A criterion for thermo-acoustic stability based on the flux of acoustic energy

Schily, Felix; Komarek, Thomas; Polifke, Wolfgang

doi:10.1016/j.combustflame.2021.01.014

Cited by 2 publications

(3 citation statements)

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“…A continuous state-space (CSS) realization of discrete flame impulse responses allows to formulate thermoacoustic stability analysis as a linear eigenvalue problem. The present paper closes the gap between state-space realizations of the simplistic n-τ flame model based on a propagation equation (PE) [11,13] and more realistic flame models based on rational-fitting [12,[16][17][18]. The distributed-time-delayed response of flames to velocity perturbations was linearly approximated by discretizing a propagation equation (PE) in pseudo space.…”

Section: Summary Conclusion and Outlookmentioning

confidence: 92%

“…In this section, the performance of the PE CSS model is compared with a rational fit based CSS, where the sixth-order rational fit was obtained with the MATLAB [24] tfest function, requiring a quality of 99 % and constraining the poles to be stable. For further information about the rational fit CSS model, the reader is referred to [12,[16][17][18]. We assess (1) the mean square error (MSE) of the continuous frequency response function to the original discrete model and (2) the influence of the CSS realization strategy on the eigenvalues of a generic Rijke tube.…”

Section: Comparison Of Pe and Data-fitting Based Css Modelsmentioning

confidence: 99%

“…The advantage of such a time-continuous model is the possibility of coupling with a variable time step computational fluid dynamics (CFD) simulation, allowing an efficient implementation of time domain impedance boundary conditions [3,15]. Common strategies to obtain CSS models from discrete FRF data are (1) fitting a rational function [12,[16][17][18], or (2) first-order bilinear/Tustin and higher-order Padé approximation [9,19] of exponential terms. For either method, the obtained rational function is subsequently transformed into a CSS model, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Linear time-continuous state-space realization of flame transfer functions by means of a propagation equation.

2023

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Low-order network models, commonly used to assess the thermo-acoustic stability of combustors, can be cast in a linear, time-continuous state-space representation. A standard linear eigenvalue problem for the system modes results, which can be solved in a robust and efficient manner. To represent the linear dynamics of any time-invariant flame in the state-space framework, this study presents an approximation of the distributed time-delayed flame response to acoustic velocity perturbations based on a spatially discretized propagation equation (PE). We derive the rational flame transfer function of a first-order-upwind-PE state-space model and discuss its relation to the Tustin approximation of flame transfer functions. For an exemplary discrete finite impulse response of a flame, a third-order-upwind-PE state-space model is shown to match the discrete flame frequency response with comparable accuracy as a rational approximation found by non-linear optimization. The numerical dissipation introduced by discretization of the PE ensures zero gain above the Nyquist frequency of the underlying discrete flame impulse response. Finally, we apply the PE state-space flame model to a generic Rijke tube and show that the predicted thermo-acoustic modes agree well with results obtained from a classical non-linearly optimized rational approximation of the frequency response function of the flame.

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