Recently, because of environmental regulations, gas turbine manufacturers are restricted to produ... more Recently, because of environmental regulations, gas turbine manufacturers are restricted to produce machines that work in the lean combustion regime. Gas turbines operating in this regime are prone to combustion-driven acoustic oscillations referred as combustion instabilities. These oscillations could have such high amplitude that they can damage gas turbine hardware. In this study, the three-step approach for combustion instabilities prediction is applied to an industrial test rig. As the first step, the flame transfer function (FTF) of the burner is obtained performing unsteady computational fluid dynamics (CFD) simulations. As the second step, the obtained FTF is approximated with an analytical time-lag-distributed model. The third step is the time-domain simulations using a network model. The obtained results are compared against the experimental data. The obtained results show a good agreement with the experimental ones and the developed approach is able to predict thermoacoustic instabilities in gas turbines combustion chambers.
Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion-dr... more Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion-driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damage of combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. We have developed a two-step method to find a set of operating parameters under which gas turbines can be operated without going into self-excited pressure oscillations. As the first step, an unsteady Reynolds-averaged Navier–Stokes simulation with the flame speed closure model implemented in the OpenFOAM Õ environment is performed to obtain the flame transfer function of the combustion setup. As the second step time-domain simulations employing low-order network model implemented in Simulink Õ are executed. In this work, we apply the proposed method to the Beschaufelter RingSpalt test rig developed at the Technische Universität München. The sensitivity of thermoacoustic stability to the length of a combustion chamber, flame position, gain and phase of flame transfer function and outlet reflection coefficient are studied.
A method for predicting the onset of acoustically driven combustion instabilities in gas turbine ... more A method for predicting the onset of acoustically driven combustion instabilities in gas turbine combustor is examined. The basic idea is that the governing equations of the acoustic waves can be coupled with a flame heat release model and solved in the frequency domain. The paper shows that a complex eigenvalue problem is obtained that can be solved numerically by implementing the governing equations in a finite element code. This procedure allows one to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behaviour of the acoustic waves can be applied.
The method can be applied virtually to any three dimensional geometry, provided the necessary computational resources that are, anyway, much less than those required by Computational Fluid Dynamics (CFD) methods proposed for analysing the combustion chamber under instability condition. Furthermore, in comparison with the “lumped” approach that characterize popular Acoustics Networks, the proposed method allows one for much more flexibility in defining the geometry of the combustion chamber.
The paper shows that different types of heat release laws, for instance, heat release concentrated in a flame sheet as well as distributed in a larger domain, can be adopted. Moreover, experimentally or numerically determined flame transfer functions, giving the response of heat release to acoustic velocity fluctuations, can be incorporated in the model.
To establish proof of concept, the method is validated at the beginning against simple test cases taken from literature. Over the frequency range considered, frequencies and growth rates both of stable and unstable eigenmodes are accurately evaluated. Then the method is applied to a much more complex annular combustor geometry in order to evaluate frequencies and growth rates of the unstable modes and to show how the variation of the parameters of the heat release law can influence the transition to instability
Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dr... more Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dry low emission combustion systems. In the case of annular combustion chambers, experimental test cases carried out on small scale test rigs equipped with single burner arrangements fail to give adequate indications for the design of the full scale combustion chamber, since they are unable to reproduce the interaction of the flame fluctuation with the azimuthal pressure waves. Therefore there is a large interest in developing techniques able to make use of data gathered from tests carried out on a single burner for predicting the thermoacoustic behavior of the combustion chamber at full scale with its actual geometry. A hybrid technique based on the use of the finite elements method and the transfer matrix method is used to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability, under the hypothesis of linear behavior of the acoustic waves. This approach is able to model complex geometries such as annular combustion chambers equipped with several burners. Heat release fluctuations are modeled through a classical n-τ Flame Transfer Function (FTF). In order to model the acoustic behavior of the burners, the computational domain corresponding to each burner is substituted by a mathematical function, that is the Burner Transfer Matrix (BTM), that relates, one to each other, pressure and velocity oscillations at either sides of the burner. Both the FTF and the BTM can be obtained from experimental tests or from CFD simulations. The use of the transfer matrix permits us to take into account parameters, such as the flow velocity and the viscous losses, which are not directly included in the model. This paper describes the introduction of the burner transfer matrix in the combustion chamber model. Different geometries of combustion chamber and burner are tested. The influence of the parameters characterizing the transfer matrix is investigated. Finally the application of the BTM to an actual annular combustion chamber is shown.
Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place i... more Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of nonnormality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
A LIMIT CYCLE FOR PRESSURE OSCILLATIONS IN A GAS TURBINE BURNER, Jul 13, 2014
Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place i... more Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
This paper shows a novel method for predicting the onset of acoustically driven combustion instab... more This paper shows a novel method for predicting the onset of acoustically driven combustion instabilities in gas turbine combustors. The basic idea is that the governing equations of the acoustic waves can be coupled with a flame heat release model and solved in the frequency domain. The paper shows that a complex eigenvalue problem is obtained that can be solved numerically by implementing the governing equations in the “Acoustic” module of COMSOL Multiphysics. The procedure allows one to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behaviour of the acoustic waves can be applied.
ASME Turbo Expo 2014, Düsseldorf, Germany, 16-20 June 2014
The influence of the introduction of a Helmholtz resonator as a passive damper in a gas turbine c... more The influence of the introduction of a Helmholtz resonator as a passive damper in a gas turbine combustion chamber on the bifurcation mechanism that characterizes the transition to instability is investigated. Bifurcation diagrams are tracked in order to identify the conditions for which the machine works in a stable zone and which are the operative parameters that bring the machine to unstable conditions. This work shows that a properly designed passive damper system increases the stable zone, moving the unstable zone and the bistable zone (in the case of a subcritical bifurcation) to higher values of the operative parameters, while have a limited influence on the amplitude of limit cycle. In order to examine the effect of the damper, a gas turbine combustion chamber is first modeled as a simple cylindrical duct, where the flame is concentrated in a narrow area at around one quarter of the duct. Heat release fluctuations are coupled to the velocity fluctuations at the entrance of the combustion chamber by means of a nonlinear correlation. This correlation is a polynomial function in which each term is an odd-powered term. The corresponding bifurcation diagrams are tracked and the passive damper is designed in order to increase the stability zone, so reducing the risk to have an unstable condition. Then both plenum and combustion chamber are modeled with annular shape and the influence of Helmholtz resonators on the bifurcation is examined.
A three-dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic... more A three-dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic combustion instabilities modeled through the Helmholtz equation. A full annular combustion chamber, equipped with several burners, is examined. Spatial distributions for the heat release intensity and for the time delay are used for the linear flame model. Burners, connecting the plenum and the chamber, are modeled by means of the transfer matrix method. The influence of the parameters characterizing the burners and the flame on the stability levels of each mode of the system is investigated. The obtained results show the influence of the 3D distribution of the flame on the modes. Additionally, the results show what types of modes are most likely to yield humming in an annular combustion chamber. The proposed methodology is intended to be a practical tool for the interpretation of the thermoacoustic phenomenon (in terms of modes, frequencies, and stability maps) both in the design stage and in the check stage of gas turbine combustion chambers.
ASME Turbo Expo 2013, San Antonio, Texas, U.S.A., 3-7 June 2013
In the recent years a great interest has been devoted to the understanding of the nonlinear dynam... more In the recent years a great interest has been devoted to the understanding of the nonlinear dynamics characterizing the thermoacoustic combustion instabilities. Although linear techniques are able to predict whether the non-oscillating steady state of a thermoacoustic system is "asymptotically" stable (without oscillations) or unstable (increasing oscillations), a thermoacoustic system can reach a permanent oscillating state (the so called "limit cycle"), even when it is linearly stable, if a sufficiently large impulse occurs. A nonlinear analysis is able to predict the existence of this oscillating state and the nature of the bifurcation process.
The aim of this work is to investigate the behavior of gas turbine combustion chambers in presence of nonlinear flame models. The bifurcation diagrams, obtained by using a "continuation" technique in the frequency domain, give the amplitude of the oscillations as a function of a chosen flame parameter. The Helmholtz equation is used to model the combustion chamber and nonlinear terms are introduced in the flame model, starting from the classical k-tau formulation. A three-dimensional finite element method (FEM) is used for discretization of the computational domain and a solver of quadratic eigenvalue problems is combined with Newton technique in order to identify the points of the bifurcation diagram. First, a simple Rijke tube configuration, as can be found in the literature, is examined in order to obtain bifurcation diagrams. Then, the nonlinear analysis is extended to simplified annular configurations. The obtained results show how the nonlinear behavior is influenced by varying some control parameters, such as the time delay, yielding useful indications to designers and experimentalists.
Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dr... more Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dry low emission combustion systems. In the case of annular combustion chambers, experimental test cases carried out on small scale test rigs equipped with single burner arrangements fail to give adequate indications for the design of the full scale combustion chamber, since they are unable to reproduce the interaction of the flame fluctuation with the azimuthal pressure waves. Therefore there is a large interest in developing techniques able to make use of data gathered from tests carried out on a single burner for predicting the thermoacoustic behavior of the combustion chamber at full scale with its actual geometry. A hybrid technique based on the use of the finite elements method and the transfer matrix method is used to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability, under the hypothesis of linear behavior of the acoustic waves. This approach is able to model complex geometries such as annular combustion chambers equipped with several burners. Heat release fluctuations are modeled through a classical n-τ Flame Transfer Function (FTF). In order to model the acoustic behavior of the burners, the computational domain corresponding to each burner is substituted by a mathematical function, that is the Burner Transfer Matrix (BTM), that relates, one to each other, pressure and velocity oscillations at either sides of the burner. Both the FTF and the BTM can be obtained from experimental tests or from CFD simulations. The use of the transfer matrix permits us to take into account parameters, such as the flow velocity and the viscous losses, which are not directly included in the model. This paper describes the introduction of the burner transfer matrix in the combustion chamber model. Different geometries of combustion chamber and burner are tested. The influence of the parameters characterizing the transfer matrix is investigated. Finally the application of the BTM to an actual annular combustion chamber is shown.
Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dr... more Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dry low emission combustion systems. A hybrid technique based on the use of the finite elements method and the transfer matrix method is used to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability, under the hypothesis of linear behavior of the acoustic waves. The Helmholtz equation is used to model the combustion chamber and the classical n-τ formulation for the flame model is adopted. The gas turbine combustion chamber by Ansaldo Energia is modeled in COMSOL. Operating conditions are taken from experimental data and from Reynolds Averaged Navier Stokes (RANS) simulations of Ansaldo combustor. File data from RANS simulations are therefore imported into COMSOL. The proposed method is therefore able to establish a theoretical relation of the characteristics of the flame to the onset of the thermoacoustic instability.
A three dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic... more A three dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic combustion problem. A practical annular combustion chamber equipped with several burners is examined. Spatial distributions for the heat release intensity and for the time delay are used inside a linear flame model. Burners, connecting the plenum and the chamber, are modeled by means of the transfer matrix method. The influence of the parameters characterizing the burners and the flame on the stability levels of each mode of the system is investigated. The obtained results show the influence of the 3D distribution of the flame on the modes and that a unique value of the time delay not always provides a more conservative stability analysis. Additionally, the results show what types of modes are most likely to yield humming in an annular combustion chamber.
"Modern gas turbines equipped with lean premixed dry low emission combustion systems suffer the p... more "Modern gas turbines equipped with lean premixed dry low emission combustion systems suffer the problem of thermoacoustic combustion instability. The acoustic characteristics of the combustion chamber and of the burners, as well as the response of the flame to the fluctuations of pressure and equivalence ratio, exert a fundamental influence on the conditions in which the instability may occur. A three-dimensional finite element code has been developed in order to solve the Helmholtz equation with a source term that models the heat release fluctuations. The code is able to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability. The code is able to treat complex geometries such as annular combustion chambers equipped with more burners. The adopted acoustic model is based upon the definition of the Flame Response Function (FRF) to acoustic pressure and velocity fluctuations in the burners. %Usually, in order to define the FRF, both numerical and experimental techniques are based on the hypothesis of a compact flame sheet, with small dimensions if compared to those of the combustion chamber, whereas in industrial gas turbine combustion chamber the flame dimensions may be not negligible.
In this paper, data from CFD simulations are used to obtain a distribution of FRF of the k-tau type as a function of the position within the chamber. The intensity coefficient, k, is assumed to be proportional to the reaction rate of methane in a two-step mechanism. The time delay tau is estimated on the basis of the trajectories of the fuel particles from the injection point in the burner to the flame front.
The paper shows the results obtained from the application of FRF with spatial distributions of both k and tau. The present paper also shows the comparison between the application of the proposed model for the FRF and the traditional application of the FRF over a concentrated flame in a narrow area at the entrance to the combustion chamber. The distribution of the intensity coefficient and the time delay proves to have an influence, both on the eigenfrequency values and on the growth rates, in several of the examined modes. The proposed method is therefore able to establish a theoretical relation of the characteristics of the flame (depending on the burner geometry and operating conditions) to the onset of the thermoacoustic instability."
"Linear techniques can predict whether the non-oscillating (steady) state of a thermoacoustic sys... more "Linear techniques can predict whether the non-oscillating (steady) state of a thermoacoustic system is stable or unstable. With a sufficiently large impulse, however, a thermoacoustic system can reach a stable oscillating state even when the steady state is also stable. A nonlinear analysis is required to predict the existence of this oscillating state. Continuation methods are often used for this but they are computationally expensive.
In this paper, an acoustic network code called LOTAN is used to obtain the steady and the oscillating solutions for a horizontal Rijke tube. The heat release is modelled as a nonlinear function of the mass flow rate. Several test cases from the literature are analysed in order to investigate the effect of various nonlinear terms in the flame model. The results agree well with the literature, showing that LOTAN can be used to map the steady and oscillating solutions as a function of the control parameters.
Furthermore, the nature of the bifurcation between steady and oscillating states can be predicted directly from the nonlinear terms inside the flame model."
"This work is based on the study of the thermoacoustic combustion instability. A new methodology... more "This work is based on the study of the thermoacoustic combustion instability. A new methodology to investigate this kind of instability in the gas turbine combustion chamber is proposed. The basic idea is to define a series of actions able to proper model the combustion chamber as a three-dimensional geometry, modeling the flame to be as close as possible to the actual one by means of RANS fluid dynamic simulations. All these analyses are carried out using a commercial software, called COMSOL Multiphysics, based on the finite element methods: a user-friendly software and relatively fast in yielding the results. In the literature several models to examine the thermoacoustic instability phenomenon have been developed, but all of them show some limitations in the computational efforts or in the use of very simple geometries.
By means of this approach a tool able to take into account the different methodologies developed in the past is shown. This tool is thought to take the positive elements of each of the traditional methodologies and to try to overcome their limits with the advantages of other tools.
A great part of this work has been carried out through a collaboration with Ansaldo Energia, which provided the geometry of the combustion chamber of the AE94.3A machine and all the information concerning the boundary conditions and the operative conditions which were needed for developing the model. The part regarding the study of the non linear flame models has been carried out at the University of Cambridge under the guide of dr. Matthew Juniper and making use of the acoustic network code LOTAN, provided by Rolls Royce."
The purpose of this paper is to demonstrate the feasibility of an innovative project of multi-rol... more The purpose of this paper is to demonstrate the feasibility of an innovative project of multi-role fishing boat based on a SWATH catamaran architecture, high efficiency propellers and an innovative wind sail auxiliary propulsion by means of a wing mast completely automated. The global save in fuel consumption, in reference to a traditional fishing boat of a similar size, the “Serena”, reach the 90%, while the save in costs due to the only wing mast allows to repay the relative investment in less than 9 years
The study of thermoacoustic combustion instabilities has an important role for safety operation i... more The study of thermoacoustic combustion instabilities has an important role for safety operation in modern gas turbines equipped with lean premixed dry low emission combustion systems. Gas turbine manufacturers often adopt simulation tools based on low order models for predicting the phenomenon of humming. These simulation codes provide fast responses and good physical insight, but only one-dimensional or two-dimensional simplified schemes can be generally examined. Large Eddy Simulation (LES) techniques are proposed in order to investigate the instability phenomenon, matching pressure fluctuations with turbulent combustion phenomena to study thermoacoustic combustion oscillations, even if they require large numerical resources. The finite element method can overcome such limitations, because it allows to examine three dimensional geometries and to search the complex eigenfrequencies of the system.
The finite element approach solves numerically the differential equation problem converted in a complex eigenvalue problem in the frequency domain. Complex eigenvalues of the system allow us to identify the complex eigenfrequencies of the combustion system analyzed, so that we can have a valid indication of the frequencies at which thermoacoustic instabilities are expected and of the growth rate of the pressure oscillations at the onset of instability. Through the collaboration among Ansaldo Energia, Genoa University and Polytechnic University of Bari, a quantitative comparison between a low order model, called LOMTI, and the three-dimensional finite element method has been created, in order to exploit the advantages of both the methodologies.
A method for predicting the onset of acoustically driven combustion instabilities in gas turbine ... more A method for predicting the onset of acoustically driven combustion instabilities in gas turbine combustor is examined. The basic idea is that the governing equations of the acoustic waves can be coupled with a flame heat release model and solved in the frequency domain. The paper shows that a complex eigenvalue problem is obtained that can be solved numerically by implementing the governing equations in a finite element code. This procedure allows one to identify the frequencies at which thermo-acoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behavior of the acoustic waves can be applied. The method can be applied virtually to any three-dimensional geometry, provided the necessary computational resources that are, anyway, much less than those required by computational fluid dynamics methods proposed for analyzing the combustion chamber under instability condition. Furthermore, in comparison with the “lumped” approach that characterizes popular acoustics networks, the proposed method allows one for much more flexibility in defining the geometry of the combustion chamber. The paper shows that different types of heat release laws, for instance, heat release concentrated in a flame sheet, as well as distributed in a larger domain, can be adopted. Moreover, experimentally or numerically determined flame transfer functions, giving the response of heat release to acoustic velocity fluctuations, can be incorporated in the model. To establish proof of concept, the method is validated at the beginning against simple test cases taken from literature. Over the frequency range considered, frequencies and growth rates both of stable and unstable eigenmodes are accurately evaluated. Then the method is applied to a much more complex annular combustor geometry in order to evaluate frequencies and growth rates of the unstable modes and to show how the variation in the parameters of the heat release law can influence the transition to instability.
Recently, because of environmental regulations, gas turbine manufacturers are restricted to produ... more Recently, because of environmental regulations, gas turbine manufacturers are restricted to produce machines that work in the lean combustion regime. Gas turbines operating in this regime are prone to combustion-driven acoustic oscillations referred as combustion instabilities. These oscillations could have such high amplitude that they can damage gas turbine hardware. In this study, the three-step approach for combustion instabilities prediction is applied to an industrial test rig. As the first step, the flame transfer function (FTF) of the burner is obtained performing unsteady computational fluid dynamics (CFD) simulations. As the second step, the obtained FTF is approximated with an analytical time-lag-distributed model. The third step is the time-domain simulations using a network model. The obtained results are compared against the experimental data. The obtained results show a good agreement with the experimental ones and the developed approach is able to predict thermoacoustic instabilities in gas turbines combustion chambers.
Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion-dr... more Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion-driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damage of combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. We have developed a two-step method to find a set of operating parameters under which gas turbines can be operated without going into self-excited pressure oscillations. As the first step, an unsteady Reynolds-averaged Navier–Stokes simulation with the flame speed closure model implemented in the OpenFOAM Õ environment is performed to obtain the flame transfer function of the combustion setup. As the second step time-domain simulations employing low-order network model implemented in Simulink Õ are executed. In this work, we apply the proposed method to the Beschaufelter RingSpalt test rig developed at the Technische Universität München. The sensitivity of thermoacoustic stability to the length of a combustion chamber, flame position, gain and phase of flame transfer function and outlet reflection coefficient are studied.
A method for predicting the onset of acoustically driven combustion instabilities in gas turbine ... more A method for predicting the onset of acoustically driven combustion instabilities in gas turbine combustor is examined. The basic idea is that the governing equations of the acoustic waves can be coupled with a flame heat release model and solved in the frequency domain. The paper shows that a complex eigenvalue problem is obtained that can be solved numerically by implementing the governing equations in a finite element code. This procedure allows one to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behaviour of the acoustic waves can be applied.
The method can be applied virtually to any three dimensional geometry, provided the necessary computational resources that are, anyway, much less than those required by Computational Fluid Dynamics (CFD) methods proposed for analysing the combustion chamber under instability condition. Furthermore, in comparison with the “lumped” approach that characterize popular Acoustics Networks, the proposed method allows one for much more flexibility in defining the geometry of the combustion chamber.
The paper shows that different types of heat release laws, for instance, heat release concentrated in a flame sheet as well as distributed in a larger domain, can be adopted. Moreover, experimentally or numerically determined flame transfer functions, giving the response of heat release to acoustic velocity fluctuations, can be incorporated in the model.
To establish proof of concept, the method is validated at the beginning against simple test cases taken from literature. Over the frequency range considered, frequencies and growth rates both of stable and unstable eigenmodes are accurately evaluated. Then the method is applied to a much more complex annular combustor geometry in order to evaluate frequencies and growth rates of the unstable modes and to show how the variation of the parameters of the heat release law can influence the transition to instability
Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dr... more Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dry low emission combustion systems. In the case of annular combustion chambers, experimental test cases carried out on small scale test rigs equipped with single burner arrangements fail to give adequate indications for the design of the full scale combustion chamber, since they are unable to reproduce the interaction of the flame fluctuation with the azimuthal pressure waves. Therefore there is a large interest in developing techniques able to make use of data gathered from tests carried out on a single burner for predicting the thermoacoustic behavior of the combustion chamber at full scale with its actual geometry. A hybrid technique based on the use of the finite elements method and the transfer matrix method is used to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability, under the hypothesis of linear behavior of the acoustic waves. This approach is able to model complex geometries such as annular combustion chambers equipped with several burners. Heat release fluctuations are modeled through a classical n-τ Flame Transfer Function (FTF). In order to model the acoustic behavior of the burners, the computational domain corresponding to each burner is substituted by a mathematical function, that is the Burner Transfer Matrix (BTM), that relates, one to each other, pressure and velocity oscillations at either sides of the burner. Both the FTF and the BTM can be obtained from experimental tests or from CFD simulations. The use of the transfer matrix permits us to take into account parameters, such as the flow velocity and the viscous losses, which are not directly included in the model. This paper describes the introduction of the burner transfer matrix in the combustion chamber model. Different geometries of combustion chamber and burner are tested. The influence of the parameters characterizing the transfer matrix is investigated. Finally the application of the BTM to an actual annular combustion chamber is shown.
Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place i... more Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of nonnormality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
A LIMIT CYCLE FOR PRESSURE OSCILLATIONS IN A GAS TURBINE BURNER, Jul 13, 2014
Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place i... more Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
This paper shows a novel method for predicting the onset of acoustically driven combustion instab... more This paper shows a novel method for predicting the onset of acoustically driven combustion instabilities in gas turbine combustors. The basic idea is that the governing equations of the acoustic waves can be coupled with a flame heat release model and solved in the frequency domain. The paper shows that a complex eigenvalue problem is obtained that can be solved numerically by implementing the governing equations in the “Acoustic” module of COMSOL Multiphysics. The procedure allows one to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behaviour of the acoustic waves can be applied.
ASME Turbo Expo 2014, Düsseldorf, Germany, 16-20 June 2014
The influence of the introduction of a Helmholtz resonator as a passive damper in a gas turbine c... more The influence of the introduction of a Helmholtz resonator as a passive damper in a gas turbine combustion chamber on the bifurcation mechanism that characterizes the transition to instability is investigated. Bifurcation diagrams are tracked in order to identify the conditions for which the machine works in a stable zone and which are the operative parameters that bring the machine to unstable conditions. This work shows that a properly designed passive damper system increases the stable zone, moving the unstable zone and the bistable zone (in the case of a subcritical bifurcation) to higher values of the operative parameters, while have a limited influence on the amplitude of limit cycle. In order to examine the effect of the damper, a gas turbine combustion chamber is first modeled as a simple cylindrical duct, where the flame is concentrated in a narrow area at around one quarter of the duct. Heat release fluctuations are coupled to the velocity fluctuations at the entrance of the combustion chamber by means of a nonlinear correlation. This correlation is a polynomial function in which each term is an odd-powered term. The corresponding bifurcation diagrams are tracked and the passive damper is designed in order to increase the stability zone, so reducing the risk to have an unstable condition. Then both plenum and combustion chamber are modeled with annular shape and the influence of Helmholtz resonators on the bifurcation is examined.
A three-dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic... more A three-dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic combustion instabilities modeled through the Helmholtz equation. A full annular combustion chamber, equipped with several burners, is examined. Spatial distributions for the heat release intensity and for the time delay are used for the linear flame model. Burners, connecting the plenum and the chamber, are modeled by means of the transfer matrix method. The influence of the parameters characterizing the burners and the flame on the stability levels of each mode of the system is investigated. The obtained results show the influence of the 3D distribution of the flame on the modes. Additionally, the results show what types of modes are most likely to yield humming in an annular combustion chamber. The proposed methodology is intended to be a practical tool for the interpretation of the thermoacoustic phenomenon (in terms of modes, frequencies, and stability maps) both in the design stage and in the check stage of gas turbine combustion chambers.
ASME Turbo Expo 2013, San Antonio, Texas, U.S.A., 3-7 June 2013
In the recent years a great interest has been devoted to the understanding of the nonlinear dynam... more In the recent years a great interest has been devoted to the understanding of the nonlinear dynamics characterizing the thermoacoustic combustion instabilities. Although linear techniques are able to predict whether the non-oscillating steady state of a thermoacoustic system is "asymptotically" stable (without oscillations) or unstable (increasing oscillations), a thermoacoustic system can reach a permanent oscillating state (the so called "limit cycle"), even when it is linearly stable, if a sufficiently large impulse occurs. A nonlinear analysis is able to predict the existence of this oscillating state and the nature of the bifurcation process.
The aim of this work is to investigate the behavior of gas turbine combustion chambers in presence of nonlinear flame models. The bifurcation diagrams, obtained by using a "continuation" technique in the frequency domain, give the amplitude of the oscillations as a function of a chosen flame parameter. The Helmholtz equation is used to model the combustion chamber and nonlinear terms are introduced in the flame model, starting from the classical k-tau formulation. A three-dimensional finite element method (FEM) is used for discretization of the computational domain and a solver of quadratic eigenvalue problems is combined with Newton technique in order to identify the points of the bifurcation diagram. First, a simple Rijke tube configuration, as can be found in the literature, is examined in order to obtain bifurcation diagrams. Then, the nonlinear analysis is extended to simplified annular configurations. The obtained results show how the nonlinear behavior is influenced by varying some control parameters, such as the time delay, yielding useful indications to designers and experimentalists.
Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dr... more Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dry low emission combustion systems. In the case of annular combustion chambers, experimental test cases carried out on small scale test rigs equipped with single burner arrangements fail to give adequate indications for the design of the full scale combustion chamber, since they are unable to reproduce the interaction of the flame fluctuation with the azimuthal pressure waves. Therefore there is a large interest in developing techniques able to make use of data gathered from tests carried out on a single burner for predicting the thermoacoustic behavior of the combustion chamber at full scale with its actual geometry. A hybrid technique based on the use of the finite elements method and the transfer matrix method is used to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability, under the hypothesis of linear behavior of the acoustic waves. This approach is able to model complex geometries such as annular combustion chambers equipped with several burners. Heat release fluctuations are modeled through a classical n-τ Flame Transfer Function (FTF). In order to model the acoustic behavior of the burners, the computational domain corresponding to each burner is substituted by a mathematical function, that is the Burner Transfer Matrix (BTM), that relates, one to each other, pressure and velocity oscillations at either sides of the burner. Both the FTF and the BTM can be obtained from experimental tests or from CFD simulations. The use of the transfer matrix permits us to take into account parameters, such as the flow velocity and the viscous losses, which are not directly included in the model. This paper describes the introduction of the burner transfer matrix in the combustion chamber model. Different geometries of combustion chamber and burner are tested. The influence of the parameters characterizing the transfer matrix is investigated. Finally the application of the BTM to an actual annular combustion chamber is shown.
Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dr... more Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dry low emission combustion systems. A hybrid technique based on the use of the finite elements method and the transfer matrix method is used to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability, under the hypothesis of linear behavior of the acoustic waves. The Helmholtz equation is used to model the combustion chamber and the classical n-τ formulation for the flame model is adopted. The gas turbine combustion chamber by Ansaldo Energia is modeled in COMSOL. Operating conditions are taken from experimental data and from Reynolds Averaged Navier Stokes (RANS) simulations of Ansaldo combustor. File data from RANS simulations are therefore imported into COMSOL. The proposed method is therefore able to establish a theoretical relation of the characteristics of the flame to the onset of the thermoacoustic instability.
A three dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic... more A three dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic combustion problem. A practical annular combustion chamber equipped with several burners is examined. Spatial distributions for the heat release intensity and for the time delay are used inside a linear flame model. Burners, connecting the plenum and the chamber, are modeled by means of the transfer matrix method. The influence of the parameters characterizing the burners and the flame on the stability levels of each mode of the system is investigated. The obtained results show the influence of the 3D distribution of the flame on the modes and that a unique value of the time delay not always provides a more conservative stability analysis. Additionally, the results show what types of modes are most likely to yield humming in an annular combustion chamber.
"Modern gas turbines equipped with lean premixed dry low emission combustion systems suffer the p... more "Modern gas turbines equipped with lean premixed dry low emission combustion systems suffer the problem of thermoacoustic combustion instability. The acoustic characteristics of the combustion chamber and of the burners, as well as the response of the flame to the fluctuations of pressure and equivalence ratio, exert a fundamental influence on the conditions in which the instability may occur. A three-dimensional finite element code has been developed in order to solve the Helmholtz equation with a source term that models the heat release fluctuations. The code is able to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability. The code is able to treat complex geometries such as annular combustion chambers equipped with more burners. The adopted acoustic model is based upon the definition of the Flame Response Function (FRF) to acoustic pressure and velocity fluctuations in the burners. %Usually, in order to define the FRF, both numerical and experimental techniques are based on the hypothesis of a compact flame sheet, with small dimensions if compared to those of the combustion chamber, whereas in industrial gas turbine combustion chamber the flame dimensions may be not negligible.
In this paper, data from CFD simulations are used to obtain a distribution of FRF of the k-tau type as a function of the position within the chamber. The intensity coefficient, k, is assumed to be proportional to the reaction rate of methane in a two-step mechanism. The time delay tau is estimated on the basis of the trajectories of the fuel particles from the injection point in the burner to the flame front.
The paper shows the results obtained from the application of FRF with spatial distributions of both k and tau. The present paper also shows the comparison between the application of the proposed model for the FRF and the traditional application of the FRF over a concentrated flame in a narrow area at the entrance to the combustion chamber. The distribution of the intensity coefficient and the time delay proves to have an influence, both on the eigenfrequency values and on the growth rates, in several of the examined modes. The proposed method is therefore able to establish a theoretical relation of the characteristics of the flame (depending on the burner geometry and operating conditions) to the onset of the thermoacoustic instability."
"Linear techniques can predict whether the non-oscillating (steady) state of a thermoacoustic sys... more "Linear techniques can predict whether the non-oscillating (steady) state of a thermoacoustic system is stable or unstable. With a sufficiently large impulse, however, a thermoacoustic system can reach a stable oscillating state even when the steady state is also stable. A nonlinear analysis is required to predict the existence of this oscillating state. Continuation methods are often used for this but they are computationally expensive.
In this paper, an acoustic network code called LOTAN is used to obtain the steady and the oscillating solutions for a horizontal Rijke tube. The heat release is modelled as a nonlinear function of the mass flow rate. Several test cases from the literature are analysed in order to investigate the effect of various nonlinear terms in the flame model. The results agree well with the literature, showing that LOTAN can be used to map the steady and oscillating solutions as a function of the control parameters.
Furthermore, the nature of the bifurcation between steady and oscillating states can be predicted directly from the nonlinear terms inside the flame model."
"This work is based on the study of the thermoacoustic combustion instability. A new methodology... more "This work is based on the study of the thermoacoustic combustion instability. A new methodology to investigate this kind of instability in the gas turbine combustion chamber is proposed. The basic idea is to define a series of actions able to proper model the combustion chamber as a three-dimensional geometry, modeling the flame to be as close as possible to the actual one by means of RANS fluid dynamic simulations. All these analyses are carried out using a commercial software, called COMSOL Multiphysics, based on the finite element methods: a user-friendly software and relatively fast in yielding the results. In the literature several models to examine the thermoacoustic instability phenomenon have been developed, but all of them show some limitations in the computational efforts or in the use of very simple geometries.
By means of this approach a tool able to take into account the different methodologies developed in the past is shown. This tool is thought to take the positive elements of each of the traditional methodologies and to try to overcome their limits with the advantages of other tools.
A great part of this work has been carried out through a collaboration with Ansaldo Energia, which provided the geometry of the combustion chamber of the AE94.3A machine and all the information concerning the boundary conditions and the operative conditions which were needed for developing the model. The part regarding the study of the non linear flame models has been carried out at the University of Cambridge under the guide of dr. Matthew Juniper and making use of the acoustic network code LOTAN, provided by Rolls Royce."
The purpose of this paper is to demonstrate the feasibility of an innovative project of multi-rol... more The purpose of this paper is to demonstrate the feasibility of an innovative project of multi-role fishing boat based on a SWATH catamaran architecture, high efficiency propellers and an innovative wind sail auxiliary propulsion by means of a wing mast completely automated. The global save in fuel consumption, in reference to a traditional fishing boat of a similar size, the “Serena”, reach the 90%, while the save in costs due to the only wing mast allows to repay the relative investment in less than 9 years
The study of thermoacoustic combustion instabilities has an important role for safety operation i... more The study of thermoacoustic combustion instabilities has an important role for safety operation in modern gas turbines equipped with lean premixed dry low emission combustion systems. Gas turbine manufacturers often adopt simulation tools based on low order models for predicting the phenomenon of humming. These simulation codes provide fast responses and good physical insight, but only one-dimensional or two-dimensional simplified schemes can be generally examined. Large Eddy Simulation (LES) techniques are proposed in order to investigate the instability phenomenon, matching pressure fluctuations with turbulent combustion phenomena to study thermoacoustic combustion oscillations, even if they require large numerical resources. The finite element method can overcome such limitations, because it allows to examine three dimensional geometries and to search the complex eigenfrequencies of the system.
The finite element approach solves numerically the differential equation problem converted in a complex eigenvalue problem in the frequency domain. Complex eigenvalues of the system allow us to identify the complex eigenfrequencies of the combustion system analyzed, so that we can have a valid indication of the frequencies at which thermoacoustic instabilities are expected and of the growth rate of the pressure oscillations at the onset of instability. Through the collaboration among Ansaldo Energia, Genoa University and Polytechnic University of Bari, a quantitative comparison between a low order model, called LOMTI, and the three-dimensional finite element method has been created, in order to exploit the advantages of both the methodologies.
A method for predicting the onset of acoustically driven combustion instabilities in gas turbine ... more A method for predicting the onset of acoustically driven combustion instabilities in gas turbine combustor is examined. The basic idea is that the governing equations of the acoustic waves can be coupled with a flame heat release model and solved in the frequency domain. The paper shows that a complex eigenvalue problem is obtained that can be solved numerically by implementing the governing equations in a finite element code. This procedure allows one to identify the frequencies at which thermo-acoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behavior of the acoustic waves can be applied. The method can be applied virtually to any three-dimensional geometry, provided the necessary computational resources that are, anyway, much less than those required by computational fluid dynamics methods proposed for analyzing the combustion chamber under instability condition. Furthermore, in comparison with the “lumped” approach that characterizes popular acoustics networks, the proposed method allows one for much more flexibility in defining the geometry of the combustion chamber. The paper shows that different types of heat release laws, for instance, heat release concentrated in a flame sheet, as well as distributed in a larger domain, can be adopted. Moreover, experimentally or numerically determined flame transfer functions, giving the response of heat release to acoustic velocity fluctuations, can be incorporated in the model. To establish proof of concept, the method is validated at the beginning against simple test cases taken from literature. Over the frequency range considered, frequencies and growth rates both of stable and unstable eigenmodes are accurately evaluated. Then the method is applied to a much more complex annular combustor geometry in order to evaluate frequencies and growth rates of the unstable modes and to show how the variation in the parameters of the heat release law can influence the transition to instability.
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Papers by Giovanni Campa
hardware. In this study, the three-step approach for combustion instabilities prediction is applied to an industrial test rig. As the first step, the flame transfer function (FTF) of the burner is obtained performing unsteady computational fluid dynamics (CFD) simulations. As the second step, the obtained FTF is
approximated with an analytical time-lag-distributed model. The third step is the time-domain simulations using a network model. The obtained results are compared against the experimental data. The obtained results show a good agreement with the experimental ones and the developed approach is able to predict thermoacoustic instabilities in gas turbines combustion
chambers.
The method can be applied virtually to any three dimensional geometry, provided the necessary computational resources that are, anyway, much less than those required by Computational Fluid Dynamics (CFD) methods proposed for analysing the combustion chamber under instability condition. Furthermore, in comparison with the “lumped” approach that characterize popular Acoustics Networks, the proposed method allows one for much more flexibility in defining the geometry of the combustion chamber.
The paper shows that different types of heat release laws, for instance, heat release concentrated in a flame sheet as well as distributed in a larger domain, can be adopted. Moreover, experimentally or numerically determined flame transfer functions, giving the response of heat release to acoustic velocity fluctuations, can be incorporated in the model.
To establish proof of concept, the method is validated at the beginning against simple test cases taken from literature. Over the frequency range considered, frequencies and growth rates both of stable and unstable eigenmodes are accurately evaluated. Then the method is applied to a much more complex annular combustor geometry in order to evaluate frequencies and growth rates of the unstable modes and to show how the variation of the parameters of the heat release law can influence the transition to instability
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of nonnormality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
the “Acoustic” module of COMSOL Multiphysics. The procedure allows one to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behaviour of the acoustic waves can be applied.
The aim of this work is to investigate the behavior of gas turbine combustion chambers in presence of nonlinear flame models. The bifurcation diagrams, obtained by using a "continuation" technique in the frequency domain, give the amplitude of the oscillations as a function of a chosen flame parameter. The Helmholtz equation is used to model the combustion chamber and nonlinear terms are introduced in the flame model, starting from the classical k-tau formulation. A three-dimensional finite element method (FEM) is used for discretization of the computational domain and a solver of quadratic eigenvalue problems is combined with Newton technique in order to identify the points of the bifurcation diagram. First, a simple Rijke tube configuration, as can be found in the literature, is examined in order to obtain bifurcation diagrams. Then, the nonlinear analysis is extended to simplified annular configurations. The obtained results show how the nonlinear behavior is influenced by varying some control parameters, such as the time delay, yielding useful indications to designers and experimentalists.
In this paper, data from CFD simulations are used to obtain a distribution of FRF of the k-tau type as a function of the position within the chamber. The intensity coefficient, k, is assumed to be proportional to the reaction rate of methane in a two-step mechanism. The time delay tau is estimated on the basis of the trajectories of the fuel particles from the injection point in the burner to the flame front.
The paper shows the results obtained from the application of FRF with spatial distributions of both k and tau. The present paper also shows the comparison between the application of the proposed model for the FRF and the traditional application of the FRF over a concentrated flame in a narrow area at the entrance to the combustion chamber. The distribution of the intensity coefficient and the time delay proves to have an influence, both on the eigenfrequency values and on the growth rates, in several of the examined modes. The proposed method is therefore able to establish a theoretical relation of the characteristics of the flame (depending on the burner geometry and operating conditions) to the onset of the thermoacoustic instability."
In this paper, an acoustic network code called LOTAN is used to obtain the steady and the oscillating solutions for a horizontal Rijke tube. The heat release is modelled as a nonlinear function of the mass flow rate. Several test cases from the literature are analysed in order to investigate the effect of various nonlinear terms in the flame model. The results agree well with the literature, showing that LOTAN can be used to map the steady and oscillating solutions as a function of the control parameters.
Furthermore, the nature of the bifurcation between steady and oscillating states can be predicted directly from the nonlinear terms inside the flame model."
By means of this approach a tool able to take into account the different methodologies developed in the past is shown. This tool is thought to take the positive elements of each of the traditional methodologies and to try to overcome their limits with the advantages of other tools.
A great part of this work has been carried out through a collaboration with Ansaldo Energia, which provided the geometry of the combustion chamber of the AE94.3A machine and all the information concerning the boundary conditions and the operative conditions which were needed for developing the model. The part regarding the study of the non linear flame models has been carried out at the University of Cambridge under the guide of dr. Matthew Juniper and making use of the acoustic network code LOTAN, provided by Rolls Royce."
and good physical insight, but only one-dimensional or two-dimensional simplified schemes can be generally examined. Large Eddy Simulation (LES) techniques are proposed in order to investigate the instability phenomenon, matching pressure fluctuations with turbulent combustion phenomena to study thermoacoustic combustion oscillations, even if they require large numerical resources. The finite element method can overcome such limitations, because it allows to examine three dimensional geometries and to search the complex eigenfrequencies of the system.
The finite element approach solves numerically the differential equation problem converted in a complex eigenvalue problem
in the frequency domain. Complex eigenvalues of the system allow us to identify the complex eigenfrequencies of the combustion system analyzed, so that we can have a valid indication of the frequencies at which thermoacoustic instabilities are expected and of the growth rate of the pressure oscillations at the onset of instability. Through the collaboration among Ansaldo Energia, Genoa University and Polytechnic University of Bari, a quantitative comparison between a low order model, called LOMTI, and the three-dimensional finite element method has been created, in order to exploit the advantages of both the methodologies.
hardware. In this study, the three-step approach for combustion instabilities prediction is applied to an industrial test rig. As the first step, the flame transfer function (FTF) of the burner is obtained performing unsteady computational fluid dynamics (CFD) simulations. As the second step, the obtained FTF is
approximated with an analytical time-lag-distributed model. The third step is the time-domain simulations using a network model. The obtained results are compared against the experimental data. The obtained results show a good agreement with the experimental ones and the developed approach is able to predict thermoacoustic instabilities in gas turbines combustion
chambers.
The method can be applied virtually to any three dimensional geometry, provided the necessary computational resources that are, anyway, much less than those required by Computational Fluid Dynamics (CFD) methods proposed for analysing the combustion chamber under instability condition. Furthermore, in comparison with the “lumped” approach that characterize popular Acoustics Networks, the proposed method allows one for much more flexibility in defining the geometry of the combustion chamber.
The paper shows that different types of heat release laws, for instance, heat release concentrated in a flame sheet as well as distributed in a larger domain, can be adopted. Moreover, experimentally or numerically determined flame transfer functions, giving the response of heat release to acoustic velocity fluctuations, can be incorporated in the model.
To establish proof of concept, the method is validated at the beginning against simple test cases taken from literature. Over the frequency range considered, frequencies and growth rates both of stable and unstable eigenmodes are accurately evaluated. Then the method is applied to a much more complex annular combustor geometry in order to evaluate frequencies and growth rates of the unstable modes and to show how the variation of the parameters of the heat release law can influence the transition to instability
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of nonnormality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
the “Acoustic” module of COMSOL Multiphysics. The procedure allows one to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behaviour of the acoustic waves can be applied.
The aim of this work is to investigate the behavior of gas turbine combustion chambers in presence of nonlinear flame models. The bifurcation diagrams, obtained by using a "continuation" technique in the frequency domain, give the amplitude of the oscillations as a function of a chosen flame parameter. The Helmholtz equation is used to model the combustion chamber and nonlinear terms are introduced in the flame model, starting from the classical k-tau formulation. A three-dimensional finite element method (FEM) is used for discretization of the computational domain and a solver of quadratic eigenvalue problems is combined with Newton technique in order to identify the points of the bifurcation diagram. First, a simple Rijke tube configuration, as can be found in the literature, is examined in order to obtain bifurcation diagrams. Then, the nonlinear analysis is extended to simplified annular configurations. The obtained results show how the nonlinear behavior is influenced by varying some control parameters, such as the time delay, yielding useful indications to designers and experimentalists.
In this paper, data from CFD simulations are used to obtain a distribution of FRF of the k-tau type as a function of the position within the chamber. The intensity coefficient, k, is assumed to be proportional to the reaction rate of methane in a two-step mechanism. The time delay tau is estimated on the basis of the trajectories of the fuel particles from the injection point in the burner to the flame front.
The paper shows the results obtained from the application of FRF with spatial distributions of both k and tau. The present paper also shows the comparison between the application of the proposed model for the FRF and the traditional application of the FRF over a concentrated flame in a narrow area at the entrance to the combustion chamber. The distribution of the intensity coefficient and the time delay proves to have an influence, both on the eigenfrequency values and on the growth rates, in several of the examined modes. The proposed method is therefore able to establish a theoretical relation of the characteristics of the flame (depending on the burner geometry and operating conditions) to the onset of the thermoacoustic instability."
In this paper, an acoustic network code called LOTAN is used to obtain the steady and the oscillating solutions for a horizontal Rijke tube. The heat release is modelled as a nonlinear function of the mass flow rate. Several test cases from the literature are analysed in order to investigate the effect of various nonlinear terms in the flame model. The results agree well with the literature, showing that LOTAN can be used to map the steady and oscillating solutions as a function of the control parameters.
Furthermore, the nature of the bifurcation between steady and oscillating states can be predicted directly from the nonlinear terms inside the flame model."
By means of this approach a tool able to take into account the different methodologies developed in the past is shown. This tool is thought to take the positive elements of each of the traditional methodologies and to try to overcome their limits with the advantages of other tools.
A great part of this work has been carried out through a collaboration with Ansaldo Energia, which provided the geometry of the combustion chamber of the AE94.3A machine and all the information concerning the boundary conditions and the operative conditions which were needed for developing the model. The part regarding the study of the non linear flame models has been carried out at the University of Cambridge under the guide of dr. Matthew Juniper and making use of the acoustic network code LOTAN, provided by Rolls Royce."
and good physical insight, but only one-dimensional or two-dimensional simplified schemes can be generally examined. Large Eddy Simulation (LES) techniques are proposed in order to investigate the instability phenomenon, matching pressure fluctuations with turbulent combustion phenomena to study thermoacoustic combustion oscillations, even if they require large numerical resources. The finite element method can overcome such limitations, because it allows to examine three dimensional geometries and to search the complex eigenfrequencies of the system.
The finite element approach solves numerically the differential equation problem converted in a complex eigenvalue problem
in the frequency domain. Complex eigenvalues of the system allow us to identify the complex eigenfrequencies of the combustion system analyzed, so that we can have a valid indication of the frequencies at which thermoacoustic instabilities are expected and of the growth rate of the pressure oscillations at the onset of instability. Through the collaboration among Ansaldo Energia, Genoa University and Polytechnic University of Bari, a quantitative comparison between a low order model, called LOMTI, and the three-dimensional finite element method has been created, in order to exploit the advantages of both the methodologies.