On the importance of time delay and noise in thermoacoustic modeling

Gant, Francesco; Ghirardo, Giulio; Bothien, Mirko R.

doi:10.1016/j.jsv.2021.116067

Cited by 6 publications

(2 citation statements)

References 68 publications

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“…This work is an extension of two previous research papers, 8,20 revisited and deepened with the inclusion of new material from recent research on autoignition flames. 11,18…”

Section: Introductionmentioning

confidence: 84%

Autoignition flame transfer matrix: Analytical model versus large eddy simulations

Gant¹,

Cuquel²,

Bothien

2022

International Journal of Spray and Combustion Dynamics

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Modern gas turbines need to fulfil increasingly stringent emission targets on the one hand and exhibit outstanding operational and fuel flexibility on the other. Ansaldo Energia GT26 and GT36 gas turbine models address these requirements by employing a combustion system in which two lean premixed combustors are arranged in series. Due to the high inlet temperatures from the first stage, the second combustor stage predominantly relies on autoignition for flame stabilization. In this paper, the response of autoignition flames to temperature, pressure and velocity excitations is investigated. The gas turbine combustor geometry is represented by a backward-facing step. Based on the conservation equations an analytical model is derived by solving the linearized Rankine-Hugoniot conditions. This is a commonly used analytical approach to describe the relation of thermodynamic quantities up- and downstream of a propagation stabilized flame. In particular, the linearized Rankine-Hugoniot jump conditions are derived taking into account the presence of a moving discontinuity as well as upstream entropy inhomogeneities. The unsteady heat release rate of the flame is modelled as a linear superposition of flame transfer functions, accounting for velocity, pressure, and entropy disturbances, respectively. This results in a 3[Formula: see text]3 flame transfer matrix relating both primitive acoustic variables and the temperature fluctuations across the flame. The obtained analytical expression is compared to large eddy simulations with excellent agreement. A discussion about the contribution of the single terms to the modelling effort is provided, with a focus on autoignition flames.

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“…This work is an extension of two previous research papers, 8,20 revisited and deepened with the inclusion of new material from recent research on autoignition flames. 11,18…”

Section: Introductionmentioning

confidence: 84%

Autoignition flame transfer matrix: Analytical model versus large eddy simulations

Gant¹,

Cuquel²,

Bothien

2022

International Journal of Spray and Combustion Dynamics

Self Cite

View full text Add to dashboard Cite

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“…Lately, some models have been proposed to account for a given characteristic time lag in the flame response (Bonciolini et al 11 ; Gant et al 12 ). Although this kind of models is powerful if combined with low-order models of the thermoacoustic system, usually in terms of linear oscillators, they remain descriptive but not predictive as they require tuning parameters that are obtained from the same data used in the analysis.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear flame response modelling by a parsimonious set of ordinary differential equations

Doehner

Haeringer

Silva

2022

International Journal of Spray and Combustion Dynamics

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In this work we present a parsimonious set of ordinary differential equations (ODEs) that describes with satisfactory precision the linear and non-linear dynamics of a typical laminar premixed flame in time and frequency domain. The proposed model is characterized by two ODEs of second-order that can be interpreted as two coupled mass-spring-damper oscillators with a symmetric, nonlinear damping term. This non-linear term is identified as function of the rate of displacement following [Formula: see text]. The model requires only four constants to be calibrated. This is achieved by carrying out an optimization procedure on one input and one output broadband signal obtained from high-fidelity numerical simulations (CFD). Note that the Transfer Function (FTF) or describing function (FDF) of the flame under investigation are not known a-priori, and therefore not used in the optimization procedure. Once the model is trained on CFD input and output time series, it is capable of recovering with quantitative accuracy the impulse response of the laminar flame under investigation and, hence, the corresponding frequency response (FTF). If fed with harmonic signals of different frequency and amplitude, the trained model is capable of retrieving with qualitative precision the flame describing function (FDF) of the studied flame. We show that the non-linear term [Formula: see text] is essential for capturing the gain saturation for high amplitudes of the input signal. All results are validated against CFD data.

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Parameter estimation of two coupled oscillator model for pure intrinsic thermo-acoustic instability

2023

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A nonlinear phenomenological model of two coupled oscillators is proposed, which is able to describe the rich nonlinear behaviour stemming from an unstable pure intrinsic thermo-acoustic (ITA) mode of a simple combustion system. In an experimental bifurcation analysis of a pure ITA mode, it was observed that for increasing mean upstream velocity the flames loose stability through a supercritical Hopf bifurcation and subsequently exhibit limit cycle, quasi-periodic and period-2 limit cycle oscillations. The quasi-periodic oscillations were characterised by low frequent amplitude and frequency modulation. It is shown that a phenomenological model consisting of two coupled oscillators is able to reproduce qualitatively all the different experimentally observed regimes. This model consists of a nonlinear Van der Pol oscillator and a linear damped oscillator, which are nonlinearly coupled to each other. Furthermore, a parameter estimation of the model parameters is conducted, which reveals a good quantitative match between the model response and the experimental data. Hence, the presented phenomenological dynamical model accurately describes the nonlinear self-excited acoustic behaviour of premixed flames and provides a promising model structure for nonlinear time-domain flame models.

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On the importance of time delay and noise in thermoacoustic modeling

Cited by 6 publications

References 68 publications

Autoignition flame transfer matrix: Analytical model versus large eddy simulations

Autoignition flame transfer matrix: Analytical model versus large eddy simulations

Nonlinear flame response modelling by a parsimonious set of ordinary differential equations

Parameter estimation of two coupled oscillator model for pure intrinsic thermo-acoustic instability

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