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Convective Scaling of Intrinsic Thermo-Acoustic Eigenfrequencies of a Premixed Swirl Combustor
Abstract
Spectral distributions of the sound pressure level (SPL) observed in a premixed, swirl stabilized combustion test rig are scrutinized. Spectral peaks in the SPL for stable as well as unstable cases are interpreted with the help of a novel criterion for the resonance frequencies of the intrinsic thermo-acoustic (ITA) feedback loop. This criterion takes into the account the flow inertia of the burner and indicates that in the limit of very large flow inertia, ITA resonance should appear at frequencies where the phase of the flame transfer function (FTF) approaches. Conversely, in the limiting case of vanishing flow inertia, the new criterion agrees with previous results, which state that ITA modes may arise when the phase of the FTF is close to. Relying on the novel criterion, peaks in the SPL spectra are identified to correspond to either ITA or acoustic modes. Various combustor configurations are investigated over a range of operating conditions. It is found that in this particular combustor, ITA modes are prevalent and dominate the unstable cases. Remarkably, the ITA frequencies change significantly with the bulk flow velocity and the position of the swirler but are almost insensitive to changes in the length of the combustion chamber (CC). These observations imply that the resonance frequencies of the ITA feedback loop are governed by convective time scales. A scaling rule for ITA frequencies that relies on a model for the overall convective flame time lag shows good consistency for all operating conditions considered in this study.
... For instance, combustor stability margins may be increased by introducing losses into the acoustic subsystem [19,20], by modifications of the up-and downstream reflection coefficients [21], or by the usage of passive actuators affecting the acoustic subsystem [22][23][24][25]. In contrast to this, stability characteristics may be improved by impacting the ITA subsystem, e.g., through a modification of the flame transfer function (FTF) [26] by introducing hydrogen in the fuel [27][28][29][30], changing operating conditions [31][32][33][34][35], convective interference [34,36], a modulation of the fuel injection impedance [37], lateral flame confinement [38] or plasma actuators [39]. In addition to this, both the acoustic and the ITA subsystem may be impacted [40] by a combination of the aforementioned strategies. ...
... For instance, combustor stability margins may be increased by introducing losses into the acoustic subsystem [19,20], by modifications of the up-and downstream reflection coefficients [21], or by the usage of passive actuators affecting the acoustic subsystem [22][23][24][25]. In contrast to this, stability characteristics may be improved by impacting the ITA subsystem, e.g., through a modification of the flame transfer function (FTF) [26] by introducing hydrogen in the fuel [27][28][29][30], changing operating conditions [31][32][33][34][35], convective interference [34,36], a modulation of the fuel injection impedance [37], lateral flame confinement [38] or plasma actuators [39]. In addition to this, both the acoustic and the ITA subsystem may be impacted [40] by a combination of the aforementioned strategies. ...
... The ITA subsystem is subject to modifications of the flame response, i.e., the flame transfer function (FTF). Such a modification may be achieved by different methods, e.g., convective acoustic interference [36], changes in the thermal power [34], application of plasma actuators [39], or the fuel composition [27,28]. While these methods most certainly impact both the FTF gain as well as the phase, we seek a more simplified model for the variation of the flame response without loss of generality. ...
In this paper, we apply the novel EPTD (Exceptional Point-based Thermoacoustic Design)-method derived in part I of this study (M. Casel & A. Ghani, Combust. Flame 2024) to two lab-scale combostor test rigs that exhbit thermoacoustic instabilities and demonstrate the method's capability and practicality for stabilizing the originally unstable systems. Furthermore, we study, and refine, certain characteristics of the proposed EPTD method when applied to realistic combustor configurations. While the first configuration is laminar and unconfined, the second features a confined turbulent swirl flame. Both combustor test rigs are modeled by thermoacoustic networks incorporating measured flame responses. The models allow to trace back full system modes to their respective mode origins, which are either of intrinsic thermoacoustic (ITA) or acoustic nature, and are validated by means of experimental data. In both configurations, we identify exceptional points (EPs) that are formed by these respective mode branches. The unconfined, laminar configuration features only one EP, that we first investigate with respect to the system parameter sensitivity, and subsequently analyze its relation to the configuration's spectrum, confirming the characteristics that were previously identified in part I of this study by means of generic (thermoacoustic) systems: not only the EP's position in the complex plane, but also the exceptional parameters have a significant impact on the resulting thermoacoustic spectrum as they incorporate a relation between the respective mode origins and the full system modes. In contrast to the first configuration of this paper, the confined turbulent combustor allows for some further analysis of the EPTD application to realistic combustors as it features a significantly larger system parameter space as well as two EPs. Besides, it exhibits two EPs, for which we show how their respective sensitivities with respect to system parameter variations may already be utilized to identify which system parameters impact on which mode origins in the spectrum. In addition to this, we describe which of the two EPs may be chosen when applying the EPTD method. Finally, in both cases, we adopt the EPTD method derived in part I of this study for stabilizing thermoacoustic systems:
Shift the EP towards smaller growth rates while constraining the exceptional parameters, i.e., shift the entire spectrum towards smaller growth rates while enforcing specific relations between the respective mode origins. Subsequently we showcase that this method in fact successfully dampens the entire spectrum of both combustion experiments and that the entire thermoacoustic spectrum shifts in growth rate with the same magnitude of the prescribed shift in EP growth rate.
While the relatively small system parameter dimension of the unconfined laminar configuration does not allow for multiple system parameter combinations that realize the same EP, we identify multiple system parameter combinations that feature the same EP in the confined turbulent case. For this, we subsequently show that, as already shown for the generic configurations in part I of this study, different system parameter combinations, realizing the same EP, in fact result in the same thermoacoustic spectrum. This finally demonstrates that our proposed method is especially suited for the design of thermoacoustic systems that feature a large number of system parameters.
... Note that the phase is stipulated to be negative, which is helpful in the analysis of causal mechanisms: fluctuations of heat release rate should lag and not lead fluctuations of upstream velocity. This condition for the phase may be recognized as the − criterion [36]. Let us now rewrite Eq. (6) aŝ d =̂u +̂q, ...
... We conclude that a three-duct configuration with strong contractions at the planes 'uc-dc' and 'u-d' exhibits a phase in the flame response of − ∕2 (modulo 2 ) in neutrally stable cases, where = 0. This result was labeled ' ∕2 criterion' in Albayrak et al. [36]. ...
... In order to obtain a simplified expression of Eq. (36), it is useful to invoke the acoustic compactness assumption of the mid-section duct, as done in [36]. Such an assumption allows the approximation e 1 ≈ 1 + 1 . ...
It is accepted that the thermoacoustic behavior of a given combustion system can be analyzed by investigating how its natural acoustic modes are perturbed by the flame dynamics. As a result, the resonance frequency and structure of the resulting thermoacoustic mode-understood as a perturbed acoustic mode-are slightly modified with respect to the natural acoustic mode counterpart. However, experimental evidence shows that the frequency of unstable thermoacoustic modes sometimes lies far away from the natural acoustic frequencies of the system under study. In many cases, this frequency cannot be associated with hydrodynamic or entropy-related instabilities. In recent years, the intrinsic thermoacoustic (ITA) feedback loop has been formally recognized as the responsible mechanism in some of those situations. Theory and devoted experiments have been developed that have enormously contributed to the understanding of the particular behavior of intrinsic thermoacoustic instabilities. The present review encapsulates in a single theoretical framework the theory presented in the collection of today existing ITA papers, which spread through different cases of study regarding acoustic boundaries-anechoic, partially or fully reflecting-and geometries-duct flames, combustors composed by three coaxial ducts and annular configurations. Several examples are shown that summarize the most relevant results on ITA theory to this day. This review paper also gives special attention to the categorization of ITA modes, given the fact that there is no current agreement on the definition of an ITA mode: one example in this review paper explicitly shows that the proposed categorization methods can indeed be contradictory. Of high interest is also the review of papers illustrating the coexistence of thermoacoustic modes of acoustic and ITA nature, which in turn relate to the recently discovered exceptional points in the thermoacoustic spectrum. Additionally, this paper discusses the 'counter-intuitive' evidence that shows that ITA modes can be destabilized when acoustic dissipative elements are added into the system. Finally, it is shown how a single-mode Galerkin expansion may be able to model some ITA eigenfrequencies. This result is suggested in some recent works and is not obvious. The practical relevance of ITA modes in industrial combustion chambers of gas turbines is also discussed together with suggestions for future studies.
... This new paradigm fundamentally changed the understanding of thermoacoustic instabilities and shed a new light on inexplicable phenomena reported in earlier studies, such as "the new set of modes" described by Dowling and Stow [14], the "bulk mode" highlighted by Eckstein and Sattelmayer [15,16], or the "convective scaling" of thermoacoustic eigenfrequencies [17]. Numerous studies then investigated the role of both types of thermoacoustic instabilities. ...
... (10,11). Such a result can be explained using phasor analysis, which has already been used in thermoacoustics [13,16,17,24,[47][48][49]. For example, if we consider the case of fully reflecting boundaries R i = R o = ±1, the acoustic mode is marginally stable, thus simplifying the phasor analysis with arrows of fixed length. ...
... For example, changing the downstream length L d induces a change in the total downstream length that is identical for all mode orders: all the modes are translated along the trajectories. Conversely, the impact of a modification in the geometry of the cross-talk area (width of the can or coupling strength) is different for each azimuthal order, since τ * m shows an explicit dependence to the mode order as shown in Eq.(17). Note also that changing the size of the gap or the width of the can have antagonist effects. ...
Thermoacoustic systems can exhibit self-excited instabilities of two nature, namely cavity modes or intrinsic thermoacoustic (ITA) modes. In heavy-duty land-based gas turbines with canannular combustors, the cross-talk between cans causes the cavity modes of various azimuthal order to create clusters, i.e. ensembles of modes with close frequencies. Similarly, in systems exhibiting rotational symmetry, ITA modes also have the peculiar behavior of forming clusters. In the present study, we investigate how such clusters interplay when they are located in the same frequency range. We first consider a simple Rijke tube configuration and derive a general analytical low-order network model using only dimensionless numbers. We investigate the trajectories of the eigenmodes when changing the downstream length and the flame position. In particular, we show that ITA and acoustic modes can switch nature and their trajectories are strongly influenced by the presence of exceptional points. We then study a generic can-annular combustor. We show that such configuration can be approximated by an equivalent Rijke tube. We demonstrate that, in the absence of mean flow, the eigenvalues of the system necessarily lie on specific trajectories imposed by the upstream conditions.
... This new paradigm fundamentally changed the understanding of thermoacoustic instabilities and shed a new light on inexplicable phenomena reported in earlier studies, such as "the new set of modes" described by Dowling and Stow [14], the "bulk mode" highlighted by Eckstein and Sattelmayer [15,16], or the "convective scaling" of thermoacoustic eigenfrequencies [17]. Numerous studies then investigated the role of both types of thermoacoustic instabilities. ...
... (10,11). Such a result can be explained using phasor analysis, which has already been used in thermoacoustics [13,16,17,24,[47][48][49]. For example, if we consider the case of fully reflecting boundaries R i = R o = ±1, the acoustic mode is marginally stable, thus simplifying the phasor analysis with arrows of fixed length. ...
... For example, changing the downstream length L d induces a change in the total downstream length that is identical for all mode orders: all the modes are translated along the trajectories. Conversely, the impact of a modification in the geometry of the cross-talk area (width of the can or coupling strength) is different for each azimuthal order, since τ * m shows an explicit dependence to the mode order as shown in Eq.(17). Note also that changing the size of the gap or the width of the can have antagonist effects. ...
Thermoacoustic systems can exhibit self-excited instabilities of two nature, namely cavity modes or intrinsic thermoacoustic (ITA) modes. In heavy-duty land-based gas turbines with can-annular combustors, the cross-talk between cans causes the cavity modes of various azimuthal order to create clusters, i.e. ensembles of modes with close frequencies. Similarly, in systems exhibiting rotational symmetry, ITA modes also have the peculiar behavior of forming clusters. In the present study, we investigate how such clusters interplay when they are located in the same frequency range. We first consider a simple Rijke tube configuration and derive a general analytical low-order network model using only dimensionless numbers. We investigate the trajectories of the eigenmodes when changing the downstream length and the flame position. In particular, we show that ITA and acoustic modes can switch nature and their trajectories are strongly influenced by the presence of exceptional points. We then study a generic can-annular combustor. We show that such configuration can be approximated by an equivalent Rijke tube. We demonstrate that, in the absence of mean flow, the eigenvalues of the system necessarily lie on specific trajectories imposed by the upstream conditions.
... The pressure and heat release rate oscillations may feature dominant modes that are usually associated with acoustic (Bonciolini and Noiray 2019;Casado 2013;Chakravarthy et al. 2007;Gotoda et al. 2011;Passarelli 2019;Tay-Wo-Chong et al. 2012;Temme, Allison, Driscoll 2014) and/or intrinsic thermoacoustic modes (Albayrak et al. 2018;Courtine et al. 2014;Courtine, Selle, Poinsot 2015;Emmert et al. 2017;Emmert, Bomberg, Polifke 2015;Hoeijmakers et al. 2014Hoeijmakers et al. , 2016Murugesan et al. 2018;Xu et al. 2020). Broadly, acoustic modes can be categorized into those pertaining to standing pressure waves or those associated with the movement of air (and as a result oscillations of pressure) inside the combustion chamber (Alster 1972;Casado 2013;Chakravarthy et al. 2007;Ingard 1953;Murugesan et al. 2018;Nair, Thampi, Sujith 2014;Rienstra and Hirschberg 2004;Schuller 2003;Temme, Allison, Driscoll 2014;Zhao et al. 2017). ...
... The intrinsic thermoacoustic modes exist as a result of a feedback mechanism between the heat release rate and pressure oscillations (Emmert et al. 2017;Orchini et al. 2020;Tay-Wo-Chong et al. 2012;Xu et al. 2020). Anechoic conditions are used in the literature to remove the acoustic modes and focus on the intrinsic thermoacoustic modes (Albayrak et al. 2018;Emmert et al. 2017;Hoeijmakers et al. 2014Hoeijmakers et al. , 2016Murugesan et al. 2018). It is shown that the frequency of intrinsic modes linearly increases by increasing the input power of the combustor either through increasing the fuel-air equivalence ratio (Hoeijmakers et al. 2016) and/or increasing the mean bulk flow velocity (Murugesan et al. 2018;Xu et al. 2020). ...
... It is shown that the frequency of intrinsic modes linearly increases by increasing the input power of the combustor either through increasing the fuel-air equivalence ratio (Hoeijmakers et al. 2016) and/or increasing the mean bulk flow velocity (Murugesan et al. 2018;Xu et al. 2020). Albayrak et al. (2018) show that the ratio of the intrinsic thermoacoustic modes frequencies is equal to the ratio of the tested mean bulk flow velocities raised to the power of 0.8 multiplied by the inverse of the flame height ratio. In contrast to the acoustic modes, the intrinsic thermoacoustic modes frequencies are independent of the combustor length (Murugesan et al. 2018;Tay-Wo-Chong et al. 2012;Xu et al. 2020). ...
Structural, acoustic, and intrinsic modes contributions to thermoacoustic oscillations of a small-scale power generator combustor are investigated experimentally. Simultaneous OH* chemiluminescence and pressure data were acquired at frequencies of 5 and 50 kHz,
respectively, and are used to study the above coupling. Experiments were performed for fuel-air equivalence ratios of 0.7 and 0.9, igniter rod locations of −5, 1.5, 2.5, and 5 mm, and air volumetric flowrates of 120, 140, 160, and 180 SLPM, generating 32 experimental conditions. The results show that, depending on the tested condition, turbulent methane-air premixed flames were stabilized either on a torus-shaped flame-holder (generating Bunsen flames) or on both the flame-holder and an igniter rod (generating M-shaped flames). At fuel-air equivalence ratio of 0.7, two dominant peaks near the structural and acoustic modes are detected. In addition to structural and acoustic modes, two intrinsic thermoacoustic modes are also detected for conditions pertaining to the fuel-air equivalence ratio of 0.9. It is shown that acoustic and structural modes mostly contribute to positive Rayleigh gain values. However, generally, intrinsic modes contribute to negative
values of the Rayleigh gain. The negative Rayleigh gain values associated with the intrinsic thermoacoustic modes are detected near the exit of the burner as well as the stagnation wall. This suggests that, for the utilized power generator combustor, compared to structural and acoustic modes, existence of intrinsic thermoacoustic modes are
desired.
... Finally, "convective scaling" of thermoacoustic eigenfrequencies -i.e. the dependence of eigenmode frequency on the bulk flow velocity inside the burner, but not on the speed of sound in plenum or combustor -may be regarded as a consequence of ITA feedback [18]. ...
... Equation (18) Eqn. (18) to a generalized linear eigenvalue problem, which facilitates the use of direct solvers to compute the complete spectrum of eigenvalues and eigenmodes. This key feature proves to be crucial to find ITA modes in a simple manner. ...
... The spatial evolution of Riemann invariants f and g along the system is modeled with phasors rotating in the complex plane. Such analysis was previously applied in the context of ITA modes [17,18] and has proven to be convenient to study linear stability. ...
The intrinsic thermoacoustic (ITA) feedbackloop constitutes a coupling between flow, flame and acoustics that does not involve the natural acoustic modes of the system. One recent study showed that ITA modes in annular combustors come in significant number and with the peculiar behavior of clusters, i.e. several modes with close frequencies. In the present work an analytical model of a typical annular combustor is derived via Riemann invariants and Bloch theory. The resulting formulation describes the full annular system as a longitudinal combustor with an outlet reflection coefficient that depends on frequency and the azimuthal mode order. The model explains the underlying mechanism of the clustering phenomena and the structure of the clusters associated with ITA modes of different azimuthal orders. In addition, a phasor analysis is proposed, which enclose the conditions for which the 1D model remains valid when describing the thermoacoustic behavior of an annular combustor.
... Finally, "convective scaling" of thermoacoustic eigenfrequencies -i.e. the dependence of eigenmode frequency on the bulk flow velocity inside the burner, but not on the speed of sound in plenum or combustor -may be regarded as a consequence of ITA feedback [18]. ...
... Equation (18) Eqn. (18) to a generalized linear eigenvalue problem, which facilitates the use of direct solvers to compute the complete spectrum of eigenvalues and eigenmodes. This key feature proves to be crucial to find ITA modes in a simple manner. ...
... The spatial evolution of Riemann invariants f and g along the system is modeled with phasors rotating in the complex plane. Such analysis was previously applied in the context of ITA modes [17,18] and has proven to be convenient to study linear stability. ...
The intrinsic thermoacoustic (ITA) feedbackloop constitutes a coupling between flow, flame and acoustics that does not involve the natural acoustic modes of the system. One recent study showed that ITA modes in annular combustors come in significant number and with the peculiar behavior of clusters, i.e. several modes with close frequencies. In the present work an analytical model of a typical annular combustor is derived via Riemann invariants and Bloch theory. The resulting formulation describes the full annular system as a longitudinal combustor with an outlet reflection coefficient that depends on frequency and the azimuthal mode order. The model explains the underlying mechanism of the clustering phenomena and the structure of the clusters associated with ITA modes of different azimuthal orders. In addition, a phasor analysis is proposed, which enclose the conditions for which the 1D model remains valid when describing the thermoacoustic behavior of an annular combustor.
... In experimental and analytical study by Albyrak et al. (Albayrak et al. 2017) the swirler position, bulk flow velocity and length of combustor were varied. It was found out that ITA mode was insensitive to the effect of length of combustor.The bulk flow velocity and swirler position plays significant role on ITA mode. ...
... From the above survey we observed that a few experimental investigations (Hoeijmakers et al. 2016) (Albayrak et al. 2017) (Murugesan et al. 2018) have been performed to show the occurrence of ITA mode driven instability in a range of operating conditions. The present work is mainly an experimental work on academic scale test rig. ...
... Velocity fluctuations cause local equivalence ratio fluctuations at fuel injection location. These fluctuations are transported with the local convective flow velocity and perturb the heat release rate (Hosseini et al. 2018).The associated time lag is approximately the time taken by the flow to convect the distance l mix which is presented in table 2. The frequency of the ITA mode is inversely proportional to the convective time lag (refer table 2 for residence time) in the flame transfer function (Albayrak et al. 2017). Therefore for a given l mix , the frequency of ITA mode increases with airflow rate (figure 6b & d).For the mechanism described above, the mean equivalence ratio does not play a role. ...
... In this case, the coupling is the consequence of an Intrinsic ThermoAcoustic (ITA) feedback loop, where the upstream traveling waves generated by the flame modulate the velocity upstream of the flame, which in turn influence the flame heat release rate, thus closing the loop [4]. Recent studies have shown that ITA eigenfrequencies and eigenmodes also play an important role in systems with strongly reflecting boundary conditions [5,6]. ...
... In our investigation, u contains only the external acoustic forcing, which will be coupled with the reflection boundary condition as described in the section Acoustic Reflection Coefficients. Equation (6) does not affect the overall dynamics of the main system, therefore, y can be defined to contain any scalar output parameter y n . In this work, the state-space matrices are obtained from COMSOL MULTI-PHYSICS using the LiveLink toolbox. ...
... The animation of the evolution has been published by the author as a Youtube video. 6 A similar evolution can also be observed in a Rijke tube, 7 where the star evolves toward parallel vertical trajectories. It should be remarked that the verticality of the loci at anechoic condition is not a universal property, but instead only specific to the Rijke tube case. ...
This study investigates the effect of partial acoustic reflection at inlet or outlet of a combustor on thermoacoustic stability. Parametric maps of the thermoacoustic spectrum are utilized for this purpose, which represent frequencies and growth rates of eigenmodes for a wide range of model parameters. It is found that a decrease of the acoustic reflection at the boundaries does not always imply an increase in the stability margin of the thermoacoustic system. As a matter of fact, a reduction in the acoustic reflection may sometimes destabilize a thermoacoustic mode. Additionally, we show that perturbed passive thermoacoustic modes may become ITA modes in the fully anechoic case. We briefly discuss the mode definitions ‘acoustic’ and ‘intrinsic’ commonly found in the literature.
The computational analysis is based on a state-space formulation of the Linearized Navier-Stokes Equations (LNSE) with discontinuous Galerkin discretization. This approach allows to describe the thermoacoustic system as a linear combination of internal acoustics, flame dynamics and acoustic boundaries. Such a segregation grants a clear analysis of the respective effects of the individual subsystems on the general stability of the system, expressed in terms of adjoint-based eigenvalue sensitivity. The state-space formulation of the LNSE proposed in this paper offers a powerful and flexible framework to carry out thermoacoustic studies of combustors with arbitrary geometry and acoustic boundary conditions.
... In this case, the coupling is the consequence of an Intrinsic ThermoAcoustic (ITA) feedback loop, where the upstream travelling waves generated by the flame modulate the velocity upstream of the flame, which in turn influence the flame heat release rate, thus closing the loop [4]. Recent studies have shown that ITA eigenfrequencies and eigenmodes also play an important role in systems with strongly reflecting boundary conditions [5,6]. ...
... Finally Eqs. (5) and (6) are combined with Eq. (9) yielding a connected state-space system that reads ...
... A similar evolution can also be observed in a Rijke tube 6 , where the star evolves towards parallel vertical trajectories. ...
This study investigates the effect of partial acoustic reflection at inlet or outlet of a combustor on thermoacoustic stability. Parametric maps of the thermoacoustic spectrum are utilized for this purpose, which represent frequencies and growth rates of eigenmodes for a wide range of model parameters. It is found that a decrease of the acoustic reflection at the boundaries does not always imply an increase in the stability margin of the thermoacoustic system. As a matter of fact, a reduction in the acoustic reflection may sometimes destabilize a thermoacoustic mode. Additionally, we show that perturbed passive thermoacoustic modes may become ITA modes in the fully anechoic case. We briefly discuss the mode definitions 'acoustic' and 'intrinsic' commonly found in the literature.
The computational analysis is based on a state-space formulation of the Linearized Navier-Stokes Equations (LNSE) with discontinuous Galerkin discretization. This approach allows to describe the thermoacoustic system as a linear combination of internal acoustics, flame dynamics and acoustic boundaries. Such a segregation grants a clear analysis of the respective effects of the individual subsystems on the general stability of the system, expressed in terms of adjoint-based eigenvalue sensitivity. The state-space formulation of the LNSE proposed in this paper offers a powerful and flexible framework to carry out thermoacoustic studies of combustors with arbitrary geometry and acoustic boundary conditions.
... ITA feedback have also been found in the practical combustor configurations with acoustic losses [7] or partially reflecting boundaries [14]. Recently, ITA modes were reported to be dominant in a perfectly premixed combustion system [15] and partially premixed turbulent combustion system [16]. In a Rijke burner, Hosseini et al. [13] analysed the interactions between the ITA modes and acoustic modes. ...
... Furthermore, these ITA modes are not determined by traditional criterion. The ITA modes predicted by the present model, within acceptable error, are consistent with the prediction made by the criterion of Albayrak et al. [15]. Interestingly, the phase of the present 6 model has very similar tendencies to that from the model of Albayrak et al. [15]. ...
... The ITA modes predicted by the present model, within acceptable error, are consistent with the prediction made by the criterion of Albayrak et al. [15]. Interestingly, the phase of the present 6 model has very similar tendencies to that from the model of Albayrak et al. [15]. ...
... For these flow conditions, the unstable modes have been attributed to the ITA feedback loop. Experimental results were supported by an acoustic network model and also confirmed a convective scaling of ITA modes as reported by Albayrak et al. [17] . ...
... Based on system element transfer matrices, the complete acoustic system is written in state space form, such that the thermoacoustic eigenvalue problem reduces to a standard linear eigenvalue problem. The concept of a linear acoustic network model has already been established and the reader is referred to [17,[27][28][29][30] for further details. Figure 8 shows schematically the acoustic elements used to represent the experiment. For the sake of brevity, we only present the acoustic transfer matrix T for a compact acoustic element with area change: ...
... Generally, acoustic mode frequencies change, if relevant length scales of the geometry are changed for a fixed operating point. However, ITA mode frequencies do not depend in a sensitive manner on this parameter, but rather change with the time delay of the flame, which in turn scales convectively with the bulk velocity [17] . We use this feature of ITA modes to parametrically change lengths and time delays in the network model and track the behavior of mode frequencies, in particular the mode f ITA = 131 Hz . ...
This paper investigates low-frequency thermoacoustic instabilities of a turbulent spray flame, a phenomenon known as ‘rumble’. Based on experimental data, a network model analysis is performed, which suggests an intrinsic thermoacoustic (ITA) feedback loop as the root cause of instability. At first, the ITA nature of the observed instability is confirmed by a parametric analysis, which reveals the sensitivity of the instability frequency to the time delay of the flame. Then, we investigate pure acoustic modes and pure ITA modes, which couple to the full system modes such that the origin and the trajectory of each mode is trackable. Finally, we show that the unstable mode frequency scales with the inlet bulk velocity: a feature that clearly separates the observed instability from classical cavity modes. The network model results are corroborated by phasor plots, in which all relevant phase information is compiled. It reveals the phase of the Flame Transfer Function (FTF) contributing to the instability and provides an estimate of the ITA frequency, which agrees well with the dominant peak in the experimental pressure spectrum. Additionally, the obtained flame phase is used to infer the instability frequency by the experimentally measured droplet burning time τB, which reproduces similar trends as experimental and network model results. This theoretical study confirms that (1) ITA feedback loops are important for spray flames, (2) that the ITA instability of the experiment scrutinized is controlled by the droplet dynamics and (3) ITA modes appear also in acoustically closed systems.
... With the introduction of lean premixed, low emission combustion systems, thermo-acoustic Fig. 1. SPL of a swirl burner test rig undergoing a LC [6] . ...
... The relation Eq. (6) , which governs the fundamental LC amplitude and frequency, is not affected by including higher harmonic FDFs in the flame model. The higher harmonic FDFs do not introduce any additional closed feedback loop in the system, because their output has n -times the frequency of the input 6 . Therefore, they are not able to establish any independent self excited oscillation. ...
... Eq. (8) describes the steady-state response of an oscillator that is driven by an external sinusoidal forcing. In the present case, ˆ Q 2 = F 2 ( ω, A 1 ) ˆ u 1 , the part of the second harmonic of the heat release rate that stems from ˆ u 1 , represents the external sinusoidal 6 Looking at Fig. 4 , one cannot draw a closed path going through H −1 and through one of the F n for n > 1. forcing. The thermo-acoustic system is the oscillator that responds to this forcing with ˆ u 2 at the forcing frequency of 2 ω. ...
The Flame Describing Function (FDF) is widely used to model non-linear thermo-acoustic phenomena, e.g. limit cycle oscillations in a combustor. The FDF is a weakly non-linear approach, because it accounts for the amplitude dependence of the flame response, but besides that relies on quasi-linear assumptions. In particular, it neglects the excitation of higher harmonics - a typical non-linear feature, which may play a major role in certain thermo-acoustic systems. Consequently, the FDF may provide inaccurate or incomplete results in such cases.In this study, we propose an efficient way to include higher harmonics of the flame response by an extended FDF, which includes additional transfer functions that relate higher harmonics of the heat release rate to the forcing velocity. The extended FDF is also a weakly non-linear approach, and requires the same effort for determination as the standard FDF. This paper shows how to determine the extended FDF and how to employ it for the prediction of limit cycle oscillations. The proposed concept is applied to predict and analyse the limit cycle of a laminar premixed burner for which the standard FDF delivered inaccurate results. Results obtained with the extended FDF show good agreement with fully compressible numerical simulation of the same configuration. Thus, the extended FDF proves its ability to provide accurate predictions in situations where higher harmonics play an important role in thermo-acoustic limit cycles.
... The first configuration (Duct), is a duct flame previously studied in the work of Hoeijmakers et al. [15]. The second configuration (BRS) is a premixed swirled combustor previously studied in the works of [5,18,20,21]. Figure 1 illustrates these two configurations, and Tab. 1 shows the geometric and thermodynamic parameters of interest. In this study, the inlet boundary condition is of Neumann type, ∂p/∂ x = 0, whereas the outlet is of Dirichlet type, p = 0. ...
... These eigenfrequencies (crosses in Figs. 3 and 4) are arbitrarily chosen from the locus plot. It should be mentioned, however, that case B1 is related to the ITA instability observed in [18,21] 1 . Following the procedure described in the previous section, we solve the linear systems ...
... We consider now the last term s a of Eqn. (21) to be a forcing term that acts exclusively in the region of the flame. Rearranging Eqn. ...
The purpose of this study is twofold. In the first part, we show that the resonance frequencies of two premixed combustors with fully acoustically reflecting boundary conditions in the re- gion of marginal stability depend only on the parameters of the flame dynamics, but do not depend on the combustor’s geometry. This is shown by means of a parametric study, where the time de- lay and the interaction index of the flame response are varied and the resulting complex eigenfrequency locus is shown. Assum- ing longitudinal acoustics and a low Mach number, a quasi-1D Helmholtz solver is utilized. The time delay and interaction index of the flame response are parametrically varied to calculate the complex eigenfrequency locus. It is found that all the eigenfre- quency trajectories cross the real axis at a resonance frequency that depends only on the time delay. Such marginally stable fre- quencies are independent of the resonant cavity modes of the two combustors, i.e. the passive thermoacoustic modes.
In the second part, we exploit the aforementioned obser- vation to evaluate the critical flame gain required for the sys- tems to become unstable at four eigenfrequencies located in the marginally stable region. A computationally-efficient method is proposed. The key ingredient is to consider both direct and adjoint eigenvectors associated with the four eigenfrequencies. Hence, the sensitivity of the eigenfrequencies to changes in the gain at the region of marginal stability is evaluated with cheap and accurate calculations.
This work contributes to the understanding of thermoacous- tic stability of combustors. In the same manner, the understand- ing of the nature of distinct resonance frequencies in unstable combustors may be enhanced by employing the analysis of the eigenfrequency locus here reported.
... The harmonic frequency response is a prevalent phenomenon in the nonlinear dynamics of flames. Extensive research, encompassing experimental investigations [25,26] and numerical simulations [27,28], have been undertaken to explore this harmonic response. Albayrak et al. [26] discovered that when self-excited oscillations occurred, significant responses were detected not only at the fundamental frequency of the intrinsic thermo-acoustic (ITA) mode, but also at its higher harmonics up to the sixth order. ...
... Extensive research, encompassing experimental investigations [25,26] and numerical simulations [27,28], have been undertaken to explore this harmonic response. Albayrak et al. [26] discovered that when self-excited oscillations occurred, significant responses were detected not only at the fundamental frequency of the intrinsic thermo-acoustic (ITA) mode, but also at its higher harmonics up to the sixth order. Balachandran et al. [25] demonstrated that applying harmonic or subharmonic disturbances to a turbulent bluff-body stabilized flame under velocity perturbations can alter the frequency of vortex formation and shedding. ...
... A more comprehensive characterisation of the nonlinear flame response is possible by considering perturbations with double or even multiple harmonics. As well as offering a more complete understanding of the flame nonlinearity, such studies are also directly relevant to experiments [36,37,38] and numerical simulations [39,40,41] exhibiting dual or multiple frequency oscillations. Balachandran et al. [36] conducted experiments investigating the nonlinear response of premixed flames at two different frequencies. ...
... The flame dynamics and corresponding combustion instabilities change significantly due to the presence of an additional disturbance, where the low and high frequencies result in bulk longitudinal oscillations and radially large flow wrinkles, respectively. Haeringer et al. [39] proposed an extended FDF based on the experimental phenomena of Albayrak et al. [38] as an efficient way to include higher harmonics of the flame response. The proposed concepts were applied to predict and analyse limit cycle oscillations in laminar premixed combustors, where conventional FDFs failed, and were in good agreement with fully compressible numerical simulations. ...
The two-way interaction between the unsteady flame heat release rate and acoustic waves can lead to combustion instability within combustors. To understand and quantify the flame response to oncoming acoustic waves, previous studies have typically considered the flame dynamic response to pure tone forcing and assumed a dynamically linear or weakly nonlinear response. In this study, the introduction of excitation with two distinct frequencies denoted $St_1$ and $St_2$ is considered, including the effect of excitation amplitude in order to gain more insight into the nature of flame nonlinearities and these associated with combustion instabilities. Corresponding results are obtained by combining a low-order asymptotic analysis (up to third order in normalised excitation amplitude) with numerical methods based on the model framework of the $G$-equation. The influence paths of the disturbance at $St_2$ on the flame dynamic response at $St_1$ are studied in detail. Due to the flame propagating forward normally to itself (named flame kinematic restoration), the perturbation at $St_2$ acts together with that at $St_1$ to induce a third-order nonlinear interaction in the flame kinematics, impressively suppressing the spatial wrinkling of the flame at $St_1$. Additionally, introducing the perturbation at $St_2$ alters the effective flame displacement speed, which is responsible for the calculation of the flame heat release rate and further affects the global response at $St_1$. Taking into account the above two factors, the nonlinear response of the flame at $St_1$ is completely quantified and the corresponding characteristics are clearly interpreted.
... The harmonic frequency response is a prevalent phenomenon in the nonlinear dynamics of flames. Extensive research, encompassing experimental investigations [25,26] and numerical simulations [27,28], have been undertaken to explore this harmonic response. Albayrak et al. [26] discovered that when self-excited oscillations occurred, significant responses were detected not only at the fundamental frequency of the intrinsic thermo-acoustic (ITA) mode, but also at its higher harmonics up to the sixth order. ...
... Extensive research, encompassing experimental investigations [25,26] and numerical simulations [27,28], have been undertaken to explore this harmonic response. Albayrak et al. [26] discovered that when self-excited oscillations occurred, significant responses were detected not only at the fundamental frequency of the intrinsic thermo-acoustic (ITA) mode, but also at its higher harmonics up to the sixth order. Balachandran et al. [25] demonstrated that applying harmonic or subharmonic disturbances to a turbulent bluff-body stabilized flame under velocity perturbations can alter the frequency of vortex formation and shedding. ...
This work investigates the response of a conical premixed flame to a dual-frequency excitation, based on the integrated CH* signal collected from a photomultiplier tube (PMT), the upstream velocity disturbance measured by a hotwire, and the chemiluminescence signal captured by high-speed imaging. The results show that, in addition to the excitation frequencies, a notable flame response can also be observed at the difference frequency, where the corresponding velocity fluctuation is relatively small. This result means that, at the difference frequency, the velocity fluctuation contributes little to the flame response. Such interacted response generally occurs at intermediate excitation frequencies but tends to disappear as either excitation frequency is below the cut-off frequency. And it increases linearly with the excitation amplitude, with nearly zero dependence on the phase difference. Furthermore, the flame front is extracted based on the chemiluminescence images to analyze the flame area fluctuation. The resultant phase response implies that the fluctuation of the difference frequency propagates downstream convectively, similar to that of the excitation frequencies. Interestingly, the flame area fluctuation at the difference frequency shows significant response and a low-pass characteristic, whereas the CH* fluctuation approaches zero at those low frequencies.
... Alternatively, proximity to a pure ITA or pure acoustic mode is used to identify an ITA or acoustic mode [11,[19][20][21] . Other studies, including [13,22] , simply made use of the established characteristics of pure ITA modes, say, independence of eigenfrequency from combustor length or eigenfrequency correspondence with a characteristic time delay of the flame response, to identify ITA modes. Aside from being impractical in situations where parametric variation is difficult or expensive, these methods suffer from multiple limitations. ...
... With this FTF, we can show that the unsteady heat release rate ˙ Q , which is represented by u q u q = u u θ F (ω) = −(1 + ξ ) u u (22) is perfectly in-phase with the pressure fluctuation (c.f., Fig. 8 ), thus satisfying the Rayleigh criterion for a thermoacoustic instability ...
Phasor diagrams of thermoacoustic interactions at a premixed flame allow to distinguish whether a given thermoacoustic mode – regardless of its stability – should be categorized as acoustic or ITA. The method proposed does not rely on any parametric sweep, but on the angle relating the velocity phasors across the flame. This method of categorization reveals distinct regions in the complex plane where acoustic and ITA eigenfrequencies are localized.
... The first configuration (Duct) is a duct flame previously studied in the work of Hoeijmakers et al. [15]. The second configuration (BRS) is a premixed swirled combustor previously studied in the works of [5,18,20,21]. Figure 1 illustrates these two configurations, and Table 1 shows the geometric and thermodynamic parameters of interest. In this study, the inlet boundary condition is of Neumann type, @p=@x ¼ 0, whereas the outlet is of Dirichlet type,p ¼ 0. ...
... We concentrate on two eigenfrequencies with zero growth rate defined as It should be mentioned, that case B1 is related to the ITA instability observed in Refs. [18] and [21]. Following the procedure described in the previous section, we solve the linear systems ...
It may be generally believed that the thermoacoustic eigenfrequencies of a combustor with fully acoustically reflecting boundary conditions depend on both flame dynamics and geometry of the system. In this work, we show that there are situations where this understanding does not strictly apply. The purpose of this study is twofold. In the first part, we show that the resonance frequencies of two premixed combustors with fully acoustically reflecting boundary conditions in the region of marginal stability depend only on the parameters of the flame dynamics but do not depend on the combustor's geometry. This is shown by means of a parametric study, where the time delay and the interaction index of the flame response are varied and the resulting complex eigenfrequency locus is shown. Assuming longitudinal acoustics and a low Mach number, a quasi-1D Helmholtz solver is utilized. The time delay and interaction index of the flame response are parametrically varied to calculate the complex eigenfrequency locus. It is found that all the eigenfrequency trajectories cross the real axis at a resonance frequency that depends only on the time delay. Such marginally stable frequencies are independent of the resonant cavity modes of the two combustors, i.e., the passive thermoacoustic modes. In the second part, we exploit the aforementioned observation to evaluate the critical flame gain required for the systems to become unstable at four eigenfrequencies located in the marginally stable region. A computationally efficient method is proposed. The key ingredient is to consider both direct and adjoint eigenvectors associated with the four eigenfrequencies. Hence, the sensitivity of the eigenfrequencies to changes in the gain at the region of marginal stability is evaluated with cheap and accurate calculations. This work contributes to the understanding of thermoacoustic stability of combustors. In the same manner, the understanding of the nature of distinct resonance frequencies in unstable combustors may be enhanced by employing the analysis of the eigenfrequency locus here reported.
... Silva et al. 12 used their previous experimental results to identify that one of their observed frequency in the spectrum of combustion noise was arising due to the ITA modes, although it was not the dominant one. Recently, Albayrak et al. 13 reported that ITA modes are predominant in their perfectly premixed combustion system. In each case mentioned above, the mechanism that drives ITA mode is different. ...
... A simplified low-order network model analysis is performed to identify that the instability in the area contracted combustor is due to intrinsic flame-acoustic feedback loop. 19,20 Past experiments 11,13 have shown that ITA modes can be dominant in perfectly premixed systems. A similar exercise in the case of partially premixed configuration is vital, owing to its practical relevance. ...
We investigate the onset of thermoacoustic instabilities in a turbulent combustor terminated with an area contraction. Flow speed is varied in a swirl-stabilized, partially premixed combustor and the system is observed to undergo a dynamical transition from combustion noise to instability via intermittency. We find that the frequency of thermoacoustic oscillations does not lock-on to any of the acoustic modes. Instead, we observe that the dominant mode in the dynamics of combustion noise, intermittency and thermoacoustic instability is a function of the flow speed. We also find that the observed mode is insensitive to the changes in acoustic field of the combustor, but it varies as a function of upstream flow time scale. This new kind of thermoacoustic instability was independently discovered in the recent theoretical analysis of premixed flames. They are known as intrinsic thermoacoustic modes. In this paper, we report the experimental observation and the route to flame intrinsic thermoacoustic instabilities in partially premixed flame combustors. A simplified low-order network model analysis is performed to examine the driving mechanism. Frequencies predicted by the network model analysis match well with the experimentally observed dominant frequencies. Intrinsic flame-acoustic coupling between the unsteady heat release rate and equivalence ratio fluctuations occurring at the location of fuel injection is found to play a key role. Further, we observe intrinsic thermoacoustic modes to occur only when the acoustic reflection co-efficients at the exit are low. This result indicates that thermoacoustic systems with increased acoustic losses at the boundaries have to consider the possibility of flame intrinsic thermoacoustic oscillations.
... Many works have also investigated the factors influencing the location and magnitude of these extrema in the FTF. The influence of the swirler location on the time delays related to vorticity and acoustic waves was suggested to affect the FTF shape (Hirsch et al. 2005;Komarek and Polifke 2010;Albayrak et al. 2017). Longitudinal disturbances travel at the speed of sound while the azimuthal disturbances created at the downstream tip of the swirler travel at convective speed creating swirl number fluctuations (Palies et al. 2010. ...
Predicting the response of swirling flames subjected to acoustic perturbations poses significant challenges due to the complex nature of the flow. In this work, the effect of swirl number on the Flame Describing Function (FDF) is explored through a computational study of four bluff-body stabilised premixed flames with swirl numbers ranging between 0.44 and 0.97 and at forcing amplitudes of 7% and 25% of the mean bulk velocity. The LES model used for the simulations is validated by comparing two of those flames to experiments. The comparison is observed to be good with the computations capturing the unforced flow structure, flame height and FDF behaviour. It is found that changes in the swirl number can affect the location of the minima and maxima of the FDF gain in the frequency space. These locations are not affected by changes in the forcing amplitude, but the gain difference between the minima and the maxima is reduced as the forcing amplitude is increased. It is then attempted to scale the FDF using Strouhal numbers based on two different flame length scales. A length scale based on the axial height of the maximum heat release rate per unit length leads to a good collapse of the FDF gain curves. However, it is also observed that flow instabilities present in the flow can affect the FDF scaling leading to an imperfect collapse.
... Alternatively, proximity to a pure ITA or pure acoustic mode is used to identify an ITA or acoustic mode [11,[19][20][21] . Other studies, including [13,22], simply made use of the established characteristics of pure ITA modes, say, independence of eigenfrequency from combustor length or eigenfrequency correspondence with a characteristic time delay of the flame response, to identify ITA modes. ...
A recent study (Yong, Silva, and Polifke, Combust. Flame 228 (2021)) proposed the use of phasor diagrams to categorize marginally stable modes in an ideal resonator with a compact, velocity-sensitive flame. Modes with velocity phasors that reverse direction across the flame were categorized as ITA modes. The present study extends this concept to growing and decaying modes. In other words, with the method proposed, it is possible to distinguish whether a given thermoacoustic mode -- regardless of its stability -- should be categorized as acoustic or ITA. The method proposed does not rely on any parametric sweep, but on the angle relating the velocity phasors across the flame. This method of categorization reveals distinct regions in the complex plane where acoustic and ITA eigenfrequencies are localized. Additionally, we analyze the medium oscillation at the flame location to construct a physically intuitive understanding of the proposed categorization method.
... The nonlinear response of the the flame can be better characterised by consider perturbations with dual or even multiple harmonics. This phenomena have been confirmed from experimental observations [14][15][16][17] and results of numerical simulations [18][19][20]. In recent research, Han et al [21] numerically investigated the effect of two perturbations at 160 Hz and 320 Hz on the flame nonlinear response and the interaction of a lean premixed flame forced externally by strong input velocity oscillations. ...
The two-way interaction between the flame and acoustic waves leads to combustion instability. To understand and quantify the response of the flame to acoustic waves, studies have typically considered single-harmonic forcing of the flame, which assumes a dynamically linear or weakly nonlinear flame response. This study extends this approach by introducing an additional disturbance at the frequency St2 to influence the flame nonlinear response to the first perturbation at the frequency St1 to gain further insight into these associated combustion instabilities. The spatial front-tracking of premixed flames were derived from the analytical and numerical solutions of the G-equation model. The
nonlinear behavior of flame response was presented and the related mechanism of that was also elucidated. Due to the flame propagating forward normal to itself, from the near-order asymptotic analysis point of view, the third-order nonlinear interaction of the additional and first perturbations induces an external flame response related to St1. It significantly affects the first fundamental frequency response of the flame.
... Meanwhile, Emmert et al. [8] and Alp Albayrak et al. [9] conducted theoretical and experimental studies based on the BRS premix swirl burner, and showed that the ITA mode also existed in the BRS burner. Silva et al. [10] and Courtine et al. [11] studied the ITA mode through the Direct Numerical Simulation (DNS) method and proved that the ITA mode existed in the laminar premixed flame. ...
Thermoacoustic instability in the combustion chamber of gas turbines, aero and rocket engines has become a topic concern. In this paper, a new instability phenomenon in the field of the thermoacoustic instability - Intrinsic ThermoAcoustic instabilities (ITA) is studied. The classic thermoacoustic instability is caused by the coupling among acoustic disturbances, flow fluctuations and heat release pulsations. When the influence of acoustic disturbance is removed, there is still a thermoacoustic instability phenomenon in the combustion chamber, which is known as ITA. In the previous research on ITA, the scholars found that the ITA is mainly determined by the flame response, but many scholars neglected the influence of the mean flow and entropy waves. In this paper, the influence of the mean flow on the ITA mode in the duct and annular combustion chambers is studied by constructing a low-order acoustic network model. At the same time, it also explores the influence of other parameters on the ITA mode. The mean flow greatly affects the growth rate of the ITA mode, and has little effect on its frequency in the duct combustion chamber model. This is also the main reason for neglecting the effect of mean flow on the ITA mode in previous studies. In addition, the influence of other parameters on the ITA mode is also reflected in the growth rate. In the annular combustion chamber, a new ITA mode, which does not meet the −π criterion, is found. And the increase of Mach number makes all ITA modes more unstable. The circumferential mode number has a great influence on the high frequency ITA mode. In addition, the ITA mode has a significant effect on the thermoacoustic mode of the system in the annular combustion chamber.
... In this work, we focus on one of the eigenmodes investigated in Ref. [10]: the quarter wave mode of the combustor, which is labeled as a cavity mode [22]. Given nominal values of the flame model parameters and jR out j, the nominal values of the modal frequencies (x) and growth rates (a) of the cavity mode are calculated via the acoustic network model (Fig. 1), i.e., ðx ¼ 287:5 Hz; a ¼ À27:7 rad=sÞ for cavity mode. ...
One of the fundamental tasks in performing robust thermoacoustic design of gas turbine combustors is calculating the modal instability risk, i.e., the probability that a thermoacoustic mode is unstable, given input uncertainties. To alleviate the high computational cost associated with conventional Monte Carlo simulation, surrogate modeling techniques are usually employed. Unfortunately, in practice, it is not uncommon that only a small number of training samples can be afforded for surrogate model training. As a result, epistemic uncertainty may be introduced by such an "inaccurate" model, provoking a variation of modal instability risk calculation. In the current study, using Gaussian Process (GP) as the surrogate model, we address the following two questions: Firstly, how to quantify the variation of modal instability risk induced by the epistemic surrogate model uncertainty? Secondly, how to reduce the variation of risk calculation given a limited computational budget for the surrogate model training? For the first question, we leverage on the Bayesian characteristic of the GP model and perform correlated sampling of the GP predictions at different inputs to quantify the uncertainty of risk calculation. We show how this uncertainty shrinks when more training samples are available. For the second question, we adopt an active learning strategy to intelligently allocate training samples, such that the trained GP model is highly accurate particularly in the vicinity of the stability margin. As a result, a more accurate and robust modal instability risk calculation is obtained without increasing the computational cost of surrogate model training.
... In the current work, we focus on one of the eigenmodes investigated in [10]: the quarter wave mode of the combustor, which is labeled as a cavity mode [22]. Given nominal values of the flame model parameters and |R out |, the nominal values of the modal frequencies (ω) and growth rates (α) of the cavity mode are calculated via the acoustic network model (Fig. 1), i.e., (ω = 287.5Hz, ...
One of the fundamental tasks in performing robust thermoa-coustic design of gas turbine combustors is calculating the modal instability risk, i.e., the probability that a thermoacoustic mode is unstable, given various sources of uncertainty (e.g., operation or boundary conditions). To alleviate the high computational cost associated with conventional Monte Carlo simulation, surrogate modeling techniques are usually employed. Unfortunately, in practice it is not uncommon that only a small number of training samples can be afforded for surrogate model training. As a result, epistemic uncertainty may be introduced by such an "in-accurate" model, provoking a variation of modal instability risk calculation. In the current study, using Gaussian Process (GP) as the surrogate model, we address the following two questions: Firstly, how to quantify the variation of modal instability risk induced by the epistemic surrogate model uncertainty? Secondly, how to reduce the variation of risk calculation given a limited computational budget for the surrogate model training? For the first question, we leverage on the Bayesian characteristic of the GP model and perform correlated sampling of the GP predictions at different inputs to quantify the uncertainty of risk calculation. We show how this uncertainty shrinks when more training samples are available. For the second question, we adopt an active learning strategy to intelligently allocate training samples, such that the trained GP model is highly accurate particularly in the vicinity of the zero growth rate contour. As a result, a more accurate and robust modal instability risk calculation is obtained without increasing the computational cost of surrogate model training.
... Even if the pure acoustic eigenfrequencies might be known from an acoustic model, the (generally unknown) flame dynamics may alter these frequencies. Furthermore, intrinsic thermoacoustic (ITA) modes may play an important role [23][24][25]. Their frequencies are not predictable without knowledge of the flame dynamics. ...
Thermoacoustic properties of can-annular combustors are commonly investigated by means of single-can test-rigs. To obtain representative results, it is crucial to mimic can-can coupling present in the full engine. However, current approaches either lack a solid theoretical foundation or are not practicable for high-pressure rigs. In the present study we employ Bloch-wave theory to derive reflection coefficients that correctly represent can-can coupling. We propose a strategy to impose such reflection coefficients at the acoustic terminations of a single-can test-rig by installing passive acoustic elements, namely straight ducts or Helmholtz resonators. In an iterative process, these elements are adapted to match the reflection coefficients for the dominant frequencies of the full engine. The strategy is demonstrated with a network model of a generic can-annular combustor and a 3D model of a realistic can-annular combustor configuration. For the latter we show that can-can coupling via the compressor exit plenum is negligible for frequencies sufficiently far away from plenum eigenfrequencies. Without utilizing previous knowledge of relevant frequencies or flame dynamics, the test-rig models are adapted within a few iterations and match the full engine with good accuracy. Using Helmholtz resonators for test-rig adaption turns out to be more viable than using straight ducts.
... Even if the pure acoustic eigenfrequencies might be known from an acoustic model, the (generally unknown) flame dynamics may alter these frequencies. Furthermore, intrinsic thermoacoustic (ITA) modes may play an important role [23][24][25]. Their frequencies are not predictable without knowledge of the flame dynamics. Therefore, the passive acoustic elements in general have to be adapted in an iterative procedure, which ensures that the dominant frequency observed in the single-can test-rig converges to the dominant frequency of the full engine of a given azimuthal mode order m. ...
Thermoacoustic properties of can-annular combustors are commonly investigated by means of single-can test-rigs. To obtain representative results, it is crucial to mimic can-can coupling present in the full engine. However, current approaches either lack a solid theoretical foundation or are not practicable for high-pressure rigs. In the present study we employ Bloch-wave theory to derive reflection coefficients that correctly represent can-can coupling. We propose a strategy to impose such reflection coefficients at the acoustic terminations of a single-can test-rig by installing passive acoustic elements, namely straight ducts or Helmholtz resonators. In an iterative process, these elements are adapted to match the reflection coefficients for the dominant frequencies of the full engine. The strategy is demonstrated with a network model of a generic can-annular combus-tor and a 3D model of a realistic can-annular combustor configuration. For the latter we show that can-can coupling via the compressor exit plenum is negligible for frequencies sufficiently far away from plenum eigenfrequencies. Without utilizing previous knowledge of relevant frequencies or flame dynamics, the test-rig models are adapted within a few iterations and match the full engine with good accuracy. Using Helmholtz resonators for test-rig adaption turns out to be more viable than using straight ducts.
... For gaseous fuels, the first two effects obviously cannot play a role, instead the time required for convective transport of fuel from the injector to the reaction zone of the flame and for mixing of fuel and oxidizer 560 takes their place [29][30][31]. The acoustic inertia of the premix injector nozzle (the "burner") may also introduce phase lags between acoustic pressure perturbations and flow response [32,68,69]. For premixed flames, another crucial time delay is related to the convective transport of perturbations of the flame shape ("flame wrinkles") from the point of flame anchoring to the flame tip [25,26]. ...
The unsteady response of a flame to acoustic or flow perturbations plays a crucial role in thermoacoustic combustion instability. The majority of studies on this subject presents and analyzes flame dynamics in the frequency domain by means of a flame transfer function or a flame describing function. The present review concentrates on work that adopts a time-domain perspective. In such a framework, the linear dynamics of an acoustically compact flame is completely characterized by its impulse response. The concept of distributed time delays emerges as an appropriate description of the convective transport of flow and flame perturbations. A time-domain perspective facilitates the physics-based interpretation of important features of the flame response and supports the development of passive or active means of stability control. The present review first provides mathematical background on linear time-invariant systems and introduces the impulse response as a quantity that fully characterizes the dynamics of such systems. It will then be shown by way of example how typical features of the frequency response of premixed flames can be generated in a very natural, physically intuitive manner from time delay distributions. Analytical results for the impulse response of laminar premixed flames to modulations of velocity or equivalence ratio are presented in a unified framework. The next chapter discusses low-order parametric models, which exploit prior knowledge on the underlying convective processes that govern the flame dynamics, but nevertheless require input from experiment or high-fidelity simulation to fix parameter values. Next, a variety of approaches devised to derive distributed time delay models of flame dynamics from simulation data are reviewed. The most recent developments, which combine large eddy simulation of turbulent combustion with system identification, have demonstrated that it is possible to estimate reduced-order models of flame dynamics that are quantitatively accurate even for complex, swirling flame in geometries of technical interest. The last chapter reviews work on acoustically non-compact flames, strategies for passive control of thermoacoustic instabilities that exploit distributed delays, and the effect of convective dispersion on the time delay distribution and strength of entropy waves.
... The other mode (ω = 139.3Hz, α = −24.8rad/s) is identified as the intrinsic thermoacoustic mode [24][25][26]. We denote this mode as ITA mode. ...
In the preliminary phase of analysing the thermoacoustic characteristics of a gas turbine combustor, implementing robust design principles is essential to minimize detrimental variations of its thermoacoustic performance under various sources of uncertainties. In the current study, we systematically explore different aspects of robust design in thermoacoustic instability analysis, including risk analysis, control design and inverse tolerance design. We simultaneously take into account multiple thermoacoustic modes and uncertainty sources from both the flame and acoustic boundary parameters. In addition, we introduce the concept of a “risk diagram” based on specific statistical descriptions of the underlying uncertain parameters, which allows practitioners to conveniently visualize the distribution of the modal instability risk over the entire parameter space. Throughout the present study, a machine learning method called “Gaussian Process” (GP) modeling approach is employed to efficiently tackle the challenge posed by the large parameter variational ranges, various statistical descriptions of the parameters as well as the multifaceted nature of robust design analysis. For each of the investigated robust design tasks, we propose an efficient solution strategy and benchmark the accuracy of the results delivered by GP models. We demonstrate that GP models can be flexibly adjusted to various tasks while only requiring one-time training. Their adaptability and efficiency make this modeling approach very appealing for industrial practices.
... The other mode (ω = 139.3Hz, α = −24.8rad/s) is identified as the intrinsic thermoacoustic mode [?, 23,24]. We denote this mode as ITA mode. ...
In the preliminary phase of analysing the thermoacoustic characteristics of a gas turbine combustor, implementing robust design principles is essential to minimize detrimental variations of its thermoacoustic performance under various sources of uncertainties. In the current study, we systematically explore different aspects of robust design in thermoacoustic instability analysis, including risk analysis, control design and inverse tolerance design. We simultaneously take into account multiple thermoacoustic modes and uncertainty sources from both the flame and acoustic boundary parameters. In addition, we introduce the concept of a "risk diagram" based on specific statistical descriptions of the underlying uncertain parameters, which allows practitioners to conveniently visualize the distribution of the modal instability risk over the entire parameter space. Throughout the present study, a machine learning method called "Gaussian Process" (GP) modeling approach is employed to efficiently tackle the challenge posed by the large parameter variational ranges, various statistical descriptions of the parameters as well as the multifaceted nature of robust design analysis. For each of the investigated robust design tasks, we propose an efficient solution strategy and benchmark the accuracy of the results delivered by GP models. We demonstrate that GP models can be flexibly adjusted to various tasks while only requiring one-time training. Their adaptability and efficiency make this modeling approach very appealing for industrial practices.
... However, even laboratory burners tend to have more complex shapes; in particular they may have a constriction in cross-sectional area, for example due to the presence of a burner tube (see Figure 26). The configuration in Figure 26, which had been studied experimentally by Komarek and Polifke 15 in 2010, before ITA modes were recognised, was revisited by Albayrak et al. 48 with a fundamental study on ITA modes. ...
This paper gives an overview of the research performed by the project TANGO – an Initial Training Network (ITN) with an international consortium of seven academic and five industrial partners. TANGO is the acronym for ‘Thermoacoustic and Aeroacoustic Nonlinearities in Green combustors with Orifice structures’). The researchers in TANGO studied many of the intricate physical processes that are involved in thermoacoustic instabilities. The paper is structured in such a way that each section describes a topic investigated by one or more researchers. The topics include:
- transition from combustion noise to thermoacoustic instability
- development of an early-warning system by detecting the precursor of an instability
- analytical flame models based on time-lags
- Green's function approach for stability predictions from nonlinear flame models
- intrinsic thermoacoustic modes
- transport phenomena in swirl waves
- model of the flame front as a moving discontinuity
- development of efficient numerical codes for instability predictions
- heat exchanger tubes inside a combustion chamber
A substantial amount of valuable new insight was gained during this four-year project.
... Silva et al. (2017) showed that ITA modes could lead to the formation of characteristic peaks in the spectral 55 distribution of the sound pressure level of broadband combustion noise of turbulent flames. Recently, ITA modes were reported to be dominant in a perfectly premixed combustion system by Albayrak et al. (2018) and partially premixed turbulent combustion system by Murugesan et al. (2018). ...
This work investigates the effects of a moving flame front on the thermoacoustic oscillations in nonuniform combustors considering both the cavity and intrinsic resonant feedbacks. This theoretical study shows that the entropic perturbations can be generated by a perfectly premixed moving flame front in combustors with changes in cross section. Comparing with Direct Numerical Simulation (DNS) results shows the influence of the perturbation of a moving flame front on the intrinsic thermoacoustic stability. Applied to the verification of experimental results of a combustor consisting of multiple components, the present work predicts correctly the frequency and growth of both chamber resonant and intrinsic thermoacoustic (ITA) modes. Numerical research shows that alteration of reflection coefficients may both stabilize the chamber resonant and ITA modes of an experimental test rig. However, stabilizing the thermoacoustic oscillation by adjusting the boundary conditions seems less efficient in complicated combustion networks.
... We consider a turbulent premixed combustor composed of a plenum, a burner, a swirled premixed flame and a combustion chamber, as illustrated in Figure 2. This system, known as BRS combustor, has been widely used for the study of combustion noise and combustion instabilities (Komarek & Polifke 2010;Silva et al. 2017b;Albayrak et al. 2017). In this work, each element (plenum, burner, flame, combustion chamber) is represented by a state-space system of equations (Schuermans et al. 2002;Emmert et al. 2016). ...
... When a longitudinal acoustic wave propagates through a swirler, the local swirl number is mainly modulated by two mechanisms: the acoustic wave perturbs the axial flow velocity and generates fluctuations in tangential velocity due to interactions with the boundaries and the mean-flow [11,[41][42][43]. The tangential perturbations are convected by the meanflow and therefore propagate slower than the acoustic wave. ...
The acoustic transmissions and reflections of plane waves at duct singularities can be represented with so-called scattering matrices. This paper shows how to extract scattering matrices utilizing linearized compressible flow equations and provides a comparative study of different governing equations, namely the Helmholtz, linearized Euler and linearized Navier–Stokes equations. A discontinuous Galerkin finite element method together with a two-source forcing is employed. With this method, the scattering matrix for a radial swirler of a combustion test-rig is computed and validated against the results of a fully compressible Large-Eddy-Simulation. Analogously, the scattering behavior of an axial swirler is investigated. The influence of acoustic-hydrodynamic interactions, viscous effects as well as unsteady boundary layers on the results is investigated for both configurations. A thermoacoustic stability analysis of the combustion test-rig housing the axial swirler is carried out, utilizing the scattering matrix of the swirler. Major influence of the reflections coming from the swirler on the thermoacoustic eigenfrequencies is found.
This paper reviewed theoretical, numerical, and experimental studies on combustion instabilities in combustors for energy‐producing devices such as gas turbines, boilers, and furnaces utilizing oxyfuel combustion technology. Oxyfuel combustion as a CO2 capture technology gives encouraging and promising solutions for controlling greenhouse gases emission from combustion devices. However, the major concerns with oxyfuel systems are the combustion instabilities mainly arising from the CO2 dilution required for controlling excessive temperatures. Higher dilution levels or significantly nonuniform distribution of CO2 in the mixture can potentially lead to static and/or dynamic instabilities associated with local flame extinction and unsteady heat release rate, respectively. As in the case of lean premixed air/fuel flames, combustion instabilities are among the most critical operational challenges encountered in CO2‐diluted oxyfuel systems as well. Existing literature on flame instabilities has predominately focused on air‐fuel flames, with very few research studies dedicated to the same phenomena in oxyfuel combustion. With an ever‐increasing push toward carbon capture and reduction in NOx emissions, it has become important for the combustion community to accelerate research efforts in the direction of oxyfuel combustion systems. This review study on flame instabilities in oxyfuel combustors is one small step in that very direction. This paper starts with discussions on the theoretical mechanisms of combustion instabilities. Then a range of numerical and experimental studies, from premixed to non‐premixed flames, are presented and discussed. The main objective is to summarize recent progress in understanding instabilities in oxyfuel combustion systems, focusing primarily on the effect of CO2 dilution on flame stability. A range of experimental and numerical studies by various groups have strongly associated both static and dynamic instabilities in oxyfuel systems with diluent concentration, suggesting higher concentrations potentially result in a stratified mixture field which leads to higher heat release fluctuations and pressure oscillations. As such, many combustion systems use hydrogen enrichment to enhance static stability while employing flow and/or fuel modulation to dampen dynamic instabilities in oxyfuel combustors. Finally, we highlight and summarize some of the key issues and unsolved questions that still challenge researchers and, therefore, need to be the focus of future research work as regards to oxyfuel combustion. Oxy‐combustion can potentially ensure carbon‐free emissions. Diluted oxidizer in oxy‐combustion like O2/CO2 mixture can lead to static and/or dynamic instabilities associated with local flame extinction and unsteady heat release rate. With the existing literature on flame instabilities predominately focused on air‐fuel flames, this paper summarizes recent progress in understanding instabilities in oxy‐combustion systems. The paper brings together contemporary challenges while highlighting future research opportunities on the subject.
This paper investigates the intrinsic thermoacoustic (ITA) feedback and its possible interaction with the cavity acoustic resonance in swirling flame combustors under the configuration of axisymmetric perturbations. The dynamics of acoustic-vortical-entropic perturbations due to the unsteady heat release rate by a swirling flame are given in the presence of azimuthal and axial base flow velocities. The critical gain of ITA oscillations is given meanwhile parametric analysis show that the phase shift between acoustic and vortical waves plays an important role on the ITA critical gain. Applied to the configuration of a plenum-swirler-chamber combustor with the presence of swirling flames, the present work predicts correctly the thermoacoustic oscillations. Meanwhile, the criterion of ITA modes is given in matrix form. Analysis on the interaction between the ITA feedback and the cavity acoustic resonant feedback shows that the thermoacoustic modes of the whole system are composed of both ITA-oriented modes and the cavity-oriented resonant modes. Increasing the transit time difference between the acoustic and vortical waves reduces frequencies of ITA and ITA-oriented modes and worsens their stabilities. The cavity-oriented thermoacoustic mode, on the other hand, forms a spiral orbit and approaches to an attractor, which is independent of the transit time difference.
Phasor diagrams are utilized to plot and analyze thermoacoustic modes in a duct with ideal closed/open acoustic boundary conditions that contains a velocity-sensitive flame. Inspection of phasor diagrams that represent fluctuations of velocity, pressure, heat release rate and characteristic wave amplitudes at the flame elicits characteristic features of marginally stable, intrinsic thermoacoustic (ITA) modes: the sign of velocity fluctuations and the sign of the gradient of pressure fluctuations change across the flame. These sign changes result from a reversal of direction of the velocity phasor across the flame, affected by unsteady heat release exactly out-of-phase with respect to upstream velocity fluctuations and of sufficient strength. Unlike alternative methods proposed for the identification of ITA modes, the proposed categorization does not involve a parameter sweep, but relies on an analogy with the structure of ITA modes in an anechoic environment. The phasor diagram also elucidates that continuous transitions from acoustic to ITA modes and vice versa can be achieved by an increase or decrease of the gain of the flame transfer function. The representation of acoustic wave propagation in terms of phasors facilitates the formulation of a compact dispersion relation of the thermoacoustic configuration under consideration. The value of the transitional gain of the flame transfer function, where acoustic/ITA transitions occur, may be deduced easily from the dispersion relation. A plot of solution branches of acoustic and ITA modes illustrates how the respective mode transition, and how they can be related to the well-known quarter wave modes of a closed/open resonator. It is observed that under variation of transfer function gain and phase, marginally stable eigenmodes may occur at almost any frequency, not only at frequencies that correspond to the quarter-wave modes.
This conceptual numerical study explores a possible strategy for control of unstable intrinsic thermoacoustic (ITA) modes. Control of the ITA feedback loop has not been discussed yet. We propose addition of hydrogen fuel as a means of control and investigate the effect of incremental addition to the fuel mixture on the stability of a laminar slit flame using a variety of approaches: first, the ITA frequencies are estimated by a chemical kinetics solver for hydrogen fuel content up to 50% of the total fuel mass flow. Second, we perform DNS for each case and compute the Flame Transfer Function (FTF), from which the ITA mode frequencies and their stability can be estimated. Additionally, for each case the unstable flame is computed to confirm the estimated ITA mode frequencies. Third, an acoustic network model is employed, which uses the FTFs and predicts the stability limits observed by the DNS. Comparison with DNS data features very good agreement and allows to model the impact of hydrogen on the stability of the combustor.
Many physical systems are subject to uncertainty in operating regimes, boundary conditions, and physical parameter values. The generalized polynomial chaos (gPC) framework offers methods to represent and propagate uncertainties through the governing equations by means of spectral expansions in random space. The present study combines intrusive gPC with a state-space thermoacoustic model to account for uncertainties in combustion noise prediction of confined flames. The acoustic waves, flame response and acoustic reflection coefficients are modeled as stochastic variables and projected onto a finite set of gPC basis functions. By solving the resulting set of equations once, it is possible to determine probability density functions of acoustic quantities at each node of the discretized domain. Results of the proposed method are satisfactorily validated against Monte Carlo simulation and compared with experiments. We show that the contribution of the flame response uncertainties (magnitude and phase) to the sound pressure level produced by combustion is particularly important within a frequency range, which is close to the frequency characterizing the intrinsic thermoacoustic feedback loop. Additionally, we demonstrate the simplicity of performing global sensitivity analysis once the gPC coefficients are available. Furthermore, non-intrusive gPC is applied to the deterministic state-space model of the system and computational costs are compared with those of the intrusive gPC counterpart.
In this study, the effect of CO2 dilution on the thermoacoustic stability of propane‐oxyfuel flames is studied in a non‐premixed, swirl‐stabilized combustor. The results, obtained at a fixed combustor power density (4 MW/m3 bar) and global stoichiometric equivalence ratio (Φ = 1.0), show that the oxy‐flame is stable at 0% and low CO2 concentrations in the oxidizer. A self‐amplifying coupling between heat release and pressure fluctuations was observed to occur at the CO2 concentration of 45%, which matches the point of flame transition from a jet‐like to a V‐shaped flame resulting from the formation of inner recirculation zone. The observed frequency for both the pressure and heat release oscillations is 465 Hz and the ensuing thermoacoustic instability is believed to have been resulted from vortexes and flame interactions. Subsequent to the coupling of the oscillations at the CO2 concentration of 45%, their amplitudes grew at 50% to 60% CO2 dilution levels. The maximum amplitude was observed at 60% CO2 concentration after which, as CO2 dilution level increases, the acoustic amplitude and that of its counterpart in the heat release spectrum decreased due to damping (energy dissipation) arising from heat loss and viscous dissipation. An increase in hydrogen concentration in the fuel and a decrease in the combustor power density were observed to lower the acoustic amplitude. Furthermore, a frequency shift is observed with a change in the combustor firing rate, which shows that the mode scales with the flow velocity, and therefore, unlikely to be a natural acoustic mode of the combustor. This study, therefore, reveals thermoacoustic instability in non‐premixed oxy‐combustion driven by changes in flame dynamics and macrostructures as the CO2 concentration in the oxidizer mixture varies.
Thermo-acoustic combustion instabilities arise from feedback between flow perturbations and the unsteady heat release rate of a flame in a combustion chamber. In the case of a premixed, swirl stabilized flame, an unsteady heat release rate results from acoustic velocity perturbations at the burner inlet on the one hand, and from azimuthal velocity perturbations, which are generated by acoustic waves propagating across the swirler, on the other. The respective time lags associated with these flow–flame interaction mechanisms determine the overall flame response to acoustic perturbations and therefore thermo-acoustic stability. The propagation of azimuthal velocity perturbations in a cylindrical duct is commonly assumed to be convective, which implies that the corresponding time lag is governed by the speed of convection. We scrutinize this assumption in the framework of small perturbation analysis and modal decomposition of the Euler equations by considering an initial value problem. The analysis reveals that azimuthal velocity perturbations in swirling flows should be regarded as dispersive inertial waves. As a result of the restoring Coriolis force, wave propagation speeds lie above and below the mean flow bulk velocity. The differences between wave propagation speed and convection speed increase with increasing swirl. A linear, time invariant step response solution for the dynamics of inertial waves is developed, which can be approximated by a concise analytical expression. This study enhances the understanding of the flame dynamics of swirl burners in particular, and contributes physical insight into the inertial wave dynamics in general.
The interplays between acoustic and intrinsic modes in a model of a Rijke burner are revealed and their influence on the prediction of thermoacoustic instabilities is demonstrated. To this end, the system is examined for a range of time delays, temperature ratios and reflection coefficients as adjustable parameters. A linear acoustic network model is used and all modes with frequency below the cut-on frequency for non-planar acoustic waves are considered. The results show that when reflection coefficients are reduced, the presence of a pure ITA mode limits the reduction in the growth rate that usually results from a reduction of the reflection coefficients. In certain conditions, the growth rates can even increase by decreasing reflections. As the time delay of the flame and thus the ITA frequency decreases, the acoustic modes couple to and subsequently decouple from the pure ITA modes. These effects cause the maximum growth rate to alternate between the modes. This investigation draws a broad picture of acoustic and intrinsic modes, which is crucial to accurate prediction and interpretation of thermoacoustic instabilities.
The influence of Intrinsic Thermoacoustic (ITA) feedback on the combustion noise spectrum produced by a confined, turbulent, premixed, swirl flame is investigated. The analysis is based on the understanding that sound is generated by unsteady heat release resulting from turbulent fluctuations on the one hand, and from the response of the flame to incoming acoustic perturbations on the other. The former effect is described by a source term for combustion noise, i.e. a spectral distribution of unsteady heat release rate, the latter by the flame transfer function. Both quantities are identified from time series data for fluctuating velocity and heat release rate, generated with large eddy simulation of premix swirl burner. The combustion noise source term and the flame transfer function are then introduced in an acoustic network model of the test rig in order to compute the spectral distribution of the sound pressure level at a certain location in the combustion chamber. Results for the noise spectrum are in good agreement with experiment, showing a broadband component and well-defined peaks. The frequencies of the peaks correspond to either acoustic cavity or ITA resonances. The acoustic network model is used for parametric studies, where the acoustic reflection coefficient at the combustor exit is varied. Remarkably, it is found that the magnitude of the ITA peak increases with decreasing values of the acoustic reflection coefficient, and vice versa. Furthermore, the influence of combustion chamber length on resonance frequencies is explored. It is observed that the frequency of the ITA resonance is insensitive to combustor length. This behaviour is observed qualitatively also in experiments.
Premixed flames are velocity sensitive, i.e., they react to a velocity perturbation at the burner mouth, say, with fluctuations in heat release rate. Unsteady heat release generates acoustic waves that travel back from the flame to the burner mouth, where they modulate the velocity and thereby close an intrinsic thermoacoustic (ITA) feedback loop. The present paper demonstrates that corresponding ITA eigenmodes are in general important for the dynamics and stability of premixed combustion systems. It is shown that the complete set of eigenmodes of a combustor test rig should be interpreted as the sum of acoustic and ITA eigenmodes. A procedure is presented which allows to distinguish between eigenmodes that may be considered as acoustic modes driven by the flame, versus those resulting from ITA feedback (but influenced by the acoustic properties of the combustor). This procedure is based on a factorization of the dispersion relation of the thermoacoustic model. Differences between the acoustic and intrinsic eigenmodes of a combustor test rig, in particular the corresponding mode shapes, are discussed. The paradoxical observation that increased acoustic losses at the boundaries may destabilize a combustion system is explained as an instability of the dominant ITA mode.
Combustion dynamics (or combustion oscillations) have emerged as a significant consideration in the development of low-emission gas turbines. To date, the effect of premix fuel nozzle geometry on combustion dynamics has not been well-documented. This paper presents experimental stability data from several different fuel nozzle geometries (i.e., changing the axial position of fuel injection in the premixer, and considering simultaneous injection from two axial positions). Tests are conducted in a can-style combustor designed specifically to study combustion dynamics. The operating pressure is fixed at 7.5 atmospheres and the inlet air temperature is fixed at 588K (600F). Tests are conducted with a nominal heat input of 1MWth (3MBTUH). Equivalence ratio and nozzle reference velocity are varied over the ranges typical of premix combustor design. The fuel is natural gas. Results show that observed dynamics can be understood from a time-lag model for oscillations, but the presence of multiple acoustic modes in this combustor makes it difficult to achieve stable combustion by simply re-locating the point of fuel injection. In contrast, reduced oscillating pressure amplitude was observed at most test conditions using simultaneous fuel injection from two axial positions.
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The present study models a thermoacoustic system in the time domain where, in the limit of small amplitudes, the linear dynamics of a heat source is incorporated in terms of a distributed time lag response function. This approach allows for a description of the heat source that is richer than that in single time lag models such as the well-known n–τ model or modifications thereof. Methods to extract the distributed time lag response function from numerical/experimental frequency response data and to conduct a linear stability analysis for distributed delay differential equations are described in this work. The theory is applied to the test case of experimentally measured frequency response data of a turbulent premixed swirl flame. The use of a distributed time lag response function model for the heat source is shown to contain the entire dynamics of the heat source, as all characteristic timescales of the flame response are inherently reflected in the response function itself. It therefore gives an accurate estimate of the linear stability map in addition to generating valuable insight into the physics behind the transient flame dynamics. In contrast, we show that a single time lag model can only yield correct stability predictions if the unstable eigenfrequency of the system is known a priori with good accuracy. We also show that a single time lag model is in general not capable of capturing the transient dynamics of a thermoacoustic system correctly. It is concluded that the linear response of the heat source in a thermoacoustic system should be represented in terms of a distributed time lag response function rather than a single time lag model, with a view to retaining the rich complexity that is available even in such a low-order model for the heat source.
A study on the velocity sensitivity and intrinsic thermoacoustic stability of a laminar, premixed, Bunsen-type flame is carried out. Direct numerical simulation (DNS) of the flame, placed in an acoustically anechoic environment and subjected to broad-band, low-amplitude acoustic forcing, generates time series of fluctuating heat release rate, velocities and pressure. The time series data is post-processed with system identification to estimate the impulse response and transfer function of the flame. The associated frequency response is validated against experiment with good accuracy. DNS results obtained with acoustic excitation from the inlet or outlet boundary, respectively, confirm that the flame responds predominantly to perturbations of velocity. The stability of eigenmodes related to intrinsic thermoacoustic feedback is investigated with a network model. Both stable and unstable intrinsic thermoacoustic modes are predicted, depending on details of the configuration. The predicted modes are directly observed in direct numerical simulations, with good agreement in frequencies and stability.
Premixed flames respond to velocity perturbations with fluctuations in heat release rate ("thermal response"), which in turn generate acoustic perturbations ("acoustic response"). The latter may subsequently influence the velocity field in such a manner that feedback leads to self-excited thermoacoustic instability. The present paper investigates interrelations between the thermal and the acoustic responses of premix flames. The analysis is formulated such that it properly represents the underlying causality of acoustics--flow--flame--acoustics interactions. A flame-intrinsic feedback loop is revealed, which is quite independent of the acoustic environment of the flame, i.e. the acoustic impedances of plenum and combustor. The eigenmodes of this flame-intrinsic feedback loop coincide with poles of the acoustic scattering matrix of the flame. The corresponding frequencies, where the acoustic response is maximum, are in general quite different from frequencies where the thermal response is strong, i.e. where the flame transfer function exhibits "excess gain". Even more remarkable, the intrinsic flame modes may result in thermoacoustic instabilities without lock-on to one of the acoustic eigenmodes of the combustor. Experimental results from two combustor test rigs with laminar conical as well as turbulent swirl flames are scrutinized and are found to confirm our analysis. In particular, unstable modes are identified that are strongly related to flame-intrinsic modes.
Large eddy simulations of compressible, turbulent, reacting flow were carried out in order to identify the Flame Transfer Function (FTF) of a premixed swirl burner at different power ratings. The Thickened Flame model with one step kinetics was used to model combustion. Time-averaged simulation results for inert and reacting flow cases were compared with experimental data for velocity and heat release distribution with good agreement. Heat losses at the combustor walls were found to have a strong influence on computed flame shapes and spatial distributions of heat release. For identification of the FTF with correlation analysis, broadband excitation was imposed at the inlet. At low power rating (30 kW), measured and computed FTFs agree very well at low frequencies (corresponding to Strouhal numbers St < 4), showing a pronounced maximum of the gain at St ≈ 2. At higher frequencies, where the flame response weakens, the agreement between experiment and computation deteriorates, presumably due to decreasing signal-to-noise ratio. At higher thermal power (50 kW), a high-frequency instability developed during the simulation runs, resulting in poor overall signal-to-noise ratio and thus to unsatisfactory prediction of the gain of the flame transfer function. The phase of the FTF, on the other hand, was predicted with good accuracy up to St < 5. An analytical expression for the FTF, which models the flame dynamics as a superposition of time-delayed responses to perturbations of mass flow rate and swirl number, respectively, was found to match the experimental results.
The influence of thermal boundary condition at the combustor wall and combustor confinement on the dynamic flame response of a perfectly premixed axial swirl burner is investigated. Large Eddy Simulations are carried out using the Dynamically Thickened Flame combustion model. Then, system identification methods are used to determine the flame transfer function (FTF) from the computed time series data.
Two configurations are compared against a reference case with 90 mm × 90 mm combustor cross section and nonadiabatic walls: 1) combustor cross section similar to the reference case with adiabatic combustor walls, and 2) different confinement (160 mm × 160 mm) with nonadiabatic walls. It is found that combustor confinement and thermal boundary conditions have a noticeable influence on the flame response due to differences in flame shape and flow field. In particular the FTF computed with adiabatic wall boundary condition, which produces a flame with significant heat release in both shear layers, differs significantly from the FTF with nonadiabatic walls, where the flame stabilizes only in the inner shear layer. The observed differences in flow field and flame shape are discussed in relation to the unit impulse response of the flame. The impact of the differences in FTF on stability limits is analyzed with a low-order thermoacoustic model.
The introduction of lean premix combustion increases the susceptibility of the combustor to thermoacoustic instabilities. To control these instabilities, information about the dynamic behavior of the combustion process is necessary. The flame transfer function offers one possibility to describe the dynamic behavior of the combustion process. It relates velocity fluctuations through the burner to an overall heat release fluctuation caused by the flame. As the transfer function for turbulent premix swirl flames can not be derived accurately from first principles, an alternative approach is needed. This paper introduces and validates a method, based on computational fluid dynamics (CFD), to reconstruct flame transfer functions. A transient simulation of the turbulent reacting flow is performed with broad band excitation of the flow variables on the boundaries. On the basis of the resulting time series for velocity and heat release, the transfer function of the flame is reconstructed by application of a system identification procedure based on the Wiener-Hopf equation. This method is applied to a lean perfectly premixed swirl burner. The resulting transfer function is validated with experimental data up to frequencies of f = 400 Hz. Good qualitative agreement is observed between the two approaches. Remarkably, the absolute value of the flame transfer function (the ‘gain’ of the flame) is found to be larger than unity over a range of frequencies, even though fluctuations of heat release and velocity are normalized with their mean flow values. To gain insight into this phenomenon, the dynamic behavior of the flame is investigated in detail. This concerns in particular the interaction of velocity, heat release fluctuations, the swirl number, and fluctuations of flame position and shape. Instead of broad band excitation, single frequency excitation is applied on the boundary for these investigations. It is found that swirl number fluctuations are convected into the flame. At the frequency where the wavelength of those fluctuations agrees with the length scale of the flame, unburned gases accumulate in the combustor. The excess heat is released periodically, which causes the overshoot in the absolute value of the flame transfer function.
The paper investigates the determination and the scaling of thermo acoustical characteristics of lean premixed flames as used in gas turbine combustion systems. In the first part, alternative methods to characterize experimentally the flame dynamics are outlined and are compared on the example of a scaled model of an industrial gas turbine burner. Transfer matrix results from the most general direct method are contrasted with data obtained from the hybrid method, which is based on Rankine-Hugoniot relations and the experimental flame transfer function obtained from OH*-chemiluminescence measurements. Also the new network model based regression method is assessed, which is based on a n - tau - sigma dynamic flame model. The results indicate very good consistency between the three techniques, providing a global check of the methods/tools used for analyzing the thermo acoustic mechanisms of flames. In the second part, scaling rules are developed that allow to calculate the dynamic flame characteristics at different operation points. Towards this a geometric flame length model is formulated. Together with the other operational data of the flame it provides the dynamic flame model parameters at these points. The comparison between the measured and modeled flame lengths as well as the n - tau - sigma parameters shows an excellent agreement.
Combustion instabilities represent a long known problem in combustion technology. The complex interactions between acoustics and turbulent swirling flames are not fully understood yet, making it very difficult to reliably predict the stability of new combustion systems. For example, the effects of fluctuations of swirl number on the heat release of the flame have to be investigated in more detail. In this paper a perfectly premixed, swirl stabilized burner with variable axial position of the swirl generator is investigated. In experiments, the position of the swirl generator has a strong impact on the dynamic flame response, although it does not influence the time-averaged distribution of the heat release significantly. This phenomenon is further investigated, using computational fluid dynamics combined with system identification. The generation of fluctuations of swirl number, their propagation to the flame, and their effect on the dynamic flame response are examined. A simple model based on convective time lags is developed, showing good agreement with experiments.
The response of a premixed flame to quasi-steady flow perturbations is considered. It is found that in this low-frequency limit, constraints on the flame transfer function can be established from global conservation laws for mass, energy, and momentum. For example, the transfer function between velocity fluctuations and heat release of a perfectly premixed flame without fluctuations of equivalence ratio should be unity in the limit of zero frequency, while for a combustion system with constant mass flow rate of fuel, the transfer function should tend toward zero. It is demonstrated that these considerations can be employed to reduce the number of unknowns in analytical flame models or identify invalid modeling assumptions.
The study is concerned with theoretical examination of thermo-acoustic instabilities in combustors and focuses on recently discovered ‘flame intrinsic modes’. These modes differ qualitatively from the acoustic modes in a combustor. Although these flame intrinsic modes were intensely studied, primarily numerically and experimentally, the instability properties and dependence on the characteristics of the combustor remain poorly understood. Here we investigate analytically the properties of intrinsic modes within the framework of a linearized model of a quarter wave resonator with temperature and cross-section jump across the flame, and a linear n−τ model of heat release. The analysis of dispersion relation for the eigen-modes of the resonator shows that there are always infinite numbers of intrinsic modes present. In the limit of small interaction index n the frequencies of these modes depend neither on the properties of the resonator, nor on the position of the flame. For small n these modes are strongly damped. The intrinsic modes can become unstable only if n exceeds a certain threshold. Remarkably, on the neutral curve the intrinsic modes become completely decoupled from the environment. Their exact dispersion relation links the intrinsic mode eigen-frequency ω i with the mode number m i and the time lag τ: ω i = ( 2 m i + 1 )( π/τ) + mπ/τ, where m = 0 , + / −1. The main results of the study follow from the mode decoupling on the neutral curve and include explicit analytic expressions for the exact neutral curve on the n−τ plane, and the growth/decay rate dependence on the parameters of the combustor in the vicinity the neutral curve. The instability domain in the parameter space was found to have a very complicated shape, with many small islands of instability, which makes it difficult, if not impossible, to map it thoroughly numerically. The analytical results have been verified by numerical examination.
This paper presents recent progress in the field of thermoacoustic combustion instabilities in propulsion engines such as rockets or gas turbines. Combustion instabilities have been studied for more than a century in simple laminar configurations as well as in laboratory-scale turbulent flames. These instabilities are also encountered in real engines but new mechanisms appear in these systems because of obvious differences with academic burners: larger Reynolds numbers, higher pressures and power densities, multiple inlet systems, complex fuels. Other differences are more subtle: real engines often feature specific unstable modes such as azimuthal instabilities in gas turbines or transverse modes in rocket chambers. Hydrodynamic instability modes can also differ as well as the combustion regimes, which can require very different simulation models. The integration of chambers in real engines implies that compressor and turbine impedances control instabilities directly so that the determination of the impedances of turbomachinery elements becomes a key issue. Gathering experimental data on combustion instabilities is difficult in real engines and large Eddy simulation (LES) has become a major tool in this field. Recent examples, however, show that LES is not sufficient and that theory, even in these complex systems, plays a major role to understand both experimental and LES results and to identify mitigation techniques.
Recent studies [Hoeijmakers etal. 2014, Emmert etal. 2015] suggest that thermoacoustic modes can appear in combustors with anechoic terminations, which have no acoustic eigenmodes. These modes, called here Intrinsic ThermoAcoustic (ITA), can be predicted with simple theoretical arguments, but have been ignored for a long time. They are reproduced in this paper using Direct Numerical Simulation (DNS) of a laminar premixed Bunsen type flame. DNS results and theory are compared showing very good agreement in terms of both frequency and mode structure. DNS confirms that the frequency of ITA modes does not depend on any acoustic characteristic of the burner. Based on a numerical evaluation of the Flame Transfer Function, stability limits of ITA modes predicted by theory are also recovered in the DNS with reasonable accuracy. Finally, DNS is used to analyze the mechanisms of ITA modes.
This paper shows that a flame can be an intrinsically unstable acoustic element. The finding is clarified in the framework of an acoustic network model, where the flame is described by an acoustic scattering matrix. The instability of the flame acoustic coupling is shown to become dominating in the limit of no acoustic reflections. This is in contrast to classical standing-wave thermoacoustic modes, which originate from the positive feedback loop between system acoustics and the flame. These findings imply that the effectiveness of passive thermoacoustic damping devices is limited by the intrinsic stability properties of the flame.
In many continuous combustion processes, such as those found in aeroengines or gas turbines, the flame is stabilized by a swirling flow formed by aerodynamic swirlers. The dynamics of such swirling flames is of technical and fundamental interest. This article reviews progress in this field and begins with a discussion of the swirl number, a parameter that plays a central role in the definition of the flow structure and its response to incoming disturbances. Interaction between the swirler response and incoming acoustic perturbations generates a vorticity wave convected by the flow, which is accompanied by azimuthal velocity fluctuations. Axial and azimuthal velocities in turn define the flame response in terms of heat--release rate fluctuations. The nonlinear response of swirling flames to incoming disturbances is conveniently represented with a flame describing function (FDF), in other words, with a family of transfer functions depending on frequency and incident axial velocity amplitudes. The FDF, however, does not reflect all possible nonlinear interactions in swirling flows. This aspect is illustrated with experimental data and some theoretical arguments in the last part of this article, which concerns the interaction of incident acoustic disturbances with the precessing vortex core, giving rise to nonlinear fluctuations at the frequency difference.
The transition in dynamics from low-amplitude, aperiodic, combustion noise to high-amplitude, periodic, combustion instability in confined, combustion environments was studied experimentally in a laboratory-scale combustor with two different flameholding devices in a turbulent flow field. We show that the low-amplitude, irregular pressure fluctuations acquired during stable regimes, termed 'combustion noise', display scale invariance and have a multifractal signature that disappears at the onset of combustion instability. Traditional analysis often treats combustion noise and combustion instability as acoustic problems wherein the irregular fluctuations observed in experiments are often considered as a stochastic background to the dynamics. We demonstrate that the irregular fluctuations contain useful information of prognostic value by defining representative measures such as Hurst exponents that can act as early warning signals to impending instability in fielded combustors.
The transition in dynamics from low-amplitude, aperiodic, combustion noise to high-amplitude, periodic, combustion instability in confined, combustion environments was studied experimentally in a laboratory-scale combustor with two different flameholding devices in a turbulent flow field. We show that the low-amplitude, irregular pressure fluctuations acquired during stable regimes, termed ‘combustion noise’, display scale invariance and have a multifractal signature that disappears at the onset of combustion instability. Traditional analysis often treats combustion noise and combustion instability as acoustic problems wherein the irregular fluctuations observed in experiments are often considered as a stochastic background to the dynamics. We demonstrate that the irregular fluctuations contain useful information of prognostic value by defining representative measures such as Hurst exponents that can act as early warning signals to impending instability in fielded combustors.
The thermoacoustic stability of velocity sensitive premixed flames is investigated. A causal representation of the flow-flame-acoustic interactions reveals a flame-intrinsic feedback mechanism. The feedback loop may be described as follows: An upstream velocity disturbance induces a modulation of the heat release rate, which in turn generates an acoustic wave traveling in the upstream direction, where it influences the acoustic velocity and thus closes the feedback loop. The resonances of this feedback dynamics, which are identified as intrinsic eigenmodes of the flame, have important consequences for the dynamics and stability of the combustion process in general and the flame in particular. It is found that the amplification of acoustic power by flame-acoustic interactions can reach very high levels at frequencies close to the intrinsic eigenvalues due to the flame-internal feedback mechanism. This is shown rigorously by evaluating the “instability potentiality” from a balance of acoustic energy fluxes across the flame. One obtains factors of maximum (as well as minimum) power amplification. Based on the acoustic energy amplification, the small gain theorem is introduced as a stability criterion for the combustion system. It allows to formulate an optimization criterion for the acoustic characteristics of burners or flames without regard of the boundary conditions offered by combustor or plenum. The concepts and methods are exemplified first with a simplistic n-τn-τ model and then with a flame transfer function that is representative of turbulent swirl burners.
The flame transfer function (FTF) of a premixed swirl burner was identified from time series generated with CFD simulation of compressible, turbulent, reacting flow at non-adiabatic conditions. Results were validated against experimental data. For large eddy simulation (LES), the Dynamically Thickened Flame combustion model with one step kinetics was used. For unsteady simulation in a Reynolds-averaged Navier-Stokes framework (URANS), the Turbulent Flame Closure model was employed. The FTF identified from LES shows quantitative agreement with experiment for amplitude and phase, especially for frequencies below 200 Hz. At higher frequencies, the gain of the FTF is underpredicted. URANS results show good qualitative agreement, capturing the main features of the flame response. However, the maximum amplitude and the phase lag of the FTF are underpredicted. Using a low-order network model of the test rig, the impact of the discrepancies in predicted FTFs on frequencies and growth rates of the lowest order eigenmodes were assessed. Small differences in predicted FTFs were found to have a significant impact on stability limits. Stability behavior in agreement with experimental data was achieved only with the LES-based flame transfer function.
The present study develops an alternative perspective on the response of premixed flames to flow perturbations. In particular, the linear response of laminar premixed flames to velocity perturbations is examined in the time domain, and the corresponding impulse response functions are determined analytically. Different flame types and shapes as well as different velocity perturbation models are considered. Two contributions to the flame response are identified: a convective displacement of the flame due to velocity perturbations, and a restoration mechanism, which is a consequence of the combined effects of flame propagation and flame anchoring. The impulse responses are used to identify the relevant time scales and to form non-dimensional frequencies. The link of the present results to previous studies formulated in the frequency domain is established. The time domain approach is found to facilitate analysis and interpretation of well-known properties of premixed flames such as excess gain, periodic cutoff and self-similar aspects of flame response. Characteristic time scales of response appear naturally and can be interpreted in a straightforward manner.
The dynamics of premixed confined swirling flames is investigated by examining their response to incident velocity perturbations. A generalized transfer function designated as the flame describing function (FDF) is determined by sweeping a frequency range extending from 0 to 400 Hz and by changing the root mean square fluctuation level between 0% and 72% of the bulk velocity. The unsteady heat release rate is deduced from the emission intensity of OH* radicals. This global information is complemented by phase conditioned Abel transformed emission images. This processing yields the distribution of light emission. By assuming that the light intensity is proportional to the heat release rate, it is possible to deduce the distribution of unsteady heat release rate in W m−3 and see how it evolves with time during the modulation cycle and for different forcing frequencies. These data can be useful for the determination of regimes of instability but also give clues on the mechanisms which control the swirling flame dynamics. It is found from experiments and demonstrated analytically that a swirler submitted to axial acoustic waves originating from the upstream manifold generates a vorticity wave on its downstream side. The flame is then submitted to a transmitted axial acoustic perturbation which propagates at the speed of sound and to an azimuthal velocity perturbation which is convected at the flow velocity. The net result is that the dynamical response and unsteady heat release rate are determined by the combined effects of these axial and induced azimuthal velocity perturbations. The former disturbance induces a shedding of vortices from the injector lip which roll-up the flame extremity while the latter effectively perturbs the swirl number which results in an angular oscillation of the flame root. This motion is equivalent to that which would be induced by perturbations of the burning velocity. The phase between incident perturbations is controlled by the convective time delay between the swirler and the injector. The constructive or destructive interference between the different perturbations is shown to yield the low and high gains observed for certain frequencies.
This work deals with modeling and control of thermoacoustic combustion instabilities in lean premixed combustion systems. Because of the complex interactions present in thermoacoustic systems, a network modeling approach is used. The model of each network element or subsystem is obtained analytically, numerically, or by making use of experimental techniques. The dynamics of a network system are determined experimentally by making use of a transfer matrix measurement technique. The transfer functions of a premixed flame have been determined experimentally on an atmospheric combustion test facility with a full-scale gas turbine burner, for a wide variety of operating conditions. An analytical model of the dynamic behavior of the reaction zone was made. In this model, the heat release fluctuations are assumed to be caused by fluctuations of the mass fraction of fuel and by fluctuations in the burning velocity. The model proved to be in good agreement with experimental results. Wave propagation in complex three-dimensional geometries is modeled by making use of a modal expansion technique. The modes used for the modal expansion can be obtained analytically for relatively simple geometries, or numerically (finite element method) for geometries of any complexity. By representing the modal expansion in state-space, a very numerically efficient and robust model is obtained. The thermoacoustic network model combines the state-space representations of the sub-systems in one system. The system can be analyzed in the time domain or in the frequency domain. The stability analysis is straightforward and does not require a numerical search. Non linear elements can easily be incorporated in the time domain simulation. This novel method has been validated by comparison with analytic solutions of simple thermoacoustic systems found in literature, by comparison with Finite Element codes, and by comparison with experimental results. An excellent agreement was found for all comparisons. When including non-linear elements in an annular system, a rotating acoustic field is predicted, which corresponds to experimental observations. This result has been verified analytically. Based on network models, a model based controller has been obtained using H∞ optimization. This controller has been tested in simulation and experiment on a single burner rig and proved to suppress acoustic levels by more than 25dB. An adaptive controller, based on a genetic algorithm, has been developed that does not require any knowledge about the system. This controller has been tested and proved to have similar performance as the model-based controllers. An active control system for multi-burner configurations has been developed and proved to perform well in simulations. Nous proposons dans ce travail une méthode de modélisation et de réglage des instabilités thermoacoustiques dues à la combustion. Le modèle s'applique au brûleur utilisant un pré-mélange air-combustible riche en comburant. Pour un système thermoacoustique complexe un réseaux de modules peut être utilisé. Chaque modules ou sous-systèmes comportent alors un modèle obtenu de façon analytique, ou numérique ou provenant de techniques expérimentales. La dynamique d'un tel système est obtenu expérimentalement, on en déduit la fonction de transfert sous forme matricielle. En effet la fonction de transfert d'une combustion à pré-mélange est déterminée, à pression atmosphérique, pour un brûleur de turbine à gaz. Et ceci est réalisé pour plusieurs régimes opératoires. Un modèle analytique du comportement dynamique de la zone de réaction en est alors déduit. Dans ce modèle, on considère que la fluctuation de libération de chaleur provient de la fluctuation, d'une part de la fraction massique de combustible et d'autre part de la vitesse dans la flamme. Il en résulte un bon accord avec les résultats expérimentaux. Pour une géométrie tridimensionnelle complexe de la chambre de combustion, la propagation d'ondes est modélisée à l'aide de la méthode d'expansion modale. Les modes acoustiques utilisés par l'expansion modale peuvent alors être obtenus analytiquement pour des géométries simples, ou pour une géométrie très complexe de façon numérique par élément finis. L'expansion modale est ensuite représentée dans un espace d'états afin d'obtenir un modèle numérique très efficace et aussi très robuste. Le modèle thermoacoustique du réseau de modules regroupe les espace d'états de sous-systèmes en un seul. Ce système peut être analysé par une représentation temporelle ou fréquentielle. L'analyse de la stabilité en ressort directement et ne requière pas d'itération. D'autre part des éléments non linéaires peuvent être facilement insérés et simulés en fonction du temps. Cette nouvelle méthode est ensuite validée par une comparaison avec des solutions analytiques d'un système thermoacoustique simple fourni par la littérature, ainsi que par une comparaison avec un programme par élément finis et finalement avec des mesures expérimentales. Dans tout les cas une excellante correspondance des résultats est obtenue. En introduisant des éléments non linéaires dans un système annulaire, un champs de rotation acoustique est simulé, ceci correspond également aux observations expérimentales. Ce résultat et alors vérifié de façon analytique. Sur la base du réseau obtenu, un réglage a été développé en utilisant l'optimisation H∞. Les résultats du contrôle, testés par simulation et sur un stand d'essai comportant un brûleur, révèlent une suppression de plus de 25dB du niveau acoustique. Le contrôleur adaptable développé sur le model d'un algorithme génétique ne demande pas la connaissances entière du processus de combustion. Les testes effectués sur le réglage adaptif montrent des performances similaires au réglage H∞. Un système de réglage active pour une configuration de plusieurs brûleurs est également développé. L'insertion du réglage dans la simulation démontre le bon fonctionnement de cette méthode.
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Aside 2.2. Effects of Simultaneous Acoustic and Vortical Velocity Disturbances
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