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.

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 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.

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.

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.

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.

scholarly journals Two-phase CFD simulation of the monodyspersed suspension hydraulic behaviour in the tank apparatus from a circulatory pipe

2008 ◽  
Vol 10 (1) ◽  
pp. 22-27 ◽  
Author(s):  
Roch Plewik ◽  
Piotr Synowiec ◽  
Janusz Wójcik
Keyword(s):  
Cfd Simulation ◽  
Fluidised Bed ◽  
Cfd Simulations ◽  
Two Phase ◽  
Hydraulic Behaviour ◽  
Hydraulic Conditions ◽  
The One ◽  
Cfd Method ◽  
Multi Phase ◽  
The Ideal

Two-phase CFD simulation of the monodyspersed suspension hydraulic behaviour in the tank apparatus from a circulatory pipe The hydrodynamics in fluidized-bed crystallizers is studied by CFD method. The simulations were performed by a commercial packet of computational fluid dynamics Fluent 6.x. For the one-phase modelling (15), a standard k-ε model was applied. In the case of the two-phase flows the Eulerian multi-phase model with a standard k-ε method, aided by the k-ε dispersed model for viscosity, has been used respectively. The collected data put a new light on the suspension flow behaviour in the annular zone of the fluidised bed crystallizer. From the presented here CFD simulations, it clearly issues that the real hydraulic conditions in the fluidised bed crystallizers are far from the ideal ones.

Cyclic Breathing Simulations in Large Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

2012 ◽  
Author(s):  
D. Keith Walters ◽  
Greg W. Burgreen ◽  
Robert L. Hester ◽  
David S. Thompson ◽  
David M. Lavallee ◽  
...  
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Large Scale ◽  
Whole Body ◽  
Patient Specific ◽  
Cfd Simulations ◽  
Reduced Order ◽  
Scale Models ◽  
Steady State Simulation ◽  
Conducting Zone

Computational fluid dynamics (CFD) simulations were performed for unsteady periodic breathing conditions, using large-scale models of the human lung airway. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to G16) obtained from a stochastically generated airway tree with statistically realistic geometrical characteristics. A reduced-order geometry was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to G16. The inlet and outlet flow boundaries corresponded to the oronasal opening (superior), the inlet/outlet planes in terminal bronchioles (distal), and the unresolved airway boundaries arising from the truncation procedure (intermediate). The cyclic flow was specified according to the predicted ventilation patterns for a healthy adult male at three different activity levels, supplied by the whole-body modeling software HumMod. The CFD simulations were performed using Ansys FLUENT. The mass flow distribution at the distal boundaries was prescribed using a previously documented methodology, in which the percentage of the total flow for each boundary was first determined from a steady-state simulation with an applied flow rate equal to the average during the inhalation phase of the breathing cycle. The distal pressure boundary conditions for the steady-state simulation were set using a stochastic coupling procedure to ensure physiologically realistic flow conditions. The results show that: 1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; 2) the predicted alveolar pressure is in good agreement with previously documented values; and 3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

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