2011
DOI: 10.1260/1756-8277.3.3.209
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Transient Growth and Triggering in the Horizontal Rijke Tube

Abstract: This theoretical paper examines a non-normal and non-linear model of a horizontal Rijke tube. Linear and non-linear optimal initial states, which maximize acoustic energy growth over a given time from a given energy, are calculated. It is found that non-linearity and non-normality both contribute to transient growth and that, for this model, linear optimal states are only a good predictor of non-linear optimal states for low initial energies. Two types of non-linear optimal initial state are found. The first h… Show more

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Cited by 12 publications
(12 citation statements)
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“…If the degree of non-normality is large 4 in the hysteresis region, a linearly stable solution can be driven to an oscillating attractor. This phenomena is therefore called triggering or bypass transition 5 [30,[34][35][36][37][38][39].…”
Section: Transient Growthmentioning
confidence: 99%
See 1 more Smart Citation
“…If the degree of non-normality is large 4 in the hysteresis region, a linearly stable solution can be driven to an oscillating attractor. This phenomena is therefore called triggering or bypass transition 5 [30,[34][35][36][37][38][39].…”
Section: Transient Growthmentioning
confidence: 99%
“…In general, thermoacoustic systems are non-normal because their eigenfunctions are not orthogonal to each other [40]. As reviewed by Sujith et al [39], non-normality in thermoacoustics was investigated in ducted diffusion flames [36,37] and heat sources [34,35,[41][42][43][44][45]; solid rocket motors [46,47]; and premixed flames [48]. Later on, the authors of [38] showed that thermoacoustic non-normality in ducted diffusion flames is not as influential as it was thought to be.…”
Section: Transient Growthmentioning
confidence: 99%
“…As in the transition problem (with now the nonlinear terms not energy-preserving), the minimal seed is found to be completely different from the linear optimal. The Rijke tube system is sufficiently simple (a couple of time-dependent 1-space dimension PDEs) to perform an exhaustive survey of transient growth possibilities over amplitude and event horizon T [64] as well as including noise [120]. It is also realistic enough to achieve some correspondence with experiments [59].…”
Section: Thermoacousticsmentioning
confidence: 99%
“…Many theoretical techniques have recently been introduced in thermo-acoustics, making this field an exciting hub of cross-disciplinary methods and theories. These include non-normality [5,6,7,8,9,10,11,12,13]; energy norms [14,15,16]; continuation methods [17,18,19,20,21]; weakly nonlinear theory [22,23,24,25]; dynamical systems theory, and time-series analysis [26,27,28,29].…”
Section: Introductionmentioning
confidence: 99%