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Jonas P. Moeck - One of the best experts on this subject based on the ideXlab platform.

  • Analysis of Thermoacoustic Modes in Can-Annular Combustors Using Effective Bloch-Type Boundary Conditions
    Journal of Engineering for Gas Turbines and Power, 2020
    Co-Authors: Jakob G.r. Von Saldern, Alessandro Orchini, Jonas P. Moeck
    Abstract:

    Abstract Heavy-duty gas turbines are commonly designed with can-Annular Combustors, in which all flames are physically separated. Acoustically, however, the cans communicate via the upstream located compressor plenum, or at the downstream gaps found at the transition to the turbine inlet. In the present study, a coupling condition that is based on a Rayleigh conductivity and acoustic flux conservation is derived. It enables acoustic communication between adjacent cans, in which one-dimensional acoustic waves propagate. In addition, because can-Annular systems commonly feature a discrete rotational symmetry, the acoustic field can be expressed as a Bloch-periodic wave in the azimuthal direction. We demonstrate how the coupling conditions resulting in a combustion system with $N$ cans can be expressed as an effective impedance for a single can. By means of this Bloch-type boundary condition, the thermoacoustics of a can-Annular system can be analyzed considering only one can, thus reducing the size of the problem by a factor of N. Using this method, we investigate in frequency domain the effect of the coupling strength of a generic can-Annular combustor consisting of 12 identical cans, which are connected at the downstream end. We describe generic features of can-Annular systems and derive results on the frequency response of the cans at various Bloch numbers in the low-frequency and high-frequency limits. Furthermore, the formation of eigenvalue clusters with eigenvalues of close frequency and growth rate, but very different mode shapes is discussed.

  • Nonlinear interaction between clustered unstable thermoacoustic modes in can-Annular Combustors
    Proceedings of the Combustion Institute, 2020
    Co-Authors: Jakob G.r. Von Saldern, Jonas P. Moeck, Alessandro Orchini
    Abstract:

    Abstract A can-Annular combustor consists of a set of nominally identical cans, in which the flames burn in an essentially isolated manner. However, adjacent cans are able to communicate acoustically, which provides dynamic coupling of the entire can-Annular arrangement. Recently, it was shown that the acoustic coupling is not negligible and can cause clustering of eigenfrequencies. In this study, we present a low-order modeling framework for self-excited thermoacoustic oscillations in generic can-Annular Combustors consisting of N identical cans. The dynamics of the flames are modeled with the nonlinear G-equation; the acoustic model accounts for plane acoustic waves inside the cans and can-to-can communication. The latter is enabled through a coupling boundary condition that is based on conservation of mass and a Rayleigh conductivity. For weak coupling between adjacent cans, the thermoacoustic feedback cycle shows clusters of linearly unstable modes of different azimuthal order, which are close in frequency and growth rate. Their interaction in the nonlinear regime is investigated using time-domain simulations. Two simulations for generic can-Annular Combustors consisting of 4 and 6 cans with weak acoustic coupling are discussed in this study. We observe a strong interaction between the modes, which can cause long transition times and allows modes that do not dominate the system dynamics in the linear regime to be dominant in the nonlinear regime. While the N = 6 case converges to a periodic oscillation pattern with one dominant frequency, the N = 4 case converges to a quasi-periodic oscillation involving modes of different azimuthal order. Moreover, we observe a synchronization of these modes. These results raise the questions whether it is possible to predict which mode(s) will dominate the system in the saturated state and under which conditions synchronization of clustered modes can occur.

  • Thermoacoustics of Can-Annular Combustors
    Journal of Engineering for Gas Turbines and Power-transactions of The Asme, 2018
    Co-Authors: Giulio Ghirardo, C. Di Giovine, Jonas P. Moeck, Mirko R. Bothien
    Abstract:

    Can-Annular Combustors consist of a set of independent cans, connected on the upstream side to the combustor plenum, and on the downstream side to the turbine inlet, where a transition duct links the round geometry of each can with the Annular segment of the turbine inlet. Each transition duct is open on the sides towards the adjacent transition ducts, so that neighbouring cans are acoustically connected through a so called cross-talk open area. This theoretical, numerical and experimental work discusses the effect that this communication has on the thermoacoustic frequencies of the combustor. We show how this communication gives rise to axial and azimuthal modes, and that these correspond to particularly synchronised states of axial thermoacoustic oscillations in each individual can. We show that these Combustors typically show clusters of thermoacoustic modes with very close frequencies and that a slight loss of rotational symmetry, e.g. a different acoustic response of certain cans, can lead to mode localization. We corroborate the predictions of azimuthal modes, clusters of eigenmodes and mode localization with experimental evidence.

  • Nonlinear thermoacoustic mode synchronization in Annular Combustors
    Proceedings of the Combustion Institute, 2018
    Co-Authors: Jonas P. Moeck, Daniel Durox, Thierry Schuller, Sébastien Candel
    Abstract:

    Nonlinear coupling between azimuthal and axisymmetric modes in Annular Combustors is studied analyti- cally. Based on the thermoacoustic wave equation, a model featuring three nonlinearly coupled oscillators is derived. Two oscillators represent the dynamics of an azimuthal mode, and the third accounts for the axisym- metric mode. A slow-time system for the evolution of the mode amplitudes and phases is obtained through the application of the method of averaging. The averaged system is shown to accurately reproduce the solu- tions of the full oscillator model. Analysis of this five-dimensional dynamical system shows that a standing azimuthal mode may synchronize with an axisymmetric mode, provided that their individual resonance fre- quencies and growth rates are similar. This phase-coupled two-mode oscillation corresponds to the so-called slanted mode, observed in recent experiments involving an Annular model combustion chamber. Quantitative conditions for the occurrence of mode synchronization are derived in terms of the growth rate ratio and a frequency detuning parameter. The analysis results are found to be consistent with experimental observations of the slanted mode.

  • effects of asymmetry on thermoacoustic modes in Annular Combustors a higher order perturbation study
    Journal of Engineering for Gas Turbines and Power-transactions of The Asme, 2018
    Co-Authors: Georg A. Mensah, Alessandro Orchini, Luca Magri, Jonas P. Moeck
    Abstract:

    Copyright © 2018 ASME Gas-turbine combustion chambers typically consist of nominally identical sectors arranged in a rotationally symmetric pattern. However, in practice the geometry is not perfectly symmetric. This may be due to design decisions, such as placing dampers in an azimuthally non-uniform fashion, or to uncertainties in the design parameters, which break the rotational symmetry of the combustion chamber. The question is whether these deviations from symmetry have impact to the thermoacoustic-stability calculation. The paper addresses this question by proposing a fast adjoint-based perturbation method. This method can be integrated into numerical frameworks that are industrial standard such as lumped-network models, Helmholtz- and linearized Euler-equations. The thermoacoustic stability of asymmetric combustion chambers is investigated by perturbing rotationally symmetric combustor models. The approach proposed in this paper is applied to a realistic three-dimensional combustion chamber model with an experimentally measured flame transfer function, which is solved with a Helmholtz solver. Results for modes of zeroth, first, and second azimuthal mode order are presented and compared to exact solutions of the problem. A focus of the discussion is set on the loss of mode-degeneracy due to symmetry breaking and the capability of the perturbation theory to accurately predict it. In particular, an “inclination rule” that explains the behavior of degenerate eigenvalues at first order is proven.

Sébastien Candel - One of the best experts on this subject based on the ideXlab platform.

  • Effect of Different Fuels On Combustion Instabilities in an Annular Combustors
    Journal of Engineering for Gas Turbines and Power, 2021
    Co-Authors: Preethi Rajendram Soundararajan, Daniel Durox, Vignat Guillaume, Antoine Renaud, Sébastien Candel
    Abstract:

    Abstract Combustion instability in Annular Combustors of jet engines is a recurring issue. In the present study, the characteristics of instabilities for different fuels are investigated by combining the instability maps obtained in a laboratory-scale Annular combustor equipped with multiple swirling spray injectors (MICCA-Spray) and flame describing functions (FDFs) from a single sector configuration (SICCA-Spray). Two types of liquid fuels are injected as hollow cone sprays: heptane, which is fairly volatile, and dodecane, which is less volatile. Experiments are also conducted with gaseous propane, premixed with air, which serves as a reference. An instability map is systematically drawn by varying the global equivalence ratio and thermal power. The data indicate that the amplitude and frequency of instabilities depend, for the same operating point, on the fuel injection conditions and fuel type. Overall trends show that premixed propane is unstable in a broad operating domain. Injection of liquid fuels induce changes in flame time lag that modify the unstable regions. For heptane, the instability map is closer to the propane reference map, whereas dodecane exhibits wider stable regions. An attempt is made to understand these features by examining the FDF, which gives the ratio of relative fluctuations in heat release rate to the relative fluctuations in velocity. The FDFs measured in a single sector configuration give access to gain and phase information that can be used to determine unstable bands and calculate an instability index guiding the interpretation of the differences in instabilities of the three fuels.

  • Effect of Different Fuels On Combustion Instabilities in an Annular Combustors
    Volume 4B: Combustion Fuels and Emissions, 2020
    Co-Authors: Preethi Rajendram Soundararajan, Daniel Durox, Vignat Guillaume, Antoine Renaud, Sébastien Candel
    Abstract:

    Abstract Combustion instabilities in Annular Combustors of jet engines is a recurring issue. In the present study, the characteristics of instabilities for different fuels are investigated by combining the instability maps obtained in an Annular combustor equipped with multiple swirling spray injectors (MICCA-Spray) and flame describing functions (FDFs) from a single sector configuration (SICCA-Spray). Two types of liquid fuels are injected as hollow cone sprays: heptane, which is fairly volatile, and dodecane, which is less volatile. Experiments are also conducted with gaseous propane, perfectly premixed with air, which serves as a reference. An instability map is systematically drawn by varying the global equivalence ratio and thermal power. The data indicate that the amplitude and frequency of instabilities depend, for the same operating point, on the fuel injection conditions (premixed or spray) and fuel type. Overall trends show that premixed propane is unstable in a broad operating domain. Injection of liquid fuels induces changes in time lag that modify the unstable regions. For heptane the instability map is closer to the propane reference map whereas dodecane exhibits wider stable regions. Variations can also be observed in the behavior of spin ratio that characterizes the azimuthal structure of the coupling mode. An attempt is made to understand these features by examining the FDF, which gives the ratio of relative fluctuations in heat release rate to the relative fluctuations in velocity. The FDFs measured in a single sector configuration gives access to gain and phase information that can be used to determine unstable bands. It is found that based on whether the MICCA-Spray instability frequency is within these bands, the instability amplitude can be high or low. This indicates that the difference in instabilities between the three fuels can be linked to the variations in FDFs.

  • Nonlinear thermoacoustic mode synchronization in Annular Combustors
    Proceedings of the Combustion Institute, 2018
    Co-Authors: Jonas P. Moeck, Daniel Durox, Thierry Schuller, Sébastien Candel
    Abstract:

    Nonlinear coupling between azimuthal and axisymmetric modes in Annular Combustors is studied analyti- cally. Based on the thermoacoustic wave equation, a model featuring three nonlinearly coupled oscillators is derived. Two oscillators represent the dynamics of an azimuthal mode, and the third accounts for the axisym- metric mode. A slow-time system for the evolution of the mode amplitudes and phases is obtained through the application of the method of averaging. The averaged system is shown to accurately reproduce the solu- tions of the full oscillator model. Analysis of this five-dimensional dynamical system shows that a standing azimuthal mode may synchronize with an axisymmetric mode, provided that their individual resonance fre- quencies and growth rates are similar. This phase-coupled two-mode oscillation corresponds to the so-called slanted mode, observed in recent experiments involving an Annular model combustion chamber. Quantitative conditions for the occurrence of mode synchronization are derived in terms of the growth rate ratio and a frequency detuning parameter. The analysis results are found to be consistent with experimental observations of the slanted mode.

  • A hysteresis phenomenon leading to spinning or standing azimuthal instabilities in an Annular combustor
    Combustion and Flame, 2017
    Co-Authors: Kevin Prieur, Thierry Schuller, D. Durox, Sébastien Candel
    Abstract:

    Thermo-acoustic instabilities in Annular Combustors equipped with swirling turbulent injectors are most often coupled by azimuthal modes with a spinning or a standing structure. Experiments, and recent large eddy simulations, indicate that switching takes place between these two types of modes while in other cases a single mode type prevails. Why and how one type arises is a subject of ongoing discussions in recent theoretical and numerical investigations. The present article considers this intriguing issue by malting use of well controlled experiments carried out in an Annular combustion system comprising 16 identical matrix injectors operating in a laminar premixed mode and allowing full optical access to the flame region. This setup is used in a first stage to determine regions of instability as a function of equivalence ratio and injection velocity. It is shown that regions corresponding to spinning and standing azimuthal modes are well separated in this diagram, but with some overlap giving rise to a "dual mode" domain. For the same operating conditions, this Annular system thus exhibits self-sustained instabilities with stable limit cycles coupled by a spinning or a standing mode. It is next shown that the mode which appears in that region depends on the path followed to reach the operating point. Starting from a lean operating condition, the system first develops a chugging instability with a broad frequency spectrum, which then gives rise to a well-established spinning oscillation with a narrow peak frequency in the dual mode region. When operation begins under rich conditions one first observes another chugging mode that finally yields a standing mode when the equivalence ratio is diminished. Away from these regimes, well defined slanted modes and longitudinal modes can also be triggered. In the dual mode region, the type of instability is controlled by an hysteresis phenomenon and the respective chugging modes act as precursors to these established azimuthal modes. It is found that the trajectories in a state space map contain indications on the kind of azimuthal oscillation that will be observed when the target operating point is reached. Beyond the various theoretical explanations of the prevalence of one type of mode on the other, the present observations indicate that spinning or standing modes may also appear in Annular Combustors as a result of the path used to enter the region of azimuthal instability. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

  • A hysteresis phenomenon leading to spinning or standing azimuthal instabilities in an Annular combustor
    Combustion and Flame, 2017
    Co-Authors: Kevin Prieur, Daniel Durox, Thierry Schuller, Sébastien Candel
    Abstract:

    Abstract Thermo-acoustic instabilities in Annular Combustors equipped with swirling turbulent injectors are most often coupled by azimuthal modes with a spinning or a standing structure. Experiments, and recent large eddy simulations, indicate that switching takes place between these two types of modes while in other cases a single mode type prevails. Why and how one type arises is a subject of ongoing discussions in recent theoretical and numerical investigations. The present article considers this intriguing issue by making use of well controlled experiments carried out in an Annular combustion system comprising 16 identical matrix injectors operating in a laminar premixed mode and allowing full optical access to the flame region. This setup is used in a first stage to determine regions of instability as a function of equivalence ratio and injection velocity. It is shown that regions corresponding to spinning and standing azimuthal modes are well separated in this diagram, but with some overlap giving rise to a “dual mode” domain. For the same operating conditions, this Annular system thus exhibits self-sustained instabilities with stable limit cycles coupled by a spinning or a standing mode. It is next shown that the mode which appears in that region depends on the path followed to reach the operating point. Starting from a lean operating condition, the system first develops a chugging instability with a broad frequency spectrum, which then gives rise to a well-established spinning oscillation with a narrow peak frequency in the dual mode region. When operation begins under rich conditions one first observes another chugging mode that finally yields a standing mode when the equivalence ratio is diminished. Away from these regimes, well defined slanted modes and longitudinal modes can also be triggered. In the dual mode region, the type of instability is controlled by an hysteresis phenomenon and the respective chugging modes act as precursors to these established azimuthal modes. It is found that the trajectories in a state space map contain indications on the kind of azimuthal oscillation that will be observed when the target operating point is reached. Beyond the various theoretical explanations of the prevalence of one type of mode on the other, the present observations indicate that spinning or standing modes may also appear in Annular Combustors as a result of the path used to enter the region of azimuthal instability.

Matthew P. Juniper - One of the best experts on this subject based on the ideXlab platform.

  • Weakly nonlinear analysis of thermoacoustic instabilities in Annular Combustors
    Journal of Fluid Mechanics, 2016
    Co-Authors: Giulio Ghirardo, Matthew P. Juniper, Jonas P. Moeck
    Abstract:

    © 2016 Cambridge University Press. Rotationally symmetric Annular Combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the Annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames' response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in Annular Combustors, which shows that rotationally symmetric Annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.

  • Weakly nonlinear analysis of thermoacoustic instabilities in Annular Combustors
    Journal of Fluid Mechanics, 2016
    Co-Authors: Giulio Ghirardo, Matthew P. Juniper, Jonas P. Moeck
    Abstract:

    Rotationally symmetric Annular Combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the Annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames’ response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in Annular Combustors, which shows that rotationally symmetric Annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.

  • Stability analysis of thermo-acoustic nonlinear eigenproblems in Annular Combustors. Part I. Sensitivity
    Journal of Computational Physics, 2016
    Co-Authors: Luca Magri, Michaël Bauerheim, Matthew P. Juniper
    Abstract:

    We present an adjoint-based method for the calculation of eigenvalue perturbations in nonlinear, degenerate and non-self-adjoint eigenproblems. This method is applied to a thermo-acoustic Annular combustor network, the stability of which is governed by a nonlinear eigenproblem. We calculate the first- and second-order sensitivities of the growth rate and frequency to geometric, flow and flame parameters. Three different configurations are analysed. The benchmark sensitivities are obtained by finite difference, which involves solving the nonlinear eigenproblem at least as many times as the number of parameters. By solving only one adjoint eigenproblem, we obtain the sensitivities to any thermo-acoustic parameter, which match the finite-difference solutions at much lower computational cost.

  • Stability analysis of thermo-acoustic nonlinear eigenproblems in Annular Combustors. Part II. Uncertainty quantification
    Journal of Computational Physics, 2016
    Co-Authors: Luca Magri, Franck Nicoud, Michaël Bauerheim, Matthew P. Juniper
    Abstract:

    Monte Carlo and Active Subspace Identification methods are combined with first- and second-order adjoint sensitivities to perform (forward) uncertainty quantification analysis of the thermo-acoustic stability of two Annular combustor configurations. This method is applied to evaluate the risk factor, i.e., the probability for the system to be unstable. It is shown that the adjoint approach reduces the number of nonlinear-eigenproblem calculations by as much as the Monte Carlo samples.

  • Stability Criteria for Standing and Spinning Waves in Annular Combustors
    Volume 4B: Combustion Fuels and Emissions, 2015
    Co-Authors: Giulio Ghirardo, Matthew P. Juniper, Jonas P. Moeck
    Abstract:

    Rotationally symmetric Annular Combustors are of practical importance because they generically resemble combustion chambers in gas turbines and aeroengines, in which thermoacoustically driven oscillations are a major concern. We focus on thermoacoustic oscillations of azimuthal type, neglect the effect of the transverse acoustic velocity in the azimuthal direction, and model the heat release rate as being dependent only on the pressure in the combustion chamber. We study the dynamics of the Annular combustor with a finite number of compact flames equi-spaced along the annulus, and characterise the flames’ response with a describing function. We discuss with broad generality the existence, amplitudes and the stability of standing and spinning waves, as a function of: 1) the number of the burners; 2) the damping in the chamber; 3) the flame describing function. These have implications on industrial applications, the future direction of investigations, and for what to look for in experimental data. We then present as an example of application the first theoretical study of triggering in Annular Combustors, and show that rotationally symmetric Annular chambers can experience stable standing solutions.Copyright © 2015 by ASME

Giulio Ghirardo - One of the best experts on this subject based on the ideXlab platform.

  • Thermoacoustics of Can-Annular Combustors
    Journal of Engineering for Gas Turbines and Power-transactions of The Asme, 2018
    Co-Authors: Giulio Ghirardo, C. Di Giovine, Jonas P. Moeck, Mirko R. Bothien
    Abstract:

    Can-Annular Combustors consist of a set of independent cans, connected on the upstream side to the combustor plenum, and on the downstream side to the turbine inlet, where a transition duct links the round geometry of each can with the Annular segment of the turbine inlet. Each transition duct is open on the sides towards the adjacent transition ducts, so that neighbouring cans are acoustically connected through a so called cross-talk open area. This theoretical, numerical and experimental work discusses the effect that this communication has on the thermoacoustic frequencies of the combustor. We show how this communication gives rise to axial and azimuthal modes, and that these correspond to particularly synchronised states of axial thermoacoustic oscillations in each individual can. We show that these Combustors typically show clusters of thermoacoustic modes with very close frequencies and that a slight loss of rotational symmetry, e.g. a different acoustic response of certain cans, can lead to mode localization. We corroborate the predictions of azimuthal modes, clusters of eigenmodes and mode localization with experimental evidence.

  • Weakly nonlinear analysis of thermoacoustic instabilities in Annular Combustors
    Journal of Fluid Mechanics, 2016
    Co-Authors: Giulio Ghirardo, Matthew P. Juniper, Jonas P. Moeck
    Abstract:

    © 2016 Cambridge University Press. Rotationally symmetric Annular Combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the Annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames' response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in Annular Combustors, which shows that rotationally symmetric Annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.

  • Weakly nonlinear analysis of thermoacoustic instabilities in Annular Combustors
    Journal of Fluid Mechanics, 2016
    Co-Authors: Giulio Ghirardo, Matthew P. Juniper, Jonas P. Moeck
    Abstract:

    Rotationally symmetric Annular Combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the Annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames’ response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in Annular Combustors, which shows that rotationally symmetric Annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.

  • Stability Criteria for Standing and Spinning Waves in Annular Combustors
    Volume 4B: Combustion Fuels and Emissions, 2015
    Co-Authors: Giulio Ghirardo, Matthew P. Juniper, Jonas P. Moeck
    Abstract:

    Rotationally symmetric Annular Combustors are of practical importance because they generically resemble combustion chambers in gas turbines and aeroengines, in which thermoacoustically driven oscillations are a major concern. We focus on thermoacoustic oscillations of azimuthal type, neglect the effect of the transverse acoustic velocity in the azimuthal direction, and model the heat release rate as being dependent only on the pressure in the combustion chamber. We study the dynamics of the Annular combustor with a finite number of compact flames equi-spaced along the annulus, and characterise the flames’ response with a describing function. We discuss with broad generality the existence, amplitudes and the stability of standing and spinning waves, as a function of: 1) the number of the burners; 2) the damping in the chamber; 3) the flame describing function. These have implications on industrial applications, the future direction of investigations, and for what to look for in experimental data. We then present as an example of application the first theoretical study of triggering in Annular Combustors, and show that rotationally symmetric Annular chambers can experience stable standing solutions.Copyright © 2015 by ASME

  • Azimuthal instabilities in Annular Combustors: standing and spinning modes
    Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 2013
    Co-Authors: Giulio Ghirardo, Matthew P. Juniper
    Abstract:

    This theoretical study investigates spinning and standing modes in azimuthally symmetric Annular combustion chambers. Both modes are observed in experiments and simulations, and an existing model predicts that spinning modes are the only stable state of the system. We extend this model to take into account the effect that the acoustic azimuthal velocity, u, has on the flames, and propose a phenomenological model based on experiments performed on transversely forced flames. This model contains a parameter, δ, that quantifies the influence that the transversal excitation has on the fluctuating heat release. For small values of δ, spinning modes are the only stable state of the system. In an intermediate range of δ, both spinning and standing modes are stable states. For large values of δ, standing modes are the only stable state. This study shows that a flame’s response to azimuthal velocity fluctuations plays an important role in determining the type of thermoacoustic oscillations found in Annular Combustors.

Michaël Bauerheim - One of the best experts on this subject based on the ideXlab platform.

  • Surrogates for Combustion Instabilities in Annular Combustors
    Uncertainty Management for Robust Industrial Design in Aeronautics, 2018
    Co-Authors: Michaël Bauerheim, Aissatou Ndiaye, Franck Nicoud
    Abstract:

    While the computational power is still increasing, thus arousing the interest for high-fidelity simulations, the need of low-order models is also felt to both predict and understand combustion instabilities at low costs. Historically applied to simple systems like longitudinal Rijke tubes to unveil the driven mechanisms leading to instability, they have recently been adapted to more complex configurations such as Annular Combustors. A network model is presented here to predict thermo-acoustic modes in an Annular combustion chamber fed by burners connected to an Annular plenum, typical of modern combustor designs. Explicit expressions of the growth rate are derived in several cases showing key parameters controlling the stability. In more general situations, no explicit solution can be obtained. Nevertheless, such an analytical model can be solved numerically at low cost compared with 3D acoustic tools and high-fidelity simulations. In this framework, efficient sensitivity techniques and UQ methods can be developed to tackle the UQ problem: “How can we assess the risk of instability in industrial Combustors at the predesign stage?".

  • Progress in analytical methods to predict and control azimuthal combustion instability modes in Annular chambers
    Physics of Fluids, 2016
    Co-Authors: Michaël Bauerheim, Franck Nicoud, Thierry Poinsot
    Abstract:

    Longitudinal low-frequency thermoacoustic unstable modes in combustion chambers have been intensively studied experimentally, numerically, and theoretically, leading to significant progress in both understanding and controlling these acoustic modes. However, modern Annular gas turbines may also exhibit azimuthal modes, which are much less studied and feature specific mode structures and dynamic behaviors, leading to more complex situations. Moreover, dealing with 10–20 burners mounted in the same chamber limits the use of high fidelity simulations or Annular experiments to investigate these modes because of their complexity and costs. Consequently, for such circumferential acoustic modes, theoretical tools have been developed to uncover underlying phenomena controlling their stability, nature, and dynamics. This review presents recent progress in this field. First, Galerkin and network models are described with their pros and cons in both the temporal and frequency framework. Then, key features of such acoustic modes are unveiled, focusing on their specificities such as symmetry breaking, non-linear modal coupling, forcing by turbulence. Finally, recent works on uncertainty quantifications, guided by theoretical studies and applied to Annular Combustors, are presented. The objective is to provide a global view of theoretical research on azimuthal modes to highlight their complexities and potential.

  • Stability analysis of thermo-acoustic nonlinear eigenproblems in Annular Combustors. Part I. Sensitivity
    Journal of Computational Physics, 2016
    Co-Authors: Luca Magri, Michaël Bauerheim, Matthew P. Juniper
    Abstract:

    We present an adjoint-based method for the calculation of eigenvalue perturbations in nonlinear, degenerate and non-self-adjoint eigenproblems. This method is applied to a thermo-acoustic Annular combustor network, the stability of which is governed by a nonlinear eigenproblem. We calculate the first- and second-order sensitivities of the growth rate and frequency to geometric, flow and flame parameters. Three different configurations are analysed. The benchmark sensitivities are obtained by finite difference, which involves solving the nonlinear eigenproblem at least as many times as the number of parameters. By solving only one adjoint eigenproblem, we obtain the sensitivities to any thermo-acoustic parameter, which match the finite-difference solutions at much lower computational cost.

  • Stability analysis of thermo-acoustic nonlinear eigenproblems in Annular Combustors. Part II. Uncertainty quantification
    Journal of Computational Physics, 2016
    Co-Authors: Luca Magri, Franck Nicoud, Michaël Bauerheim, Matthew P. Juniper
    Abstract:

    Monte Carlo and Active Subspace Identification methods are combined with first- and second-order adjoint sensitivities to perform (forward) uncertainty quantification analysis of the thermo-acoustic stability of two Annular combustor configurations. This method is applied to evaluate the risk factor, i.e., the probability for the system to be unstable. It is shown that the adjoint approach reduces the number of nonlinear-eigenproblem calculations by as much as the Monte Carlo samples.

  • A theoretical study of mean azimuthal flow and asymmetry effects on thermo-acoustic modes in Annular Combustors
    Proceedings of the Combustion Institute, 2015
    Co-Authors: Michaël Bauerheim, Michel Cazalens, Thierry Poinsot
    Abstract:

    The objective of this paper is to develop an analytical model to capture two symmetry breaking effects controlling the frequency and nature (spinning, standing or mixed) of azimuthal modes appearing in Annular chambers: (1) Using two different burner types distributed along the chamber (2) Considering the mean azimuthal flow due to the swirlers or to effusion cooling. The ATACAMAC (Analytical Tool to Analyze and Control Azimuthal Modes in Annular Chambers) methodology is applied using the linearized acoustic equations with a steady and uniform azimuthal mean flow. It provides an analytical implicit dispersion relation which can be solved numerically. A fully analytical resolution is possible when the Annular chamber is weakly coupled to the burners. Results show that symmetry breaking, either by mixing burners types or with a mean azimuthal flow, splits the azimuthal modes into two waves with different frequencies and structures. Breaking symmetry promotes standing modes but adding even a low azimuthal mean flow fosters spinning modes so that the azimuthal mean flow must be taken into account to study azimuthal modes.