Heat Release Rate Fluctuations Research Articles

Combustion dynamic stability analysis in stratified-rotation ethanol/air flame

The flame-dynamic stability and internal mechanism in a stratified-rotation ethanol/air flame are investigated through the utilization of a stratified vortex-tube combustor based on an advanced numerical calculation method. The performance of flame-dynamic and combustion stability is examined by evaluating the stability limit, pressure fluctuation, and flame topology. Results demonstrate that the stratified vortex-tube combustor exhibits excellent combustion and flame-dynamic stabilities, with the lean stability limit consistently below 0.2 and pressure fluctuations within 2000 Pa, accompanied by a uniform flame topology without significant temporal variations over time. The burning velocity displays good adaptability to flow field disturbances, aligning well with the normal flow velocity on the flamelet throughout time. Slight variations in flame topology result in weak heat release fluctuations, effectively suppressing fluid disturbances in the post-flame zone. Decreased momentum flux and its alterations in the post-flame zone play a crucial role in achieving flame-dynamic stability due to intense momentum exchange within this highly rotating reactive flow environment. The Rayleigh parameter and flame transfer function are employed to quantify flame-dynamic stability, revealing that both weak thermo-acoustic coupling degree and limited response level of heat release rate fluctuations to fluid fluctuations significantly contribute to maintaining stable flames. These findings systematically elucidate underlying mechanisms responsible for achieving robust flame-dynamic stability observed within this highly rotating reactive environment.

Direct combustion noise: Nearfield and non-compactness influences on pressure–heat release coherence

There are several mechanisms through which turbulent flames produce sound. In low Mach number, unconfined flows, direct combustion noise – i.e., unsteady gas expansion generated by heat release fluctuations – is known to be a dominant contributor. This study is motivated by the fact that in the farfield, the coherence between spatially integrated heat release fluctuations from acoustically compact flames and direct combustion noise is unity. This suggests that the role of direct combustion noise relative to other sources can be ascertained from the value of the coherence. However, in practice it is difficult to fully satisfy the requirements to achieve a unity coherence, even in cases where direct combustion noise is the dominant noise source. This paper explores the contribution of noncompactness and nearfield effects on coherence. For the noncompactness part, while it is often the case that flames are small relative to a wavelength, they are never infinitesimally small. For the nearfield aspect, it is often not possible or practical to obtain farfield measurements, particularly in confined environments. This paper presents calculations that quantify how these noncompactness and nearfield effects influence coherence values. These calculations provide guidance on frequency ranges over which direct combustion noise will lead to near-unity coherence values, as well as required distances and optimal angles for acoustic instrumentation.Novelty and significance statementThis study presents a theoretical study on the coherence between heat release rate and acoustic pressure fluctuations, which has been mostly overlooked in prior literature. To the extent of the author’s knowledge, this is the first attempt that identify and investigate the inconsistencies between traditional theory and experimental literature on coherence. Results have implications for our previous understanding of the relationship between the heat release rate fluctuations and direct noise, aiding in future studies on combustion noise.

Feedback directions governing self-sustained thermoacoustic instability in rocket engine combustors

The occurrence of high-frequency (>1000 Hz) thermoacoustic instability (TAI) sustained by mutual feedback among the acoustic field, heat release rate oscillations, and hydrodynamic oscillations poses severe challenges to the operation and structural integrity of rocket engines. Hence, quantifying the differing levels of feedback between these variables can help uncover the underlying mechanisms behind such high-frequency TAI, enabling redesign of combustors to mitigate TAI. However, so far, no concrete method exists to decipher the varying levels of mutual feedback during high-frequency TAI. In the present study, we holistically investigate the mutual influence based on the spatiotemporal directionality among acoustic pressure, heat release rate, and hydrodynamic and thermal oscillations during TAI of a single-element rocket engine combustor. Using symbolic transfer entropy, we identify the spatiotemporal direction of feedback interactions between those primary variables when acoustic waves significantly emerge during TAI. We unveil the influence of vorticity dynamics at the fuel collar (or the propellant splitter plate) as the primary stimulant over the heat release rate fluctuations to rapidly amplify the amplitude of the acoustic field. Furthermore, depending on the quantification of the degree of the mutual information (i.e., the net direction of information), we identify the switches in dominating the thermoacoustic driving between the variables during TAI, each representing a distinct mechanism of a thermoacoustic state. Additionally, from this quantification, we analyze the relative dominance of the variables and rank-order the mutual feedback according to their impact on driving TAI.

Intermittency transition to azimuthal instability in a turbulent annular combustor

We experimentally study the transition from a state of combustion noise to azimuthal thermoacoustic instability in a laboratory-scale turbulent annular combustor. This combustor has sixteen swirl-stabilized burners to facilitate continuous and spatially distributed combustion along the annular region. Our approach involves simultaneous measurement of CH* chemiluminescence emission of the flame using two high-speed cameras and the acoustic pressure fluctuations using eight piezoelectric pressure transducers mounted on the backplane of combustor. We observe that the transition from combustion noise to azimuthal instability occurs through mode shifting, where the system switches from a longitudinal mode to an azimuthal mode as the equivalence ratio is decreased. Throughout this progression, the combustor exhibits various dynamical behaviors, including intermittency, dual-mode instability, standing azimuthal instability, and beating azimuthal instability. These dynamical states are determined from the acquired pressure signals by decomposing the acoustic pressure fluctuations into clockwise (CW) and counterclockwise (CCW) waves, enabling a reconstruction of the amplitude of acoustic pressure fluctuations, nature angle, (anti-)nodal line location, and spin ratio. The global heat release response is then examined during various dynamical states, contrasting their behavior at different non-dimensional time steps by phase-averaging the fluctuations of the heat release rate over the acoustic pressure cycle. Distinctive flame behaviors were observed based on the direction of pressure wave propagation, showcasing characteristic CCW spinning, standing, and CW spinning heat release patterns. Moreover, our examination of relative phase distributions during various dynamical states, computed by analyzing the phase of heat release rate fluctuations across all burners with respect to one burner, reveals the emergence of diverse patterns in the interaction of neighboring flames influenced by acoustic field.

Spray swirling flame dynamic under combined modulation of air and fuel

Combustion instability is still a main challenge in developing advanced gas turbine combustors. It is essential to conduct instability control once it occurs. In this paper, liquid fuel modulation by a high-speed on/off valve is used to control flame oscillation generated by loudspeakers. Spray swirling flame dynamic under the combined modulation of air and fuel is experimentally studied. Flame dynamical characteristics and coherent structures at different excitation phase delays are discussed with nonlinear time-series analysis and proper orthogonal decomposition method. Experimental results show flame heat release rate fluctuation is decreased by 86% at 40° while flame instability is intensively enhanced at 220°. Phase portraits and recurrence plots show the flame is in a chaotic oscillation with low amplitude aperiodic oscillations at 40° while it suffers from the largest fluctuation at 220°. Difference in flame dynamic is caused by the destructive (out of phase) and constructive (in phase) interference of heat release rate fluctuations induced by air excitation and fuel modulation. Flame returns back to its nature dynamical behavior under out-of-phase modulation. Longitudinal modes of the spray flame are enhanced while the spiral modes are inhibited under in-phase modulation.

Interaction of acoustic pressure and heat release rate fluctuations in a model rocket engine combustor.

We experimentally clarify the interaction of acoustic pressure and heat release rate fluctuations during a transition to high-frequency combustion instability in a model rocket engine combustor. The dynamical state of acoustic pressure fluctuations undergoes a transition from high-dimensional chaotic oscillations to strongly correlated limit cycle oscillations. The coherent structure in the heat release rate field emerges with the initiation of weakly correlated limit cycle oscillations. The effect of the heat release rate on acoustic pressure fluctuations predominates during high-dimensional chaotic oscillations. In contrast, the effect of acoustic pressure on the heat release rate fluctuations markedly increases during the correlated limit cycle oscillations. These are reasonably shown by an ordinal pattern-based analysis involving the concepts of information theory, synchronization, and complex networks.

Effects of fuel/air mixing distances on combustion instabilities in non-premixed combustion

Combustion instability has been widely reported in several combustion types; however, there is limited information on different fuel/air mixing distances in non-premixed combustion. Setting different distances between air tube and fuel tubes, the fuel/air mixing distances (δ) are changed by structural variations of nozzles. Keeping the heat load and equivalence ratios constant, the present work aims to examine the effects of fuel/air mixing distances on combustion instability in non-premixed combustion. Experimental observations suggest that combustion oscillations occur in non-premixed combustion with flame ignited outside the nozzle rather than other types of non-premixed combustion. Quasiperiodic oscillations, limit cycle modes, and intermittency modes are found in three fuel/air mixing distances in non-premixed combustion. The calculation methods of convection time for non-premixed combustion are established in the present work. The convection time of the limit cycle oscillations is then calculated, which is further found to trigger the second resonance modes of the combustion system. The further analysis reveals that varying fuel/air mixing distances can cause influences on local equivalence ratio distributions, and the convection time are correspondingly varied. The changes in convection time affects the coupling characteristics between heat release rate fluctuations and the acoustic modes in the combustion chamber. When the thermoacoustic coupling occurs, combustion instabilities appear. This work establishes a link between combustion instability and fuel/air mixing distances in non-premixed combustion and highlights the influences on spatial distributions of local equivalence ratios and then convection time, which can provide technical guidance for actual applications in various fuel/air mixing types.

Continuous and explosive synchronization transition in turbulent combustors

Thermoacoustic instabilities in turbulent combustors have disastrous consequences and present notorious challenges in their modeling, prediction, and control. Such instabilities are characterized by self-excited periodic oscillations, arising from a positive feedback between the acoustic pressure and heat release rate fluctuations. We present a mean-field approach to model thermoacoustic transitions. The nonlinear flame response is modeled using an ensemble of phase oscillators constrained to collectively evolve at the rhythm of acoustic fluctuations. Starting from the acoustic wave equation coupled with the phase oscillators, we derive the evolution equations for the amplitude and phase for acoustic oscillations. The model captures abrupt and continuous transitions to thermoacoustic instability observed in disparate combustors. We also discover that continuous and abrupt transitions happen through paradigmatic continuous and explosive synchronization, respectively. Importantly, our approach explains spatiotemporal synchronization and pattern formation underlying the transition to thermoacoustic instability. The versatility of the model in capturing different types of transitions suggests promising prospects for its extension to encompass a wide range of fluid dynamics phenomena.

Spatiotemporal patterns corresponding to phase synchronization and generalized synchronization states of thermoacoustic instability.

Thermoacoustic instability in turbulent combustion systems emerges from the complex interplay among the flame, flow, and acoustic subsystems. While the onset of thermoacoustic instability exhibits a global order, the characteristics of local interactions between subsystems responsible for this order are not well understood. Here, we utilize the framework of synchronization to elucidate the spatiotemporal interactions among heat release rate fluctuations in the flame, velocity fluctuations in the flow, and acoustic pressure fluctuations in a turbulent combustor, across the bluff-body stabilized flame. We examine two forms of thermoacoustic instability, characterized by phase synchronization and generalized synchronization of the acoustic pressure and global heat release rate oscillations. Despite the presence of global synchrony, we uncover a coexistence of frequency synchrony and desynchrony in the local interaction of these oscillations within the reaction field. In regions of frequency-locked oscillations, various phase-locking patterns occur, including phase synchrony and partial phase synchrony. We observe that the local formation of small pockets of phase synchrony and strong amplitude correlation between these oscillations is sufficient to trigger the state of global phase synchronization. As the global dynamics approach generalized synchronization, these local regions of synchrony expand in the reaction field. Additionally, through coupled analysis of acoustic pressure and local flow velocity fluctuations, we infer that the spatial region of flow-acoustic synchrony plays a significant role in governing thermoacoustic instabilities. Our findings imply that, in turbulent combustors, an intrinsic local balance between order, partial order, and disorder within the coupled subsystems sustains the global order during thermoacoustic instability.

Adjoint-accelerated Bayesian inference applied to the thermoacoustic behaviour of a ducted conical flame

We use Bayesian inference, accelerated by adjoint methods, to construct a quantitatively accurate model of the thermoacoustic behaviour of a conical flame in a duct. We first perform a series of automated experiments on a ducted flame rig. Next, we propose several candidate models of the rig's components and assimilate data into each model to find the most probable parameters for that model. We rank the candidate models based on their marginal likelihood (evidence) and select the most likely model for each component. We begin this process by rigorously characterizing the acoustics of the cold rig. When the flame is introduced, we propose several candidate models for the fluctuating heat release rate. We find that the most likely flame model considers velocity perturbations in both the burner feed tube and the outer duct, even though studies in the literature typically neglect either one of these. Using the most likely model, we infer the flame transfer functions for 24 flames and quantify their uncertainties. We do this with the flames in situ, using only pressure measurements. We find that the inferred flame transfer functions render the model quantitatively accurate, and, where comparable, broadly consistent with direct measurements from several studies in the literature.

Explosive synchronization in a turbulent reactive flow system.

The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely, a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.

Mitigating thermoacoustic instabilities in premixed hydrogen flames using axial staging

In this paper we demonstrate how axial staging can be utilised to mitigate thermoacoustic instabilities in a combustion system by flame redistribution. This is achieved by moving flow to a second stage flame while keeping the combined thermal power and total flow fixed. The stability of the system was first characterised for premixed H2-CH4-air flames operated with hydrogen volume fraction in the range 80%–100%. As observed in recent work, increasing the hydrogen concentration led to the onset of strong self-excited instabilities. Increasing the flow velocity for a fixed hydrogen concentration was shown to have the same effect. Both of these are linked to a decrease in the convective time scale — causing the flame to become more convectively compact and responsive to higher frequencies. We then show that these instabilities could be reduced for all conditions, by distributing flow to the secondary flame. Two main driving mechanisms causing suppression were observed and analysed. Firstly, a reduction in the flow rate provided to the first stage flame, leading to a corresponding change in the flame structure. This leads to an increase in the convective time scale. This effect is quantified by a reduced gain at higher frequencies, and a change in the time delay of the flame transfer function. Secondly, introducing a second flame with a different convective time scale results in interference between the two flames. This acts to suppress or enhance the global fluctuations in heat release rate and hence, the amplitude of the pressure oscillations in the system.

Dynamical state and driving region of combustion instability in a turbulent combustor with a variable swirling flow system

We experimentally study the dynamical state and driving region of combustion instability in a turbulent combustor under low- and high-swirling flow conditions by the complex-systems approach. As the swirl number is increased, the combustion state undergoes a transition from stable combustion to complex combustion instability with large-amplitude modulations via low- and high-amplitude combustion instability. A chaotic state emerges during combustion instability with large-amplitude modulations. A symbolic dynamics-based thermoacoustic power network can identify the emergence of the thermoacoustic power source during combustion instability. The driving region of combustion instability can be clearly extracted from the symbolic dynamics-based synchronization index and the local node entropy in the Rayleigh index-based transition network. Reservoir computing has a potential use in clarifying the phase synchronized state between acoustic pressure and heat release rate fluctuations during the chaotic state in combustion instability with large-amplitude modulations.

Shape sensitivity of thermoacoustic oscillations in an annular combustor with a 3D adjoint Helmholtz solver

We model acoustic oscillations driven by velocity-coupled heat release rate fluctuations. We obtain an inhomogeneous wave equation and convert it to the frequency domain with a modal decomposition. We impose acoustic boundary conditions and, using a finite element discretization with Lagrange elements, express this as a nonlinear eigenvalue problem for the complex angular frequency, ω. We solve this using the open source platform FEniCS combined with the SLEPc, PETSc and OpenMPI libraries. In Hadamard form we write the derivative of the eigenvalue, ω, with respect to generic geometry changes. This requires the solution of the adjoint equation, which we obtain with the same method as the direct equation. The output is a thermoacoustic Helmholtz solver that cheaply calculates the effect of generic shape changes on the growth rate and frequency of thermoacoustic oscillations. We then consider symmetry-preserving and symmetry-breaking geometry modifications. For demonstration we model a 30kW laboratory-scale annular combustor (MICCA from EM2C). We parametrize the surfaces of the three-dimensional geometry with NURBS using control points. For the plenum and the combustion chamber, we find the eigenvalue shape derivatives with respect to the parameters of these control points. We apply two different strategies, perpendicular boundary movements and control point perturbations, to implement shape changes proportional to these shape derivatives, thereby reducing the growth rate of the unstable mode by increasing the phase shift between the pressure and the heat release rate oscillations. This computational method shows how to significantly alter thermoacoustic oscillations by making small geometry changes. The framework in this paper can handle arbitrarily complex three-dimensional geometries, which will be useful for the design of industrial combustion systems.

Effect of Hydrogen Enrichment on Transfer Matrices of Fully and Technically Premixed Swirled Flames

Abstract Knowledge of flame responses to acoustic perturbations is of utmost importance to predict thermoacoustic instabilities in gas turbine combustors. However, measuring transfer functions linking acoustic quantities upstream and downstream of flames are very challenging in practical systems and these measurements can significantly deviate from state-of-the-art models. Moreover, there is a lack of studies investigating the effect of hydrogen enrichment on the response of natural gas (NG) flames. In this work, measurements of flame transfer matrices (FTMs) of turbulent H2/NG flames in an atmospheric combustor featuring an axial swirler burner have been performed, allowing us to unravel the transition between FTM in fully premixed (FP) and in technically premixed (TP) conditions. Furthermore, imaging of OH* chemiluminescence and OH-planar laser induced fluorescence are obtained for characterizing the topology of the flame for varying H2 fraction and mixing conditions. Transfer matrices are measured using the multimicrophone method for H2 fractions ranging from 12% to 43% in power. Afterward, the flame transfer functions (FTFs), which linearly relate the coherent fluctuations of the heat release rate to the acoustic velocity oscillations, are obtained from the FTM by using the Rankine–Hugoniot jump conditions across the flame. Using the OH* chemiluminescence intensity as a surrogate for the heat release rate, the FTF based on this optical measurement is also extracted and compared to the one exclusively obtained with the multimicrophone method. As expected, the two different methods are in very good agreement for the FP case and significantly differ for the TP case. Indeed, chemiluminescence fluctuations cannot be directly linked to heat release rate fluctuations when the acoustic forcing induces equivalence ratio fluctuations at the flame, making the optical method unusable for TP configurations. We also show that the two methods agree in the high end of the explored excitation frequency range and we provide an explanation to this intriguing finding. Moreover, we investigate the sensitivity of the FTM measurement to the estimate of the speed of sound in the rig in FP conditions. Finally, the measured FTFs are fitted with FTF models based on multiple distributed time delays. This allows us to explain the frequency dependence and the hydrogen fraction dependence of the gain and the phase in FP and TP conditions.

Parametric instability in propagating flames and the impact of hydrogen enrichment on the onset of secondary instability

A self-excited acoustic instability of laminar premixed flames propagating in an open-ended tube with a length of 700 mm and a radius of 10 mm was simulated by solving the reacting unsteady compressible Navier–Stokes equations, to understand the way of massive acoustic generation and its onset behaviors. Four fuel–air mixtures with an equivalence ratio of 1.2 were considered, namely, methane–air and methane–hydrogen–air mixtures, to identify the role of hydrogen in rich methane–air mixture. Parametric instability, which generated huge acoustic disturbance and violent flame pulsations, was observed only for a particular methane–hydrogen–air mixture with RH = 0.2, consistent with previously reported experimental observations. For the investigation of the reinforcement mechanism of acoustic instability under parametric instability, the flame surface area modulation was examined. It was found that violent subharmonic flame front pulsations could strongly modulate the flame surface area in the fundamental mode, resulting in a fluctuating heat release rate and increased thermoacoustic coupling. When hydrogen addition was small, attaining a higher level of primary instability, which is the precursor of the parametric instability, was more dominant than increasing the threshold level for the onset of the parametric instability. With larger hydrogen addition, the increase in the threshold level was more dominant than attaining a higher level of the primary instability. In particular, as the flame propagation time decreased, the level of the primary instability was saturated in larger hydrogen addition. This study elucidates the mechanism for the acoustic generation of propagating flames under the parametric instability, and the effects of hydrogen enrichment within rich methane–air mixtures.

Experimental study on effects of ammonia enrichment on the thermoacoustic instability of lean premixed swirling methane flames

Ammonia (NH3) has recently emerged as a promising carbon-free energy carrier. Further development and application of NH3 as fuel in the gas turbine industry can significantly reduce the emissions of carbon dioxide (CO2) and contribute to the achievement of a carbon–neutral society. This study experimentally examined the thermoacoustic instability characteristics of a laboratory-scaled lean premixed gas turbine model combustor operated with different NH3 blending ratios with methane (CH4). Experiments conducted under a wide range of inlet velocities and equivalence ratios suggest that NH3 concentration is critical in determining the characteristics of the instability. Specifically, when the NH3 proportion is less than 50 %, the addition of NH3 causes a mode transition of the instability. However, when the content of NH3 is greater than 50 %, it is shown that the instabilities are suppressed, indicating that the addition of a certain amount of NH3 can enhance the stability of CH4 flames. Additional analysis of flame dynamics reveals that the introduction of NH3 causes the lengthening of the flame front and weakens heat release rate fluctuations in the flame root regions. Further Proper Orthogonal Decomposition (POD) analysis of the flow field shows that the instability modes are strongly coupled with periodic vortex motions of the flow dynamics along the shear layers. Finally, the mode shifting phenomena is successfully predicted by low-order thermoacoustic network modeling. It is suggested that the change in convective time delay caused by NH3 addition is responsible for such transitions.

Impact of the injector lateral offset on the dynamics of a lean premixed flame and the thermoacoustic stability of a burner

The response of a laminar lean premixed flame to excitations based on its position in the combustion chamber and the stability of a burner are numerically investigated. A finite-volume large-eddy simulation method is used to solve the compressible Navier-Stokes equations and a combined G-equation progress variable approach is used to model the flame. Various injector positions in the combustion chamber are investigated in a computational setup with an acoustically non-reflecting outflow boundary condition to analyze the impact on the response of the flame to an external excitation. Due to the changes in the flow field the shape of the flames depends on the displacement offset of the injector. Consequently, the instantaneous, local distribution of the heat release rate fluctuations which is caused by wrinkles on the flame surface is determined by the position of the injector. The heat release rate fluctuations are the dominant source of sound in the investigated configurations. Due to the discrepancies in the local heat release rate fluctuations the flame response to an excitation depends on the lateral offset of the injector. The overall trend of the integrated heat release is the same in most configurations, however, the phase is significantly altered. Since the phase angle of the response of the flame to an excitation determines the stability of a burner, self-excited instabilities can be avoided by adjusting the position of the injector. This is demonstrated using a modified computational domain with an acoustically reflecting outflow boundary condition, which causes the burner to have an acoustic quarter-wave eigenmode. Based on the results of the previous analysis of the flame responses, two injector positions in the combustion chamber are chosen such that the response of the flames is mutually phase-shifted by approximately π. Therefore, it is expected that one of the configurations will lead to a stable burner while the other one exhibits a self-excited instability. The results show that the injector position determines the stability of the burner configuration for the investigated flames.

Acoustic Triggering of Combustion Instability in a Swirling Flame: An Experimental Study

Combustion instability is a common thermoacoustic coupling problem in combustion systems, and the pressure oscillations generated inevitably damage the combustion system. Studying the mechanism of combustion instability, especially the triggering problem of combustion instability, is particularly important for understanding combustion instability. This article adopts experimental research methods. The flame transfer function and flame describing function governing pressure pulsation were hereby measured to study the effect of heat release rate fluctuation on acoustic disturbance. By triggering combustion instability through ignition, the growth process of combustion instability was also studied. The results showed that flame pulsation amplitude shows a complex curvature when the frequency is lower than 200 Hz, while the growth rate of pulsation amplitude monotonically decreases as frequencies increase above 200 Hz. According to the considerable self−excited combustion instability tests, the oscillation amplitudes in the limit cycle state are generally greater than 0.4, while the pressure amplitudes in the limited state are less than 0.2, thus verifying the concept of a trigger threshold for low−frequency oscillation. In addition, analysis of the growth rate, the pressure and the attractor of the heat release pulsation observed after the triggering of combustion instability reveals that the triggering of combustion instability is a gradual coupling process between oscillation pressure and heat release rate pulsation.

Period-2 Thermoacoustics in a Swirl-Stabilised Partially Premixed Flame Computed Using Large Eddy Simulation

A partially premixed swirl-stabilised flame under thermoacoustically unstable conditions is studied using large eddy simulation with an unstrained flamelet model for the filtered reaction rate. The simulation results agree well with measured statistics of velocity, temperature and mixture fraction. Two thermoacoustic modes at approximately 300 and 590 Hz are excited for the case studied. The second mode pressure amplitude is comparable to that of the first mode. However, the second mode of heat release rate fluctuations is not as significant as for the pressure which results in a 2:1 frequency locking behaviour. The analysis offers insights into the physical mechanism involved in the excitation of the two modes and the 2:1 frequency locking behaviour. The index based on the Rayleigh Criterion in frequency domain is analysed to understand the coupling between the heat release rate and pressure fluctuations. It is observed that there is a nonlinear interaction between the two modes resulting in energy exchange across the two modes. The conventional Rayleigh Index has limitations in explaining the observed dynamics and therefore, a modified Rayleigh Index is defined to understand the effects of nonlinear mode interactions on thermoacoustic characteristics. A mode shape analysis using LES and acoustic-modelling reveals that the first mode may be a Helmholtz mode with internal damping that is excited by an acoustic source, and the second mode has the characteristic shape of a chamber mode.