Efficient Computation of Thermoacoustic Modes in Annular Combustion Chambers Based on Bloch-Wave Theory

2015 ◽  
Author(s):  
Georg A. Mensah ◽  
Jonas P. Moeck
Keyword(s):  
Rotational Symmetry ◽  
Three Dimensional ◽  
Wave Theory ◽  
Bloch Wave ◽  
Computational Effort ◽  
Mode Shapes ◽  
Efficient Computation ◽  
Burner Flame ◽  
Flame Response ◽  
Type Boundary

Most annular combustors feature a discrete rotational symmetry so that the full configuration can be obtained by copying one burner–flame segment a certain number of times around the circumference. A thermoacoustic model based on the Helmholtz equation then admits special solutions of the so-called Bloch type that can be obtained by considering one segment only. We show that a significant reduction in computational effort for the determination of thermoacoustic modes can be achieved by exploiting this concept. The framework is applicable even in complex cases including a non-homogeneous temperature field and a frequency-dependent, spatially distributed flame response. A parametric study on a three-dimensional combustion chamber model is conducted using both the full scale chamber simulation and a one-segment model with the appropriate Bloch-type boundary conditions. The results for both computations are compared in terms of mode frequencies and growth rates as well as the corresponding mode shapes. This comparison demonstrates the benefits of the Bloch-wave based analysis. It is further shown that even the effect of circumferential asymmetries can be assessed based on computations of one burner–flame segment only by resorting to spectral perturbation theory.

Efficient Computation of Thermoacoustic Modes in Industrial Annular Combustion Chambers Based on Bloch-Wave Theory

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Georg A. Mensah ◽  
Giovanni Campa ◽  
Jonas P. Moeck
Keyword(s):  
Rotational Symmetry ◽  
Three Dimensional ◽  
Wave Theory ◽  
Bloch Wave ◽  
Computational Effort ◽  
Mode Shapes ◽  
Efficient Computation ◽  
Spatially Distributed ◽  
Flame Response ◽  
Type Boundary

Most annular combustors feature a discrete rotational symmetry so that the full configuration can be obtained by copying one burner-flame segment a certain number of times around the circumference. A thermoacoustic model based on the Helmholtz equation then admits special solutions of the so-called Bloch type that can be obtained by considering one segment only. We show that a significant reduction in computational effort for the determination of thermoacoustic modes can be achieved by exploiting this concept. The framework is applicable even in complex cases including an inhomogeneous temperature field and a frequency-dependent, spatially distributed flame response. A parametric study on a three-dimensional combustion chamber model is conducted using both the full-scale chamber simulation and a one-segment model with the appropriate Bloch-type boundary conditions. The results for both computations are compared in terms of mode frequencies and growth rates as well as the corresponding mode shapes. The same is done for a more complex industrial configuration. These comparisons demonstrate the benefits of the Bloch-wave based analysis.

Time-Domain Bloch Boundary Conditions for Efficient Simulation of Thermoacoustic Limit Cycles in (Can-)Annular Combustors

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Matthias Haeringer ◽  
Wolfgang Polifke
Keyword(s):  
Boundary Conditions ◽  
State Space ◽  
Time Domain ◽  
Cfd Simulation ◽  
Rotational Symmetry ◽  
Wave Theory ◽  
Bloch Wave ◽  
Cfd Simulations ◽  
Suggested Approach ◽  
Combustion Dynamics

Abstract Thermo-acoustic eigenmodes of annular or can-annular combustion chambers, which typically feature a discrete rotational symmetry, may be computed in an efficient manner by utilizing the Bloch-wave theory. Unfortunately, the application of the Bloch-wave theory to combustion dynamics has hitherto been limited to the frequency domain. In this study, we present a time-domain formulation of Bloch boundary conditions (BBC), which allows to employ them in time domain simulations, e.g., computational fluid dynamics (CFD) simulations. The BBCs are expressed as acoustic scattering matrices and translated to complex-valued state-space systems. In a hybrid approach an unsteady, compressible CFD simulation of the burner-flame zone is coupled via characteristic-based state-space boundary conditions to a reduced order model of the combustor acoustics that includes BBCs. The acoustic model with BBC accounts for cross-can acoustic coupling and the discrete rotational symmetry of the configuration, while the CFD simulation accounts for the nonlinear flow–flame acoustic interactions. This approach makes it possible to model limit cycle oscillations of (can-)annular combustors at drastically reduced computational cost compared to CFD simulations of the full configuration and without the limitations of weakly nonlinear approaches that utilize a flame describing function. In this study, the suggested approach is applied to a generic multican combustor. Results agree well with a fully compressible CFD simulation of the complete configuration.

Low-Order Modeling of Can-Annular Combustors

2021 ◽  
Author(s):  
Guillaume J. J. Fournier ◽  
Max Meindl ◽  
Camilo F. Silva ◽  
Giulio Ghirardo ◽  
Mirko R. Bothien ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Gas Turbines ◽  
Characteristic Length ◽  
Rotational Symmetry ◽  
Wave Theory ◽  
Bloch Wave ◽  
Geometrical Parameters ◽  
Flow Parameters ◽  
Annular Gap ◽  
Low Order

Abstract Heavy-duty land-based gas turbines are often designed with can-annular combustors, which consist of a set of identical cans, acoustically connected on the upstream side via the compressor plenum, and, downstream, with a small annular gap located at the transition with the first turbine stage. The modeling of this cross-talk area is crucial to predict the thermo-acoustic modes of the system. Thanks to the discrete rotational symmetry, Bloch wave theory can be exploited to reduce the system to a longitudinal combustor with a complex-valued equivalent outlet reflection coefficient, which models the annular gap. The present study reviews existing low-order models based purely on geometrical parameters and compares them to 2D Helmholtz simulations. We demonstrate that the modeling of the gap as a thin annulus is not suited for can-annular combustors and that the Rayleigh conductivity model only gives qualitative agreement. We then propose an extension for the equivalent reflection coefficient that accounts not only for geometrical but also flow parameters, by means of a characteristic length. The proposed model is in excellent agreement with 2D simulations and is able to correctly capture the eigenfrequencies of the system. We then perform a Design of Experiments study that allows us to explore various configurations and build correlations for the characteristic length. Finally, we discuss the validity limits of the proposed low-order modeling approach.

Limit Cycles of Spinning Thermoacoustic Modes in Annular Combustors: A Bloch-Wave and Adjoint-Perturbation Approach

2017 ◽  
Author(s):  
Georg A. Mensah ◽  
Jonas P. Moeck
Keyword(s):  
Helmholtz Equation ◽  
Limit Cycle ◽  
Rotational Symmetry ◽  
Wave Theory ◽  
Bloch Wave ◽  
Generic Model ◽  
Perturbation Approach ◽  
Dependent Manner ◽  
Combustion System ◽  
Linear Character

The most straightforward way to assess the thermoacoustic stability of a combustion system is based on modal approaches. The modes are typically computed from linearized equations in the frequency domain, such as the Helmholtz equation. Due to the linear character, nonlinear saturation effects cannot be computed with such models. Flame describing functions have been suggested to fill this gap. They describe the flame response in an amplitude-dependent manner and have been successfully used in recent work for the prediction of limit-cycle amplitudes in single-burner systems and annular combustors. This paper presents a more efficient approach of computing limit-cycle amplitudes of spinning thermoacoustic modes in an annular combustion chamber. As one important feature, adjoint perturbation theory is utilized for the solution of the thermoacoustic Helmholtz equation associated with a flame describing function. This avoids iterations over different amplitude levels to find the limit cycle amplitude, i.e., the amplitude level at which the modal growth rate is zero, as required in previous approaches. Moreover, based on the discrete rotational symmetry of the system, the computation is also accelerated by means of Bloch-wave theory, which reduces computations for annular combustors to a single burner/flame segment. Results for a generic model and a laboratory-scale annular combustion system are presented and discussed.

scholarly journals Analysis of Thermoacoustic Modes in Can-Annular Combustors Using Effective Bloch-Type Boundary Conditions

2020 ◽  
Author(s):  
Jakob von Saldern ◽  
Alessandro Orchini ◽  
Jonas Moeck
Keyword(s):  
Acoustic Waves ◽  
Gas Turbines ◽  
Rotational Symmetry ◽  
Low Frequency ◽  
Periodic Wave ◽  
Mode Shapes ◽  
Coupling Condition ◽  
Annular Combustor ◽  
Close Frequency ◽  
Type Boundary

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.

Time Domain Bloch Boundary Conditions for Efficient Simulation of Thermoacoustic Limit-Cycles in (Can-)Annular Combustors

2019 ◽  
Author(s):  
Matthias Haeringer ◽  
Wolfgang Polifke
Keyword(s):  
Boundary Conditions ◽  
State Space ◽  
Time Domain ◽  
Cfd Simulation ◽  
Rotational Symmetry ◽  
Wave Theory ◽  
Bloch Wave ◽  
Cfd Simulations ◽  
Suggested Approach ◽  
Combustion Dynamics

Abstract Thermo-acoustic eigenmodes of annular or can-annular combustion chambers, which typically feature a discrete rotational symmetry, may be computed in an efficient manner by utilizing the Bloch-wave theory. Unfortunately, the application of the Bloch-wave theory to combustion dynamics has hitherto been limited to the frequency domain. In this study we present a time domain formulation of Bloch boundary conditions (BBC), which allows to employ them in time domain simulations, e.g. CFD simulations. The BBCs are expressed as acoustic scattering matrices and translated to complex-valued state-space systems. In a hybrid approach an unsteady, compressible CFD simulation of the burner-flame zone is coupled via characteristic-based state-space boundary-conditions to a reduced order model of the combustor acoustics that includes BBCs. The acoustic model with BBC accounts for cross-can acoustic coupling and the discrete rotational symmetry of the configuration, while the CFD simulation accounts for the nonlinear flow-flame-acoustic interactions. This approach makes it possible to model limit cycle oscillations of (can-)annular combustors at drastically reduced computational cost compared to CFD simulations of the full configuration, and without the limitations of weakly nonlinear approaches that utilize a flame describing function. In the current study the suggested approach is applied to a generic multi-can combustor. Results agree well with a fully compressible CFD simulation of the complete configuration.

Low-order Modeling of Can-annular Combustors

2021 ◽  
Author(s):  
Guillaume Jean Jacques Fournier ◽  
Maximilian Meindl ◽  
Camilo Silva ◽  
Giulio Ghirardo ◽  
Mirko R. Bothien ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Gas Turbines ◽  
Characteristic Length ◽  
Rotational Symmetry ◽  
Wave Theory ◽  
Bloch Wave ◽  
Geometrical Parameters ◽  
Flow Parameters ◽  
Annular Gap ◽  
Low Order

Abstract Heavy-duty land-based gas turbines are often designed with can-annular combustors, which consist of a set of identical cans, acoustically connected on the upstream side via the compressor plenum, and, downstream, with a small annular gap located at the transition with the first turbine stage. The modeling of this cross-talk area is crucial to predict the thermo-acoustic modes of the system. Thanks to the discrete rotational symmetry, Bloch wave theory can be exploited to reduce the system to a longitudinal combustor with a complex-valued equivalent outlet reflection coefficient, which models the annular gap. The present study reviews existing low-order models based purely on geometrical parameters and compares them to 2D Helmholtz simulations. We demonstrate that the modeling of the gap as a thin annulus is not suited for can-annular combustors and that the Rayleigh conductivity model only gives qualitative agreement. We then propose an extension for the equivalent reflection coefficient that accounts not only for geometrical but also flow parameters, by means of a characteristic length. The proposed model is in excellent agreement with 2D simulations and is able to correctly capture the eigenfrequencies of the system. We then perform a Design of Experiments study that allows us to explore various configurations and build correlations for the characteristic length. Finally, we discuss the validity limits of the proposed low-order modeling approach.

scholarly journals Analysis of Thermoacoustic Modes in Can-Annular Combustors Using Effective Bloch-Type Boundary Conditions

2020 ◽  
Author(s):  
Jakob G. R. von Saldern ◽  
Alessandro Orchini ◽  
Jonas P. Moeck
Keyword(s):  
Acoustic Waves ◽  
Gas Turbines ◽  
Rotational Symmetry ◽  
Low Frequency ◽  
Periodic Wave ◽  
Mode Shapes ◽  
Coupling Condition ◽  
Annular Combustor ◽  
Close Frequency ◽  
Type Boundary

Abstract Heavy-duty gas turbines are commonly designed with canannular 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 that can be efficiently addressed with this framework 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.

scholarly journals Identification of Mode Shapes of a Composite Cylinder Using Convolutional Neural Networks

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2801
Author(s):  
Bartosz Miller ◽  
Leonard Ziemiański
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Composite Structures ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Identification Algorithm ◽  
Material Degradation ◽  
Local Material ◽  
Noisy Input ◽  
Shape Vector

The aim of the following paper is to discuss a newly developed approach for the identification of vibration mode shapes of multilayer composite structures. To overcome the limitations of the approaches based on image analysis (two-dimensional structures, high spatial resolution of mode shapes description), convolutional neural networks (CNNs) are applied to create a three-dimensional mode shapes identification algorithm with a significantly reduced number of mode shape vector coordinates. The CNN-based procedure is accurate, effective, and robust to noisy input data. The appearance of local damage is not an obstacle. The change of the material and the occurrence of local material degradation do not affect the accuracy of the method. Moreover, the application of the proposed identification method allows identifying the material degradation occurrence.

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