Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Tobias Hummel ◽  
Klaus Hammer ◽  
Pedro Romero ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Dynamical System ◽  
Gas Turbine ◽  
High Frequency ◽  
Linear Part ◽  
Combustion Noise ◽  
Dynamical System Theory ◽  
Flame Dynamics ◽  
The Impact ◽  
Thermoacoustic Oscillations ◽  
Low Order

This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit-cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D combustor configuration are modeled and reconstructed by means of a low-order dynamical system simulation. The source of nonlinearity is solely allocated to flame dynamics, saturating the growth of acoustic amplitudes, while the oscillation amplitudes are assumed to always remain within the linearity limit. First, a reduced order model (ROM) which reproduces the combustor's modal distribution and damping of acoustic oscillations is derived. The ROM is a low-order state-space system, which results from a projection of the linearized Euler equations (LEE) into their truncated eigenspace. Second, flame dynamics are modeled as a function of acoustic perturbations by means of a nonlinear transfer function. This function has a linear and a nonlinear contribution. The linear part is modeled analytically from first principles, while the nonlinear part is mathematically cast into a cubic saturation functional form. Additionally, the impact of stochastic forcing due to broadband combustion noise is included by additive white noise sources. Then, the acoustic and the flame system is interconnected, where thermoacoustic noncompactness due to the transversal modes' high frequency (HF) is accounted for by a distributed source term framework. The resulting nonlinear thermoacoustic system is solved in frequency and time domain. Linear growth rates predict linear stability, while envelope plots and probability density diagrams of the resulting pressure traces characterize the thermoacoustic performance of the combustor from a dynamical systems theory perspective. Comparisons against experimental data are conducted, which allow the rating of the flame modes in terms of their capability to reproduce the observed combustor dynamics. Ultimately, insight into the physics of high-frequency, transversal thermoacoustic systems is created.

Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors

2016 ◽  
Author(s):  
Tobias Hummel ◽  
Klaus Hammer ◽  
Pedro Romero ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Dynamical System ◽  
Gas Turbine ◽  
High Frequency ◽  
Linear Part ◽  
Combustion Noise ◽  
Dynamical System Theory ◽  
Flame Dynamics ◽  
The Impact ◽  
Thermoacoustic Oscillations ◽  
Low Order

This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D combustor configuration are modeled, and reconstructed by means of a low order dynamical system simulation. The source of nonlinearity is solely allocated to flame dynamics, saturating the growth of acoustic amplitudes, while the oscillation amplitudes are assumed to always remain within the linearity limit. First, a Reduced Order Model (ROM), which reproduces the combustor’s modal distribution and damping of acoustic oscillations is derived. The ROM is a low-order state-space system, which results from a projection of the Linearized Euler Equations (LEE) into their truncated eigenspace. Second, flame dynamics are modeled as a function of acoustic perturbations by means of a nonlinear transfer function. This function has a linear and a nonlinear contribution. The linear part is modeled analytically from first principles, while the nonlinear part is mathematically cast into a cubic saturation functional form. Additionally, the impact of stochastic forcing due to broadband combustion noise is included by additive white noise sources. Then, the acoustic and the flame system is interconnected, where thermoacoustic non-compactness due to the transversal modes’ high frequency is accounted for by a distributed source term framework. The resulting nonlinear thermoacoustic system is solved in frequency and time domain. Linear growth rates predict linear stability, while envelope plots and probability density diagrams of the resulting pressure traces characterize the thermoacoustic performance of the combustor from a dynamical systems theory perspective. Comparisons against experimental data are conducted, which allow the rating of the flame modes in terms of their capability to reproduce the observed combustor dynamics. Ultimately, insight into the physics of high-frequency, transversal thermoacoustic systems is created.

Pulsation-Amplitude-Dependent Flame Dynamics of High-Frequency Thermoacoustic Oscillations in Lean-Premixed Gas Turbine Combustors

2017 ◽  
Author(s):  
Frederik M. Berger ◽  
Tobias Hummel ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Gas Turbine ◽  
Growth Rates ◽  
High Frequency ◽  
Individual Growth ◽  
Mean Flow ◽  
Flame Dynamics ◽  
Pulsation Amplitude ◽  
The Mean ◽  
Thermoacoustic Oscillations

This paper presents the experimental investigation of pulsation-amplitude-dependent flame dynamics associated with transverse thermoacoustic oscillations at screech level frequencies in a generic gas turbine combustor. Specifically, the flame behavior at different levels of pulsation amplitudes is assessed and interpreted. Spatial dynamics of the flame are measured by imaging the OH* chemiluminescence signal synchronously to the dynamic pressure at the combustor’s face plate. First, linear thermoacoustic stability states, modal dynamics, as well as flame-acoustic phase relations are evaluated. It is found that the unstable acoustic modes converge into a predominantly rotating character in the direction of the mean flow swirl. Furthermore, the flame modulation is observed to be in phase with the acoustic pressure at all levels of the oscillation amplitude. Second, distributed flame dynamics are investigated by means of visualizing the mean and oscillating heat release distribution at different pulsation amplitudes. The observed flame dynamics are then compared against numerical evaluations of the respective amplitude-dependent thermoacoustic growth rates, which are computed using analytical models in the fashion of a non-compact flame-describing function. While results show a nonlinear contribution for the individual growth rates, the superposition of flame deformation and displacements balances out to a constant flame driving. This latter observation contradicts the state-of-the-art perception of root-causes for limit-cycle oscillations in thermoacoustic gas turbine systems, for which the heat release saturates with increasing amplitudes. Consequently, the systematic observations and analysis of amplitude-dependent flame modulation shows alternative paths to the explanation of mechanisms that might cause thermoacoustic saturation in high frequency systems.

Pulsation-Amplitude-Dependent Flame Dynamics of High-Frequency Thermoacoustic Oscillations in Lean-Premixed Gas Turbine Combustors

2017 ◽  
Vol 140 (4) ◽  
Author(s):  
Frederik M. Berger ◽  
Tobias Hummel ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Gas Turbine ◽  
Growth Rates ◽  
High Frequency ◽  
Individual Growth ◽  
Mean Flow ◽  
Flame Dynamics ◽  
Pulsation Amplitude ◽  
The Mean ◽  
Thermoacoustic Oscillations

This paper presents the experimental investigation of pulsation-amplitude-dependent flame dynamics associated with transverse thermoacoustic oscillations at screech level frequencies in a generic gas turbine combustor. Specifically, the flame behavior at different levels of pulsation amplitudes is assessed and interpreted. Spatial dynamics of the flame are measured by imaging the OH⋆ chemiluminescence (CL) signal synchronously to the dynamic pressure at the combustor's face plate. First, linear thermoacoustic stability states, modal dynamics, and flame-acoustic phase relations are evaluated. It is found that the unstable acoustic modes converge into a predominantly rotating character in the direction of the mean flow swirl. Furthermore, the flame modulation is observed to be in phase with the acoustic pressure at all levels of the oscillation amplitude. Second, distributed flame dynamics are investigated by means of visualizing the mean and oscillating heat release distribution at different pulsation amplitudes. The observed flame dynamics are then compared against numerical evaluations of the respective amplitude-dependent thermoacoustic growth rates, which are computed using analytical models in the fashion of a noncompact flame-describing function. While results show a nonlinear contribution for the individual growth rates, the superposition of flame deformation and displacement balances out to a constant flame driving. This latter observation contradicts the state-of-the-art perception of root-causes for limit-cycle oscillations in thermoacoustic gas turbine systems, for which the heat release saturates with increasing amplitudes. Consequently, the systematic observations and analysis of amplitude-dependent flame modulation shows alternative paths to the explanation of mechanisms that might cause thermoacoustic saturation in high frequency systems.

Amplitude-Dependent Damping and Driving Rates of High-Frequency Thermoacoustic Oscillations in a Lab-Scale Lean-Premixed Gas Turbine Combustor

2021 ◽  
Author(s):  
Thomas Hofmeister ◽  
Thomas Sattelmayer
Keyword(s):  
Flow Field ◽  
Gas Turbine ◽  
Limit Cycle ◽  
High Frequency ◽  
Mean Flow ◽  
Gas Turbine Combustor ◽  
Cfd Simulations ◽  
The Mean ◽  
Amplitude Dependency ◽  
Thermoacoustic Oscillations

Abstract This paper presents numerical investigations of the amplitude-dependent stability behavior of thermoacoustic oscillations at screech level frequencies in a lean-premixed, swirl-stabilized, lab-scale gas turbine combustor. A hybrid Computational Fluid Dynamics / Computational AeroAcoustics (CFD / CAA) approach is applied to individually compute thermoacoustic damping and driving rates for various acoustic amplitude levels at the combustors' first transversal (T1) eigenfrequency. Forced CFD simulations with the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations mimic the real combustor's rotating T1 eigenmode. An increase of the forcing amplitude over time allows observation of the amplitude-dependent flow field and flame evolution. In accordance with measured OH*-chemiluminescence images, a pulsation amplitude-dependent flame contraction is reproduced in the CFD simulations. At several amplitude levels, period-averaged flow fields are then denoted as reference states, which serve as inputs for the CAA part. There, eigenfrequency simulations with linearized flow equations are performed with the Finite Element Method (FEM). The outcomes are damping and driving rates as a response to the amplitude-dependency of the mean flow field. It is found that driving due to flame-acoustics interactions governs a weak amplitude-dependency, which agrees with experimentally based studies at the authors' institute. This disqualifies the perception of heat release saturation as the root-cause for limit-cycle oscillations in this high-frequency thermoacoustic system. Instead, significantly increased dissipation due to the interaction of acoustically induced vorticity perturbations with the mean flow is identified, which may explain the formation of a limit-cycle.

Effects of Nozzle Helmholtz Number on Indirect Combustion Noise by Compositional Perturbations

2017 ◽  
Author(s):  
Luca Magri ◽  
Jeffrey O’Brien ◽  
Matthias Ihme
Keyword(s):  
Velocity Profile ◽  
Combustion Chamber ◽  
Gas Turbine ◽  
Transfer Functions ◽  
Mixture Fraction ◽  
Supersonic Nozzle ◽  
Noise Pollution ◽  
Combustion Noise ◽  
Dipole Source ◽  
Thermoacoustic Oscillations

By modeling a multi-component gas, a new source of indirect combustion noise is identified, which is named compositional indirect noise. The advection of mixture inhomogeneities exiting the gas-turbine combustion chamber through subsonic and supersonic nozzles is shown to be an acoustic dipole source of sound. The level of mixture inhomogeneity is described by a difference in composition with the mixture fraction. An n-dodecane mixture, which is a kerosene fuel relevant to aeronautics, is used to evaluate the level of compositional noise. By relaxing the compact-nozzle assumption, the indirect noise is numerically calculated for Helmholtz numbers up to 2 in nozzles with linear velocity profile. The compact-nozzle limit is discussed. Only in this limit, it is possible to derive analytical transfer functions for (i) the noise emitted by the nozzle and (ii) the acoustics travelling back to the combustion chamber generated by accelerated compositional inhomogeneities. The former contributes to noise pollution, whereas the latter has the potential to induce thermoacoustic oscillations. It is shown that the compositional indirect noise can be at least as large as the direct noise and entropy noise in chocked nozzles and lean mixtures. As the frequency with which the compositional inhomogeneities enter the nozzle increases, or as the nozzle spatial length increases, the level of compositional noise decreases, with a similar, but not equal, trend to the entropy noise. The noisiest configuration is found to be a compact supersonic nozzle.

High Frequency Thermoacoustic Modulation Mechanisms in Swirl-Stabilized Gas Turbine Combustors: Part One — Experimental Investigation of Local Flame Response

2016 ◽  
Author(s):  
Frederik M. Berger ◽  
Tobias Hummel ◽  
Michael Hertweck ◽  
Jan Kaufmann ◽  
Bruno Schuermans ◽  
...  
Keyword(s):  
Heat Release ◽  
Gas Turbine ◽  
High Frequency ◽  
Transfer Functions ◽  
Temporal Dynamics ◽  
Dynamic Pressure ◽  
Radon Transforms ◽  
Gas Turbine Combustors ◽  
High Modulation ◽  
The Impact

This paper presents the experimental approach for determination and validation of non-compact flame transfer functions of high frequency, transverse combustion instabilities observed in a generic lean premixed gas turbine combustor. The established non-compact transfer functions describe the interaction of the flame’s heat release with the acoustics locally, which is necessary due to the respective length scales being of the same order of magnitude. Spatio-temporal dynamics of the flame are measured by imaging the OH* chemiluminescence signal, phase-locked to the dynamic pressure at the combustor’s front plate. Radon transforms provide a local insight into the flame’s modulated reaction zone. Applied to different burner configurations, the impact of the unsteady heat release distribution on the thermoacoustic driving potential, as well as distinct flame regions that exhibit high modulation intensity are revealed. Utilizing these spatially distributed transfer functions within thermoacoustic analysis tools (addressed in this joint publication’s part two) allows then to predict transverse linear stability of gas turbine combustors.

High-Frequency Thermoacoustic Modulation Mechanisms in Swirl-Stabilized Gas Turbine Combustors—Part I: Experimental Investigation of Local Flame Response

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Frederik M. Berger ◽  
Tobias Hummel ◽  
Michael Hertweck ◽  
Jan Kaufmann ◽  
Bruno Schuermans ◽  
...  
Keyword(s):  
Heat Release ◽  
Gas Turbine ◽  
High Frequency ◽  
Transfer Functions ◽  
Dynamic Pressure ◽  
Radon Transforms ◽  
Gas Turbine Combustors ◽  
High Modulation ◽  
Order Of Magnitude ◽  
The Impact

This paper presents the experimental approach for determination and validation of noncompact flame transfer functions of high-frequency, transverse combustion instabilities observed in a generic lean premixed gas turbine combustor. The established noncompact transfer functions describe the interaction of the flame's heat release with the acoustics locally, which is necessary due to the respective length scales being of the same order of magnitude. Spatiotemporal dynamics of the flame are measured by imaging the OH⋆ chemiluminescence signal, phase-locked to the dynamic pressure at the combustor's front plate. Radon transforms provide a local insight into the flame's modulated reaction zone. Applied to different burner configurations, the impact of the unsteady heat release distribution on the thermoacoustic driving potential, as well as distinct flame regions that exhibit high modulation intensity, is revealed. Utilizing these spatially distributed transfer functions within thermoacoustic analysis tools (addressed in this joint publication's Part II) allows then to predict transverse linear stability of gas turbine combustors.

scholarly journals Detection and prevention of blowout in a lean premixed gas-turbine model combustor using the concept of dynamical system theory

2015 ◽  
Vol 35 (3) ◽  
pp. 3245-3253 ◽  
Author(s):  
Shohei Domen ◽  
Hiroshi Gotoda ◽  
Taku Kuriyama ◽  
Yuta Okuno ◽  
Shigeru Tachibana
Keyword(s):  
Dynamical System ◽  
System Theory ◽  
Gas Turbine ◽  
Dynamical System Theory ◽  
Lean Premixed ◽  
Turbine Model

Self-Excited High-Frequency Transverse Limit-Cycle Oscillations and Associated Flame Dynamics in a Gas Turbine Reheat Combustor Experiment

2021 ◽  
Author(s):  
Jonathan McClure ◽  
Frederik M. Berger ◽  
Michael Bertsch ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Combustion Chamber ◽  
Gas Turbine ◽  
Limit Cycle ◽  
High Frequency ◽  
Dynamic Pressure ◽  
High Amplitude ◽  
Limit Cycle Oscillations ◽  
Flame Dynamics ◽  
Auto Ignition

Abstract This paper presents the investigation of high-frequency thermoacoustic limit-cycle oscillations in a novel experimental gas turbine reheat combustor featuring both auto-ignition and propagation stabilised flame zones at atmospheric pressure. Dynamic pressure measurements at the faceplate of the reheat combustion chamber reveal high-amplitude periodic pressure pulsations at 3 kHz in the transverse direction of the rectangular cross-section combustion chamber. Further analysis of the acoustic signal shows that this is a thermoacoustically unstable condition undergoing limit-cycle oscillations. A sensitivity study is presented which indicates that these high-amplitude limit-cycle oscillations only occur under certain conditions: namely high power settings with propane addition to increase auto-ignition propensity. The spatially-resolved flame dynamics are then investigated using CH* chemiluminescence, phase-locked to the dynamic pressure, captured from all lateral sides of the reheat combustion chamber. This reveals strong heat release oscillations close to the chamber walls at the instability frequency, as well as axial movement of the flame tips in these regions and an overall transverse displacement of the flame. Both the heat release oscillations and the flame motion occur in phase with the acoustic mode. From these observations, likely thermoacoustic driving mechanisms which lead to the limit-cycle oscillations are inferred. In this case, the overall flame-acoustics interaction is assumed to be a superposition of several effects, with the observations suggesting strong influences from autoignition-pressure coupling as well as flame displacement and deformation due to the acoustic velocity field. These findings provide a foundation for the overall objective of developing predictive approaches to mitigate the impact of high-frequency thermoacoustic instabilities in future generations of gas turbines with sequential combustion systems.

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