This thesis describes an experimental investigation of the flame transfer function between flow disturbances and heat release oscillations in lean, premixed combustors. This research effort was motivated by the fact that modern gas turbines, operating fuel-lean to minimize exhaust emissions, are susceptible to self-excited combustion oscillations. These instabilities generally occur when the unsteady combustion process couples with the acoustic modes of the combustion chamber. The resultant flow and structural vibrations can substantially reduce hot section part life. As such, avoiding operating regimes where high dynamics occur often requires operating at lower power outputs and/or higher pollutant emissions than the turbine is otherwise capable. This work demonstrated nonlinearities in the chemiluminescence response at large amplitude velocity oscillations in a turbulent, swirling flame. It is observed that the nonlinear flame response can exhibit a variety of behaviors, both in the shape of the response curve and the forcing amplitude at which nonlinearity is first observed depending on the operating conditions of the combustor. The phase between the flow oscillations and heat release is also seen to have substantial amplitude dependence. In addition, the interactions between the fundamental frequency and the higher and subharmonics of the measured signals can significantly influence the flame as well as the frequency response of the system. The nonlinear flame dynamics are governed by different mechanisms in different frequency and flowrate regimes. Three mechanisms, vortex rollup, unsteady flame liftoff, and parametric instability, are identified to influence the nonlinear flame response in these combustors. Analysis of the results shows that the mechanisms responsible for nonlinearity in the flame response are influenced by the Strouhal number, the mean velocity at the combustor dump plane, and the ratio of the oscillating velocity amplitude to the laminar flame speed.

LLean premixed combustion systems, attractive for low NOx performance, are inherently susceptible to thermo-acoustic instabilities - the interaction between unsteady heat release and excited acoustic wave effects. In the present work, a hybrid, coupled Large Eddy Simulation (LES) CFD approach is described, combining the computational efficiency of incompressible reacting LES with acoustic wave effects captured via an acoustic network model. A flamelet approach with an algebraic Flame Surface Density (FSD) combustion model was used. The ORACLES experiments - a perfectly premixed flame stabilised in a 3D sudden expansion - are used for validation. Simulations of the inert flow agree very well with experimental data, reproducing the measured amplitude and distribution of turbulent fluctuations as well as capturing the asymmetric mean flow. With reaction the measured data exhibit a plane wave acoustic mode at 50Hz. The influence of this plane wave must be incorporated into the LES calculation. Thus, a new approach to sensitise the incompressible LES CFD to acoustic waves is adopted. First an acoustic network model of the experimental geometry is analysed to predict the amplitude of the 50Hz mode just before the flame zone. This is then used to introduce a coherent plane wave at the LES inlet plane at the appropriate amplitude, unlike previous LES studies, which have adopted a "guess and adjust" approach. Incompressible LES predictions of this forced flow then show good agreement with measurements of mean and turbulent velocity, as well as for flame shape, with a considerable improvement relative to unforced simulations. To capitalise on the unsteady flame dynamics provided by LES, simulations with varying forcing amplitude were conducted and analysed. Amplitude dependent Flame Transfer Functions (FTFs) were extracted and fed into an acoustic network model. This allowed prediction of the stable/unstable nature of the flame at each forcing amplitude. An amplitude at which the flame changed from unstable to stable would be an indication that this coupled approach was capable of predicting a limit cycle behaviour. With the current simple FSD combustion model almost all cases studied showed a stable flame. Predictions showed considerable sensitivity to the value chosen for the combustion model parameter but specially to the acoustic geometric configuration and boundary conditions assumed showing evidence of limit cycle behaviour for some combinations. Nevertheless, further work is required to improve both combustion model and the accuracy of acoustic configuration and boundary condition specification.

Ce travail traite de la dynamique des flammes turbulentes prémélangées confinées et swirlées soumises à des perturbations de vitesses acoustiques. L'objectif général est d'acquérir une compréhension des mécanismes régissant la réponse de ces flammes et d'en tirer des méthodes de prévision des instabilités de combustion. Les écoulements swirlés sont d'abord examinés en termes de nombre de swirl et de nouvelles expressions sont données pour cette quantité. On traite notamment des effets de perturbations de vitesse et une expression est proposée qui tient compte des fluctuations de vitesses dans l'écoulement. Le système utilisé pour l'étude expérimentale comprend une cavité amont, un injecteur équipé d'un swirler et un tube à flamme transparent permettant la visualisation directe du mouvement de la flamme. Deux points de fonctionnement sont étudiés correspondant à des vitesses débitantes différentes. La cavité amont et le tube à flamme du brûleur peuvent être facilement changés pour étudier plusieurs configurations différentes. L'acoustique du brûleur est également analysée au moyen d'une approche de cavités couplées pour déterminer les fréquences de résonance du système en configuration non-réactive. Des expériences sont menées pour mesurer les fréquences propres du système et l'estimation du coefficient d'amortissement est réalisée à partir de la réponse du système à une modulation externe. Un critère de découplage des mode acoustiques est proposé. La dynamique de l'écoulement est examinée en termes de conversion de modes au niveau de la vrille (swirler) ou dans une grille d'aubes. Cette partie du travail, effectuée au moyen de simulations numériques montre que lorsqu'une grille ou une vrille sont soumis à une onde acoustique, le swirler donne naissance à une onde azimutale convective en plus de l'onde acoustique axiale transmise. Les deux types de swirlers, axial et radial, donnent lieu à ce mécanisme, un fait confirmé par des expériences. Il est montré que ce processus de conversion de mode a un impact important sur la dynamique de la flamme swirlée. La dynamique de la combustion est ensuite analysée en mesurant la fonction de transfert généralisée ainsi que les distributions de taux de dégagement de chaleur au cours du cycle d'oscillation. La fonction de transfert est utilisée pour déterminer la réponse de la flamme à des perturbations acoustiques se propageant dans l'écoulement en amont de la flamme. Il est aussi montré que le nombre de Strouhal est un groupe sans dimensions qui permet de caractériser la réponse de la flamme. La dynamique est également analysée au moyen d'un ensemble de diagnostics comprenant des sondes de pression, un photomultiplicateur et un vélocimètre laser Doppler. Un modèle pour la fonction de transfert linéaire de la flamme est dérivé théoriquement à partir d'une description de la flamme au moyen de l'équation pour une variable de champ G. Les mécanismes physiques de la réponse de la flamme sont identifiés : enroulement tourbillonnaire et fluctuations du nombre de swirl. L'enroulement tourbillonnaire est associé à l'onde acoustique transmise en aval du swirler et qui pénètre dans la chambre de combustion. Tandis que les fluctuations du nombre de swirl sont directement liées aux mécanismes de conversion de mode au swirler qui induit différentes vitesses pour les perturbations axiales et azimutales. L'enroulement tourbillonnaire enroule l'extrémité de la flamme tandis que les fluctuations du nombre de swirl agissent sur l'angle de la flamme. Ces deux mécanismes en compétition se combinent de manière constructive ou destructive conduisant à des gains faibles ou élevés dans la réponse de la flamme en fonction de la fréquence. Ces mécanismes sont retrouvés par simulation aux grandes échelles (LES). / This work is concerned with the dynamics of premixed confined turbulent swirling flames submitted to acoustic velocity disturbances. The general objective is to gain an understanding of the mechanisms governing the response of these flames and to derive predictive methods for combustion instabilities. Swirling flows are first reviewed in terms of swirl numbers and novel expressions for them are given. Perturbed form of the swirl number are suggested taking into account acoustic disturbances in the flow. The experimental system comprises an upstream manifold, an injector equipped with a swirler and a transparent flame tube allowing direct visualization of the flame motion. Two operating points are investigated corresponding to different bulk velocities. The upstream manifold and the flame tube of the burner can be easily change to test several configurations. The burner acoustic is also analyzed in term of coupled cavities approach to determined the resonant frequencies of the system in non reactive cases. Experiments are carried out to measure the system eigen frequencies and the estimate damping coefficient of the various burners arrangements. A criterion for decoupling acoustic mode is suggested. The flow dynamics is examined in terms of mode conversion occurring at the swirler or downstream an airfoil cascade. This part of the work, carried out with numerical simulations, shows that when submitted to an acoustic wave, a swirler gives rise to an azimuthal convective wave in addition to the transmitted acoustic wave. Both axial and radial swirlers are prone to this mechanism as confirmed by experiments. It is found that this mode conversion process has a strong impact on the flame dynamics in swirling flames combustors. Combustion dynamics is then analyzed by measuring the flame describing function (FDF) of this burner. This FDF is used to determine the response of the flame to acoustic velocity disturbances propagating on the upstream flow. It is shown that the Strouhal number is a suitable dimensionless group to characterize the swirling flame response. The flame dynamics is also analyzed with an ensemble of diagnostics including pressure probes, photomultipliers and laser Doppler velocimeter (LDV). A model for the linear swirling flame transfer function is derived theoretically. The physical mechanisms driving the response of the flame are identified : vortex rollup and swirl number fluctuations. The vortex rollup is associated to the acoustic wave transmitted downstream of the swirler and entering in the combustor while the swirl number fluctuations are directly linked to the mode conversion mechanisms downstream the swirler which induced different axial and azimuthal speeds upstream the flame. The rollup phenomena acts at the extremity of the flame while swirl number fluctuations act on the flame angle. These competiting mechanisms act constructively or destructively leading to low or high gains in the flame response depending on the frequency. These mechanisms are retrieved by large eddy simulations of the flame dynamics. Finally, an instability analysis is carried out by combining the experimental flame describing function (FDF) and an acoustic model of the combustor to determine the frequency and the amplitude of the velocity disturbances at the limit cycle. A good agreement between predictions and experiments is obtained in most cases indicating that the method is suitable subject to further developments.

No description available.

This present research effort was directed towards developing reduced order models for the dynamics of laminar flat flames, swirl stabilized turbulent flames, and in evaluating the effects of the variation in fuel composition on flame dynamics. The laminar flat flame study was conducted on instrument grade methane, propane, and ethane flames for four total flow rates from 145 cc/sec to 200 cc/sec, and five equivalence ratios from 0.5 to 0.75. The analysis was done by measuring the frequency resolved velocity perturbations, u', and the OH* chemiluminescence, as a measure of unsteady heat release rate, q'. The experimental data showed the corresponding flame dynamics to be fourth order in nature with a pure time delay. One of the resonance was shown to represent the pulsation of the flame location caused by fluctuation in the flame speed and fluctuating heat losses to the flame stabilizer. The other resonance was correlated to the dynamics of the chemical kinetics involved in the combustion process. The time delay was correlated to the chemical time delay. Upon comparing the results of the experiments with the three fuels, it was concluded that for all equivalence ratios studied, propane flame had a higher dynamic gain than methane flames. Ethane flames exhibited a higher dynamic gain than methane flame in the frequency range of 20-100 Hz. Thus, burning of propane instead of methane increased the likelihood of the occurrence of thermo-acoustic instabilities. The experimental techniques developed during the dynamic studies conducted on laminar flat flames were applied to swirl stabilized turbulent flames. Experiments were performed for QAir = 15 scfm and 20 scfm, F = 0.55, 0.6, 0.65, and S = 0.79 and 1.19. The results of fully premixed experiments showed that the flame behaved as a 8th order low pass filter. The results of the partially premixed experiment exhibited a rich spectra, which maintained its bandwidth over the entire range of frequency studied. Comparison of fully and partially premixed flames in the frequency range of 200-400 Hz, indicated that at overall lean conditions the dynamic gain of the totally premixed flames was almost an order of magnitude lower than that of the partially premixed conditions. Thus, it was concluded that combustors with fully premixed flames have a higher probability of being thermo-acoustically stable than those with partially premixed flames. / Ph. D.

Lean premixed fuel-air conditions in large gas turbines are used to improve efficiency and reduce emissions. These conditions give rise to large undamped pressure oscillations at the combustor's natural frequencies which reduce the turbine's longevity and reliability. Active control of the pressure oscillations, called thermoacoustic instabilities, has been sought as passive abatement of these instabilities does not provide adequate damping and is often impractical on a large scale. Phase shift control of the instabilities is perhaps the simplest and most popular technique employed but often does not provide good performance in that controller induced secondary instabilities are generated with increasing loop gain. This thesis investigates the general underlying cause of the secondary instabilities and shows that high average group delay through the frequency region of the instability is the root of the problem. This average group delay is then shown to be due not only the controller itself but can also be associated with other components and inherent characteristics of the control loop such as actuators and time delay, respectively. An "optimum" phase shift controller, consisting of an appropriate shift in phase and a low order, wide bandwidth bandpass filter, is developed for a Rijke tube combustor and shown to closely match the response of an LQG controller designed only for system stabilization. Both the optimal phase shifter and the LQG controller are developed based on a modified model of the thermoacoustic loop which takes into account the change in density of the combustion reactants at the flame location. Additionally, the system model is coupled with a model of the control loop and then validated by comparison of simulated results to experimental results using nearly identical controllers. / Master of Science

Many industries have entered a new global phase which takes the environment in mind. The gas turbine industry is no exception, where the utilization of green fuels is the future to spare the environment from carbon dioxide and NOx emissions. Hydrogen has been identified as a fuel which can fulfil the global requirements set by governments worldwide. Combustion instabilities are not inevitable during gas turbine operations, especially when using a highly reactive and diffusive fuel as hydrogen. These thermoacoustics instabilities can damage mechanical components and have economic consequences in terms of maintenance and reparation. Understanding these thermoacoustic instabilities in gas turbine burners is of great interest. COMSOL Multiphysics offers a robust acoustic module compared to other available acoustic simulation programs. In this thesis, an Acoustic finite element model was built representing an atmospheric combustion rig (ACR), used to test the burners performance and NOx emissions. Complementary computational fluid dynamics (CFD) simulations were performed for 100 % hydrogen as fuel by using the Reynolds average Navier-Stokes (RANS) lag EB k - epsilon turbulence model. Necessary data was successfully imported to the Acoustic finite element model. Different techniques of building the mesh were used in COMSOL Multiphysics and NX. Similar results were obtained, proving that both mesh tools work well in acoustic simulations. Two different ways of solving the eigenvalue problem in acoustics were implemented, the classic Helmholtz equation and Linearized Navier-Stokes equations, both in the frequency domain. The Helmholtz equation proved to be efficient and detected multiple modes in the frequency range of interest. Critical modes which lived in the burner and the combustion chamber were identified. Defining a hard and soft wall boundary condition at the inlets and outlet of the atmospheric combustion rig gave similar eigenfrequencies when comparing the two boundary conditions. The soft wall boundary condition was defined with a characteristic impedance, giving a high uncertainty whether the results were trustworthy or not. A boundary condition study revealed that the boundary condition at the outlet was valid for modes living in the burner and combustion chamber. Solving the eigenvalue problem with the Linearized Navier-Stokes equations proved to be computationally demanding compared to the Helmholtz equation. Similar modes shapes were found at higher frequencies, but pressure perturbations were observed in the region where the turbulence was dominant. A prestudy for a stability analysis was established, where the ACR and the flame was represented as a generic model. Implementing a Flame Transfer Function (FTF), more specifically a linear n - tau model, showed that the time delay tau is most sensible for a parametric change and hence needs to be chosen cautiously

Les réglementations toujours plus drastiques sur les émissions de polluants ont conduit au développement de systèmes de combustion opérant en régimes pauvres qui sont malheureusement sujet aux instabilités thermo acoustiques. La capacité de la Simulation aux Grandes Echelles (SGE) à simuler des turbines à gaz industrielles complexes de grande puissance est mise en évidence au cours de ce travail de thèse. Tout d’abord, la SGE est appliquée à un brûleur académique et validée par comparaison à des mesures effectuées à l’Université de Berlin ainsi qu’à des simulations SGE effectuées avec OpenFOAM chez Siemens. Afin de déterminer la stabilité de ce bruleur le couplage entre l’acoustique et la combustion est modélisé par l’approche de type fonction de transfert de flamme (FTF). Suite à ces calcules et l’évaluation de la FTF les fluctuations du nombre de swirl sont identifiées comme un paramètre à même de modifier cette réponse de flamme. Après cette première étape de validation, une turbine à gaz industrielle est simulée en SGE pour deux géométries différentes du brûleur et pour deux points de fonctionnement. La FTF issue de ces calculs est peu influencée par les deux points de fonctionnement. A l’inverse, des légères modifications de la géométrie du swirler modifient les caractéristiques de la FTF montrant que plusieurs mécanismes sont en jeu. Ces mécanismes sont identifiés comme étant la vitesse d’entrée, les fluctuations de swirl et les fluctuations de fraction de mélange. Cette dernière est causée par: 1) la pulsation du débit de carburant injecté et 2) la trajectoire fluctuante des jets de carburant. Bien que le swirler soit conçu pour fournir un mélange le plus homogène possible, d’importantes hétérogénéités de mélange à l’entrée de la chambre de combustion sont présentes. Les perturbations de mélange se combinent avec les fluctuations de vitesse (et donc avec les fluctuations de swirl) aboutissant à des résultats de FTF différents. Un modèle étendu pour la FTF reliant le dégagement de chaleur à la vitesse d’entrée et à la fluctuation de fraction de mélange (modèle MISO) se révèle être une bonne solution pour ces systèmes complexes. Une analyse non linéaire montre en outre que l’amplitude de forçage conduit non seulement à une saturation de la flamme, mais aussi à un changement de la réponse de flamme. La saturation de la flamme n’est vérifiée que pour la FTF globale et le gain augmente localement avec une amplitude croissante. Pour ce système on notera enfin que la flamme linéaire, comme la flamme non linéaire, ne sont pas compactes: certaines zones pourtant situées l’une à coté de l’autre, ont des différences significatives de délai de FTF, montrant que certaines parties de la flamme amortissent l’excitation alors que d’autres l’amplifient. / Modern pollutant regulation have led to a trend towards lean combustion systems which are prone to thermo-acoustic instabilities. The ability of Large Eddy Simulation (LES) to handle complex industrial heavy-duty gas turbines is evidenced during this thesis work. First, LES is applied to an academic single burner in order to validate the modeling against measurements performed at TU Berlin and against OpenFoam LES simulations done at Siemens. The coupling between acoustic and combustion is modeled with the Flame Transfer Function (FTF) approach and swirl number fluctuations are identified changing the FTF amplitude response of the flame. Then, an industrial gas turbine is analyzed for two different burner geometries and operating conditions. The FTF is only slightly influenced for the two operating points but slight modifications of the swirler geometry do modify the characteristics of the FTF showing that a simple model taking only into account the flight time is not appropriate and additional mechanisms are at play. Those mechanisms are identified being the inlet velocity, the swirl and the inlet mixture fraction fluctuations. The latter is caused by two mechanisms: 1) the pulsating injected fuel flow rate and 2) the fluctuating trajectory of the fuel jets. Although the diagonal swirler is designed to provide good mixing, effects of mixing heterogeneities at the combustion chamber inlet occur. Mixture perturbations phase with velocity (and hence with swirl) fluctuations and combine with them to lead to different FTF results. Another FTF approach linking heat release to inlet velocity and mixture fraction fluctuation (MISO model) shows further to be a good solution for complex systems. A nonlinear analysis shows that the forcing amplitude not only leads to a saturation of the flame but also to changes of the delay response. Flame saturation is only true for the global FTF and the gain increases locally with increasing forcing amplitude. Both, the linear and the nonlinear flames, are not compact: flame regions located right next to each other exhibited significant differences in delay meaning that at the same instant certain parts of the flame damp the excitation while others feed it.

The persistent thrust for a cleaner, greener environment has prompted air pollution regulations to be enforced with increased stringency by environmental protection bodies all over the world. This has prompted gas turbine manufacturers to move from non-premixed combustion to lean, premixed combustion. These lean premixed combustors operate quite fuel-lean compared to the stochiometric, in order to minimize CO and NOx productions, and are very susceptible to oscillations in any of the upstream flow variables. These oscillations cause the heat release rate of the flame to oscillate, which can engage one or more acoustic modes of the combustor or gas turbine components, and under certain conditions, lead to limit cycle oscillations. This phenomenon, called thermoacoustic instabilities, is characterized by very high pressure oscillations and increased heat fluxes at system walls, and can cause significant problems in the routine operability of these combustors, not to mention the occasional hardware damages that could occur, all of which cumulatively cost several millions of dollars. In a bid towards understanding this flow-flame interaction, this research works studies the heat release response of premixed flames to oscillations in reactant equivalence ratio, reactant velocity and pressure, under conditions where the flame preheat zone is convectively compact to these disturbances, using the G-equation. The heat release response is quantified by means of the flame transfer function and together with combustor acoustics, forms a critical component of the analytical models that can predict combustor dynamics. To this end, low excitation amplitude (linear) and high excitation amplitude (nonlinear) responses of the flame are studied in this work. The linear heat release response of lean, premixed flames are seen to be dominated by responses to velocity and equivalence ratio fluctuations at low frequencies, and to pressure fluctuations at high frequencies which are in the vicinity of typical screech frequencies in gas turbine combustors. The nonlinear response problem is exclusively studied in the case of equivalence ratio coupling. Various nonlinearity mechanisms are identified, amongst which the crossover mechanisms, viz., stoichiometric and flammability crossovers, are seen to be responsible in causing saturation in the overall heat release magnitude of the flame. The response physics remain the same across various preheat temperatures and reactant pressures. Finally, comparisons between the chemiluminescence transfer function obtained experimentally and the heat release transfer functions obtained from the reduced order model (ROM) are performed for lean, CH4/Air swirl-stabilized, axisymmetric V-flames. While the comparison between the phases of the experimental and theoretical transfer functions are encouraging, their magnitudes show disagreement at lower Strouhal number gains show disagreement.

This thesis describes an experimental investigation of the response of lean turbulent swirling flames with different degrees of premixedness (i.e. different mixture patterns) to acoustic forcing using the same burner configuration and varying only the fuel injection strategy. Special emphasis was placed on the amplitude dependence of their response. Also, the behaviour of self-excited fully premixed flames was examined. kHz OH* chemiluminescence was used to study qualitatively the heat release response of the flames, while kHz OH Planar Laser Induced Fluorescence (PLIF) was employed to understand the response of the flame structure and the behaviour of the various parts of the flame. The Proper Orthogonal Decomposition (POD) method was used to extract the dominant structures of the flame and their periodicity. In the first part of the thesis, self-excited oscillations were induced by extending the length of the duct downstream of the bluff body. It was found that the longer the duct length and the higher the equivalence ratio, the stronger the self-excited oscillations were, with the effect of duct length being much stronger. The dominant frequencies of the system were found to increase with equivalence ratio and bulk velocity and decrease with duct length. For some conditions, three simultaneous periodic motions were observed, where the third motion oscillated at a frequency equal to the difference of the other two frequencies. A novel application of the POD method was proposed to estimate the convection velocity from the most dominant reaction zone structures detected by OH* chemiluminescence imaging. For a range of conditions, the convection velocity was found to be in the range of 1.4-1.7 bulk flow velocities at the inlet of the combustor. In the second part, the response of fully premixed, non-premixed with radial fuel injection (NPR) and axial fuel injection (NPA) flames was investigated and compared. All systems exhibited a nonlinear response to acoustic forcing. The highest response was observed by the NPR flame, followed by the fully premixed and the non-premixed with axial fuel injection flame. The proximity of forced flames to blow-off was found to be critical in their heat release response, as close to blow-off the flame response was significantly lower than that farther from blow-off. In the NPR and NPA systems, it was shown that the acoustic forcing reduced the stability of the flame and the stability decreased with the increase in forcing amplitude. In the fully premixed system, the flame area modulations constituted an important mechanism of the system, while in the NPR system both flame area and equivalence ratio modulations were important mechanisms of the heat release modulations. The quantification of the local response of the various parts of the flame at the forcing frequency showed that the ratio RL (OH fluctuation at 160 Hz to the total variance of OH) was greater in the inner shear layer region than in the other parts in the case of NPR and NPA flames. In fully premixed flames, greater RL values were observed in large regions on the downstream side of the flame than those in the ISL region close to the bluff body. The ratio of the convection velocity to the bulk velocity was estimated to be 0.54 for the NPR flame, while it was found to be unity for the respective fully premixed flame. In the last part of the thesis, the response of ethanol spray flames to acoustic oscillations was investigated. The nonlinear response was very low, which was reduced closer to blow-off. The ratio RL was the highest in the spray outer cone region, downstream of the annular air passage, while RL values were very low in the inner cone region, downstream of the bluff body. Unlike NPR and fully premixed flames, in case of spray and NPA systems, it was found that forcing did not affect greatly the flame structure. The understanding of the nonlinear response of flames with different degrees of premixedness in a configuration relevant to industrial systems contributes to the development of reliable flame response models and lean-burn devices, because the degree of premixedness affects greatly the flame response. Also, the understanding of the behaviour of forced spray flames is of great interest for industrial applications, contributing to the development of thermoacoustic models for liquid fuelled combustors. Finally, the estimation of the convection velocity is of importance in the modelling of self-excited flames and flame response models, since the convection velocity affects the flame response significantly.