TY - GEN
T1 - Linear time-continuous state-space realization of flame transfer functions by means of a propagation equation
AU - Brokof, Philipp
AU - Fournier, Guillaume J.J.
AU - Polifke, Wolfgang
N1 - Publisher Copyright:
© 2022 Internoise 2022 - 51st International Congress and Exposition on Noise Control Engineering. All rights reserved.
PY - 2022
Y1 - 2022
N2 - 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 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 an accuracy comparable to that of a rational approximation found by non-linear optimization. The numerical dissipation introduced by discretization of the PE ensures negligible 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 thermoacoustic modes agree well with results obtained from a classical non-linearly optimized rational approximation of the frequency response function of the flame.
AB - 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 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 an accuracy comparable to that of a rational approximation found by non-linear optimization. The numerical dissipation introduced by discretization of the PE ensures negligible 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 thermoacoustic modes agree well with results obtained from a classical non-linearly optimized rational approximation of the frequency response function of the flame.
UR - http://www.scopus.com/inward/record.url?scp=85142285452&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85142285452
T3 - Internoise 2022 - 51st International Congress and Exposition on Noise Control Engineering
BT - Internoise 2022 - 51st International Congress and Exposition on Noise Control Engineering
PB - The Institute of Noise Control Engineering of the USA, Inc.
T2 - 51st International Congress and Exposition on Noise Control Engineering, Internoise 2022
Y2 - 21 August 2022 through 24 August 2022
ER -