instability in solid rocket motors, taking into account the non-orthogonality of the eigenmodes of the unsteady coupled system.Abstract:
An analytical framework is developed to understand and predict the thermoacoustic instability in solid rocket motors, taking into account the non-orthogonality of the eigenmodes of the unsteady coupled system. The coupled system comprises the dynamics of the acoustic field and the propellant burn rate. In general, thermoacoustic systems are non-normal leading to non-orthogonality of the eigenmodes. For such systems, the classical linear stability predicted from the eigenvalue analysis is valid in the asymptotic (large time) limit. However, the short-term dynamics can be completely different and a generalized stability theory is needed to predict the linear stability for all times. Non-normal systems show an initial transient growth for suitable initial perturbations even when the system is stable according to the classical linear stability theory. The terms contributing to the non-normality in the acoustic field and unsteady burn rate equations are identified. These terms, which were neglected in the earlier analyses, are incorporated in this analysis. Furthermore, the short-term dynamics are analysed using a system of differential equations that couples the acoustic field and the burn rate, rather than using ad hoc response functions which were used in earlier analyses. In this paper, a solid rocket motor with homogeneous propellant grain has been analysed. Modelling the evolution of the unsteady burn rate using a differential equation increases the degrees of freedom of the thermoacoustic system. Hence, a new generalized disturbance energy is defined which measures the growth and decay of the oscillations. This disturbance energy includes both acoustic energy and unsteady energy in the propellant and is used to quantify the transient growth in the system. Nonlinearities in the system are incorporated by including second-order acoustics and a physics-based nonlinear unsteady burn rate model. Nonlinear instabilities are analysed with special attention given to ‘pulsed instability’. Pulsed instability is shown to occur with pressure coupling for burn rate response. Transient growth is shown to play an important role in pulsed instability.read more
Citations
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Pseudospectra of the Convection-Diffusion Operator
TL;DR: The norm of the resolvent is exponentially large as a function of the Peclet number throughout a certain parabolic region, suggesting that conventional spectral analysis for convection-diffusion operators may be of limited value in some applications.
Journal ArticleDOI
Nonorthogonality analysis of a thermoacoustic system with a premixed V-shaped flame
TL;DR: In this article, a model of a choked combustor with a gutter confined is used to study the non-normal interaction between acoustic disturbances and a premixed V-shaped flame anchored to the tip of the gutter.
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Amplitude modulated instability in reactants plenum of a rotating detonation combustor
TL;DR: In this paper, the amplitude modulated instability in the air inlet is spatially varying, and rotates in a direction opposite to the direction of the detonation wave, and a preliminary hypothesis is proposed to explain this amplitude modulation.
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Adjoint Methods as Design Tools in Thermoacoustics
TL;DR: In this article, the authors provide a review of the application of adjoint sensitivity analysis to thermoacoustics, which is characterized by degenerate and non-degenerate nonlinear eigenvalue problems.
Journal ArticleDOI
Characterizing nonlinear dynamic features of self-sustained thermoacoustic oscillations in a premixed swirling combustor
TL;DR: In this article, the effects of the equivalence ratio Φ, the volume flow rate Va of inlet air and the swirling number SN are examined, and the authors explore the rich physics of how a methane-burnt swirling flame sustains periodic pulsating combustion oscillations, and its nonlinear dynamics features via recurrence plots and 0-1 chaotic test.
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