Sensitivity and Nonlinearity of Thermoacoustic Oscillations

Abstract

Nine decades of rocket engine and gas turbine development have shown that thermoacoustic oscillations are difficult to predict, but can usually be eliminated with relatively small ad hoc design changes. These changes can, however, be ruinously expensive to devise. This review explains why linear and nonlinear thermoacoustic behaviour is so sensitive to parameters such as operating point, fuel composition, and injector geometry. It shows how non-periodic behaviour arises in experiments and simulations and discusses how fluctuations in thermoacoustic systems with turbulent reacting flow, which are usually filtered or averaged out as noise, can reveal useful information. Finally, it proposes tools to exploit this sensitivity in the future: adjoint-based sensitivity analysis to optimize passive control designs, and complex systems theory to warn of impending thermoacoustic oscillations and to identify the most sensitive elements of a thermoacoustic system.

Exceptional points in the thermoacoustic spectrum

“…The thermoacoustic stability problem is generally non-Hermitian because of the flame response term and dissipative boundary conditions. On numerical discretization or travelling-wave decomposition [5], thermoacoustic stability is governed by a nonlinear eigenvalue problem [6,7] L(ω; ε)p = 0,…”

“…We consider a prototypical thermoacoustic system, which contains the essential physical mechanisms of many thermoacoustic systems [5]. We assume that (i) the frequency of the oscillation is smaller than the cutoff frequency of the duct, i.e.…”

“…Interesting physical phenomena associated with EPs appear across various disciplines from quantum mechanics through optics and acoustics [2,3,4]. To the best of the authors' knowledge, the role of exceptional points has not yet been explored in thermoacoustic systems, although points in the parameter space with infinite sensitivity were discussed in a recent review article [5]. In this letter, we show that these points in the thermoacoustic spectrum are exceptional, and that they can be found in a generic thermoacoustic system when two real parameters are varied.…”

Universality in the emergence of oscillatory instabilities in turbulent flows

“…In turbulent flows, spatially extended patterns such as large coherent structures are formed due to self-organization, for example, devastating cyclones in atmospheric flows. Self-organization driven by feedback between subsystems in turbulent systems can lead to oscillatory instabilities as observed in thermoacoustic [3], aeroacoustic [4], and aeroelastic systems [5]. These oscillatory instabilities cause high amplitude vibrations which may incur catastrophic effects in engineering systems.…”

Combined state and parameter estimation in level-set methods

“…Each snapshot from left to right is distanced by a quarter of the forcing period. pinch-off events [77], which in turn depend on the phase speed at which perturbations travel along with the flame. In our reduced-order model based on the G-equation, the phase speed is regulated by the parameter K, which makes it highly observable even in the presence of observation noise.…”