A method to identify thermoacoustic growth rates in combustion chambers from dynamic pressure time series

Noiray, Nicolas; Денисов, А. М.

doi:10.1016/j.proci.2016.06.092

Cited by 66 publications

(60 citation statements)

References 31 publications

(38 reference statements)

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“…This differs from thermoacoustic instabilities in rocket motors where nonlinear acoustics governs the limit cycle amplitude [37]. A minimal model to account for saturation of the flame response in the case of supercritical Hopf bifurcations [15,4,38] consists in adding a 3 rd order term to the relationship linking Q σ and p a :…”

Section: B Thermoacoustic Feedbackmentioning

confidence: 99%

Symmetry breaking of azimuthal waves: Slow-flow dynamics on the Bloch sphere

Faure-Beaulieu

Noiray

2020

Phys. Rev. Fluids

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Depending on the reflectional and rotational symmetries of annular combustors for aeroengines and gas turbines, self-sustained azimuthal thermoacoustic eigenmodes can be standing, spinning or mix of these two types of waves. These thermoacoustic limit cycles are unwanted because the resulting intense acoustic fields induce high-cycle fatigue of the combustor components. This paper presents a new theoretical framework for describing, in an idealized annular combustor, the dynamics of the slow-flow variables, which define the state of an eigenmode, i.e. if the latter is standing, spinning or mixed. The acoustic pressure is expressed as a hypercomplex field and this ansatz is inserted into a one dimensional wave equation that describes the thermoacoustics of a thin annulus. Slowflow averaging of this wave equation is performed by adapting the classic Krylov-Bogoliubov method to the quaternion field in order to derive a system of coupled first order differential equations for the four slow-flow variables, i.e. the amplitude, the nature angle, the preferential direction and the temporal phase of the azimuthal thermoacoustic mode. The state of the mode can be conveniently depicted by using the first three slowflow variables as spherical coordinates for a Bloch sphere representation. Stochastic forcing from the turbulence in annular combustors is also accounted for. This new analytical model describes both rotational and reflectional symmetry breaking bifurcations induced by the non-uniform distribution of thermoacoustic sources along the annulus circumference and by the presence of a mean swirl. * abelf@ethz.ch † noirayn@ethz.ch arXiv:1911.02830v3 [physics.flu-dyn] 9 Jan 2020

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Section: B Thermoacoustic Feedbackmentioning

confidence: 99%

Symmetry breaking of azimuthal waves: Slow-flow dynamics on the Bloch sphere

Faure-Beaulieu

Noiray

2020

Phys. Rev. Fluids

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“…In the linearly stable regime, growth rates can be identified using pressure auto-correlation functions [15] or pressure frequency spectra [32]. Recently, it has been shown that dynamic pressure time series contain a wealth of information, and can be used to develop robust output-only system identification (SI) methods even in the linearly unstable regime [22,20,19], which enables the development of stability monitoring tools, the quantitative validation of linear stability prediction methods, or the design of passive damping technologies. Turbulent reactive flows subject to thermoacoustic instabilities can be considered as complex systems with a large number of degrees of freedom, from which emerges a stochastically perturbed coherent dynamics.…”

Section: Introductionmentioning

confidence: 99%

Quantifying acoustic damping using flame chemiluminescence

Boujo¹,

Денисов

Schuermans³

et al. 2016

J. Fluid Mech.

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Thermoacoustic instabilities in gas turbines and aeroengine combustors falls within the category of complex systems. They can be described phenomenologically using nonlinear stochastic differential equations, which constitute the grounds for output-only model-based system identification. It has been shown recently that one can extract the governing parameters of the instabilities, namely the linear growth rate and the nonlinear component of the thermoacoustic feedback, using dynamic pressure time series only. This is highly relevant for practical systems, which cannot be actively controlled due to a lack of costeffective actuators. The thermoacoustic stability is given by the linear growth rate, which results from the combination of the acoustic damping and the coherent feedback from the flame. In this paper, it is shown that it is possible to quantify the acoustic damping of the system, and thus to separate its contribution to the linear growth rate from the one of the flame. This is achieved by post-processing in a simple way simultaneously acquired chemiluminescence and acoustic pressure data. It provides an additional approach to further unravel from observed time series the key mechanisms governing the system dynamics. This straightforward method is illustrated here using experimental data from a combustion chamber operated at several linearly stable and unstable operating conditions.

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“…In the specific case of thermoacoustic systems in combustion chambers, equation (2.1) faithfully reproduces the dynamics of pressure oscillations associated with one thermoacoustic mode [25][26][27]. The pressure field is projected with a Galerkin method onto a basis of spacedependent acoustic eigenmodes with time-dependent coefficients η(t) [8,23], and band-pas filtering around the mode's frequency isolates its contribution and yields a quasi-harmonic signal [7,22].…”

Section: Stochastic Oscillator Model (A) Dynamical Descriptionmentioning

confidence: 93%

“…Noiray and Schuermans [27] proposed another system identification method based on estimating the Kramers-Moyal coefficients and fitting the analytical expressions (2.10) and applied it to data from a gas turbine combustor. Noiray and Denisov [26] series of ON→OFF and OFF→ON control switching. The principle of the method is recalled in section 3(b).…”

Section: System Identification With the Km Coefficientsmentioning

confidence: 99%

“…Repeating for different amplitudes A and fitting to the extrapolated values the analytical expressions (2.10) of D (n) (A), allows the identification of the parameters ν, κ and Γ that govern the system [26,27], as shown in figure 6c. Hereafter, we will denote the KM coefficients estimated from measurements with a hat .…”

Section: (A) Finite-time Km Coefficientsmentioning

confidence: 99%

See 1 more Smart Citation

Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation

Boujo¹,

Noiray²

2017

Proc. R. Soc. A.

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We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations-for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker-Planck equation is solved to compute Kramers-Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.

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A method to identify thermoacoustic growth rates in combustion chambers from dynamic pressure time series

Cited by 66 publications

References 31 publications

Symmetry breaking of azimuthal waves: Slow-flow dynamics on the Bloch sphere

Symmetry breaking of azimuthal waves: Slow-flow dynamics on the Bloch sphere

Quantifying acoustic damping using flame chemiluminescence

Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation

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