Analysis Of Combustion Instability Research Articles

A theoretical analysis of entropy-induced combustion instability

This paper presents theoretical results on entropy-induced thermoacoustics and combustion instability in combustors. The entropy model derived from the thin flame hypothesis, commonly adopted in most network combustor models, inherently assumes that heat and acoustic fluctuations, which serve as sources of entropy waves, are always in-phase. This in-phase property remains unchanged despite the dispersion and dissipation of entropy waves, potentially leading to an underestimation of the entropy wave effect on combustion instability compared to other models that account for flame thickness. This finding suggests that flame thickness should be considered in combustion instability analyses when boundary conditions involve entropy waves, even in one-dimensional cases. Furthermore, this paper demonstrates that the entropy dispersion and dissipation models used in most combustor network models might only partially compensate for the neglected flame width. This perspective, along with a comparative analysis of entropy models that either include or exclude flame thickness, indicates how the free parameters of the dispersion/dissipation models relate to the geometry and operating conditions of a given combustor. Additionally, we present an explicit form of the reflection coefficient for the outlet choking boundary condition under the influence of combustor acoustics. Our theoretical findings are illustrated through numerical examples.

High-fidelity numerical simulation of longitudinal thermoacoustic instability in a high-pressure subscale rocket combustor

A detailed analysis of thermoacoustic combustion instability in a subscale rocket combustor at high pressure is reported in this paper using the high-fidelity large-eddy simulation (LES). Self-sustained longitudinal combustion instability is observed in the experiments for this combustor configuration. The computational setup follows the past experimental study of a rig called the Continuously Variable Resonance Combustor (CVRC). In this combustor, both stable combustion and unstable combustion dynamics have been observed by varying the oxidizer injector length. A combustor configuration with an oxidizer injector length of 12 cm is chosen for this study based on the experimental evidence of longitudinal combustion instability. An autonomous meshing using the modified cut-cell Cartesian grid generation approach, coupled with on-the-fly Adaptive Mesh Refinement (AMR) is employed in this study. Chemical reactions during turbulent combustion in this configuration are modeled by solving the species transport equations with a detailed chemistry solver using a kinetic mechanism with 21 species and 84 steps. Similar to the findings of the experiments, we observe a self-sustained combustion instability in the present study, which is characterized by a limit cycle behavior of the acoustic fluctuations. The spectral analysis of these acoustic fluctuations shows good agreement with experimental data for the frequency of the three dominant modes. We further analyze the features of time-averaged and instantaneous reacting flow to study the effects of combustion instability on the flame holding dynamics, vortex shedding, mixing, and combustion regime due to flame movement along the longitudinal direction of the combustor during a limit cycle. These phenomena are effectively captured through the integration of AMR with complex chemistry in the present study. A particular focus of the study is on understanding the role of minor species (OH, HO2, and CH2O) in the physical and state-space in sustaining the flame during the combustion instability. Additionally, the physical mechanisms responsible for the production and dissipation of enstrophy are examined to demonstrate that their contribution can create significant fluctuations in the reacting flow field, which can assist in sustaining the combustion instability.

Large Eddy Simulation and Acoustic Analysis of Combustion Instability in an Annular Combustor with Low-Swirl Flames.

Self-excited combustion instability in an annular combustor with low-swirl flames is studied with a combination of large eddy simulation (LES) and acoustic solvers. Acoustic analysis with a Helmholtz solver provides an estimate of frequencies and modal structures in the annular combustor. LES gives detailed modal dynamics for specific instability modes. Combustion instabilities in the annular combustor including longitudinal, spinning, and standing modes are successfully captured in a single LES. Numerical results show that the instability modes are not constant; they switch among these modes randomly and rapidly. The flow oscillates back and forth in phase with the largest pressure amplitude located near the outlet of the injectors for the longitudinal mode. The azimuthal instability oscillates in the 1A2L mode of the annular system. In the spinning mode, the pressure antinodes move forward while the modal structure keeps constant. For the standing mode, the locations of pressure antinodes are fixed in the annular combustor and the fluctuations at the pressure antinodes keep out of phase. The near-zero value of the mean spin ratio indicates that the dominant azimuthal mode is the standing mode. The azimuthal modes captured by LES are in good agreement with that predicted by Helmholtz solver in terms of frequency and modal structure. The maximum deviation of the predicted frequency is less than 5%. This adds values before the low-swirl injector is placed into the actual annular combustor.

Flame visualization and spectral analysis of combustion instability in a premixed methane/air-fueled micro-combustor

The present study experimentally explores the combustion instability characteristics of premixed methane/air flames in a planar micro-combustor by utilizing the high-speed camera and the noise data acquisition system. It aims to identify the sound pressure fluctuation of unstable flames and shed light on the relationship between flame structure and thermoacoustic instability under micro-scale conditions. Four types of flame structures, i.e., flame with repetitive extinction and ignition (FREI), weak flame, steady flame, and oscillating flame, are experimentally observed by varying operating parameters. Among them, the weak flame at low flow velocities and the oscillating flame at high flow velocities form thermoacoustic oscillation. For weak flames, the collision with the wall and the local deformation of the flame result in high-frequency harmonics. Varying the inlet velocity from 0.14 m/s to 0.15 m/s leads to the pressure fluctuation of the weak flame being reduced by 10 Pa, and the dominant frequency being changed from 125 Hz to 167 Hz. As for oscillating flame, the variation of the inlet velocity plays a decisive role in the sound pressure fluctuation. At the equivalence ratio of 0.7, an increase of 0.01 m/s in the inlet velocity reduces the pressure fluctuation by 4 Pa.

Laser interferometric detection of heat release rate perturbation field of acoustically perturbed laminar premixed flames

Laser interferometry, which was originally used to measure density perturbation, has been previously used to determine the heat release rate perturbation, which is a key factor in the analysis of combustion instability. However, its spatial accuracy is still unsatisfied. In the present work, an improved fringe Fourier analysis method is proposed to process the results obtained from the laser interferometry measurement, aiming to accurately determine the spatial distribution of flame heat release rate perturbation. The measurement of heat release rate perturbation was performed on a acoustic perturbed laminar premixed flame, with the burner outlet diameter of 8 mm. Interference patterns generated by two laser beams with a diameter of 70 mm were recorded at a frame rate of 6000 Hz. A spatial dependent fringe processing method, referred as the improved fringe Fourier analysis, was developed to demodulate the interference phase from the fringe patterns. The proper orthogonal decomposition analysis was performed on these results to analyze the component of interference signals. Validation of the present technique was conducted by comparing the heat release rate perturbation field resulting from the laser interferometric technique to those from the CH* chemiluminescence from the flame. Comparisons were performed both for the global and local values, and the low-frequency natural oscillation effects were analyzed. Finally, a refraction correction method based on background-oriented Schlieren is proposed to compensate the beam deflection caused by flame.

Comparison of pressure-based flame describing functions measured in an annular combustor under self-sustained oscillations and in an externally modulated linear combustor

One important aspect in the analysis of combustion instabilities in multiple-injector annular systems is that of representing such oscillations with a linear array of injectors. This issue is considered in the present work by comparing flame dynamics in a self-sustained oscillations situation in the annular configuration MICCA-Spray, with experiments carried out in TACC-Spray, a rectangular combustor equipped with five injectors externally modulated by driver units. In the annular system, the coupling mode is azimuthal, and in the linear array, the flames are submitted to a transverse acoustic field. An original method is used to change the limit-cycle pressure oscillations amplitude in the annular system and favor a standing mode with a well-defined nodal line position. It consists in using different arrangements of two types of injectors, leading to various azimuthal staging patterns. The range of pressure oscillation amplitudes is swept in TACC-Spray by changing the external acoustic forcing level. It is thus possible to compare the flame dynamics in forced and self-sustained situations using these two experimental facilities. This is done by examining flame describing functions (FDFs) based on downstream pressure fluctuations measured in the two configurations for different pressure oscillation amplitudes. The trends observed in the two systems are in good agreement, and there is a reasonably good match between the values of the gains and phases determined in the two configurations. The pressure-based FDFs are determined for flames located at different positions with respect to the acoustic mode. It is found that the transverse or azimuthal velocity component has only a weak influence on the pressure-based FDF, the strongest impact being observed in the neighborhood of the velocity antinode. This study demonstrates the ability of a linear-array setup modulated by a transverse mode to reproduce conditions of azimuthal coupling leading to self-sustained limit cycles in an annular combustor.

Combustion instability analysis in an ethylene-fueled scramjet combustor under various fuel penetration height conditions using an image-based nonlinear dimensionality reduction method

The present study investigates the effects of fuel penetration height on combustion instabilities in an ethylene-fueled scramjet model combustor with a cavity flameholder. Experiments were performed at the stagnation temperature of 1900 K, the stagnation pressure of 0.37 MPa, and the Mach number of 2. Three fuel injection orifice diameters:2.3, 2.4, and 2.5 mm, were tested to elucidate the effects of ethylene penetration height on combustion instabilities. Furthermore, high-speed measurements of CH* chemiluminescence and shadowgraphs were performed with high-speed video cameras. To examine the dynamics of the combustion instabilities, time-resolved CH* chemiluminescence images and shock parameters, extracted from snapshots of shadowgraphs, were analyzed using a non-linear dimensionality reduction algorithm: Gaussian Process Dynamical Model (GPDM). Thereafter, further analyses on the acquired latent variables were conducted with Recurrence Plot (RP). The experimental results showed that the fuel equivalence ratio (ϕ) range for cavity shear-layer combustion mode expanded as d decreased. Furthermore, for ϕ = 0.18, the instability behavior remarkably changed at around d = 2.4 mm. Therefore, the instability dynamics for ϕ = 0.18 were investigated using GPDM and RP including results from our previous study (d = 2, 3, and 4 mm), revealing differences in the instability behaviors. For d = 3 and 4 mm, jet-wake combustion and ram combustion modes were established alternately with a frequency of about 1600 Hz. In contrast, at d = 2.4 and 2.5 mm, although a similar instability in the d = 4 mm case was present at almost the same oscillation frequency, a different instability behavior was also confirmed. This additional instability exhibited an intermediate state between jet-wake combustion and ram combustion modes. These two instabilities emerged aperiodically. For an unstable combustion in shear layer observed for d = 2 and 2.3 mm, corresponding RPs exhibited black patches, indicating that the oscillation amplitude diminished substantially.

Multi methods for combustion instability analysis of Atkinson cycle engine based on time series analysis

Researching the combustion instability of ACE is meaningful no matter for HEVs development or for combustion control of the Atkinson cycle. Based on a gasoline ACE, EGR sweeping tests are conducted and thermodynamics time series are obtained. CCV is calculated versus cycle numbers for dominant thermal parameters. According to the acquired time series, PSR, RP, and RQA methods are employed to analyse chaotic characteristics and combustion instability. Through the current investigation, the influence of EGR on ACE combustion instability is studied with the largest IMEP variation of 13.6% at EGR valve fully opened condition. The effect on the combustion centre is much larger than SOC. Time series RPs depict abundant structures representing determinism, laminarity, and other characteristics corresponding to the typical chaos character of the unstable system. Beyond typical measures of RQA, two new quantitative indicators are proposed to quantify fluctuation property. Besides, CCV analysis based on multiple time series is employed as a supplement explanation to emphasize correlations characters and a new PCC analysis method is first proposed and evaluated efficiently to research instability with intuitiveness and simplicity. In conclusion, combustion instability is researched which provides guidance for ACE technology, combustion instability analysis is enriched by classical and newly proposed single or multi time series based analysis methods.

Analysis of Combustion Instability of Methane-Air Premixed Swirling Flame Based on OH-PLIF Measurements.

A method for determining combustion instability using flame structure parameters is presented. A speaker is used to provide controllable external excitation for the combustion system. The experimental object is a methane-air swirl premixed flame. The flame structure parameters such as height, width, and flame surface density extracted from the hydroxyl planar laser-induced fluorescence image were used to analyze combustion instability at different equivalence ratios (0.8-1.2) and inlet flow rates. It is confirmed that the inflection point of the flame structure parameters corresponds to the evolution of combustion instability verified by the flame transfer function. The results show that with the increase of inlet velocity v, the flame aspect ratio h/b, average OH* concentration, and surface density Σ gradually decrease. The thickness δ of the flame brush shows an increasing trend under the same conditions. With the increase of equivalence ratio Φ, the average OH* concentration and flame surface density Σ increase continuously. The changing trend of flame brush thickness decreases first and then increases to a peak. Finally, it continues to decline after reaching the peak. The flame responds strongly to the sound field when the equivalence ratio is 0.9 and 1.0. In the range of 80-240 Hz, the flame response near 110 and 190 Hz is stronger at each equivalence ratio (0.8-1.0). When the equivalent ratio is 0.9 and 1.0, the amplitude fluctuations of the flame transfer function are much larger than those under other conditions. Meanwhile, the specific performances of the flame structure parameters are that the flame height, average OH* concentration, and flame surface density decrease, and the flame brush thickness increases. These results can be used as a basis for judging combustion instability. This method proves that the parameter information monitored during the flame combustion process can be used to judge the changes in combustion conditions and can adjust the corresponding conditions more accurately and quickly.

Modeling analysis of combustion instability in an annular combustor equipped with circumferentially segmented perforated liner

Hazardous azimuthal thermoacoustic modes often occur in lean-premixed annular combustors. One practical control method is the application of perforated liners with bias flow. However, circumferentially uniform perforated liners are not competent to control them, because the perforated plate covered by a single azimuthally uniform backing cavity cannot provide sufficient acoustic pressure difference across the perforated plate to bring in adequate acoustic damping. In this work, we developed a three-dimensional thermoacoustic model to consider the effects of a novel passive control damper of the circumferentially segmented perforated liner. Emphasis is placed on the effects of the segmented liner on controlling the azimuthal modes. It is found that the azimuthal mode in the premixed annular combustor can be either plenum-dominant or combustor-dominant, with the frequency of the latter one larger than the former. The stabilities of the two kinds of modes behave differently with the change of time delay. The results of the lined combustor cases indicate that the circumferentially segmented perforated liner generally improves the control effectiveness compared with the circumferentially uniform perforated liner thanks to the rigid plates inserted in the backing cavity. At the locally inserted position, the rigid plate enforces a rigid boundary condition that changes the azimuthal pressure mode shape in the backing cavity. As a result, more acoustic damping through the pressure difference across the plate is produced. Symmetry-breaking effects are found if the segmentation is asymmetric or two-fold symmetric. The behavior of the splitting frequencies caused by the segmented liner is also studied, and the symmetric segmented liner turns out to be a better choice because the resulting azimuthal mode is degenerate with two equivalent suppressed growth rates. In order to further enhance the control effect, one significant effective measure is to increase the depth of the backing cavity.

Study on Unstable Combustion Characteristics of Model Combustor with Different Swirler Schemes

In this paper, the effect of the swirler scheme on combustion instability is studied. Through the proper orthogonal decomposition (POD) of flame images, Abel inverse transform and other methods, the influence of swirl intensity on the characteristic frequency of combustion instability was emphatically studied. Based on the low order thermoacoustic network (LOTAN) of the combustor, the flame transfer function (FTF) under different swirl schemes was obtained by the optimization method. The experimental results show that the stable combustion equivalence ratio boundary of the system decreases monotonously with the decrease in swirl intensity, while the characteristic frequency of unstable combustion is not monotonous with the swirl intensity (the oscillating frequency of swirler A with the largest swirl intensity is approximately 319 Hz, swirler B is approximately 280 Hz, swirler C with the smallest swirl intensity is approximately 290 Hz). The optimization results of FTF can easily introduce this non monotonic phenomenon. The swirl intensity mainly affects the hysteresis time of the system (the lag time of swirlers A, B and C are 5.98 ms, 6.82 ms and 6.20 ms, respectively), which is mainly caused by affecting the flame structure and convection velocity. At the same time, the FTF obtained by optimization reflects the same trend with the experimental results, and there is no significant difference in value, which proves the rationality of the optimization method. This work emphasizes the importance of FTF for combustion instability analysis.

Numerical analysis of self-excited tangential combustion instability for an MMH/NTO rocket combustor

This study presented the numerical simulation of the tangential combustion instability in a hypergolic liquid bipropellant rocket thrust chamber, which applied fuel liquid film cooling method and unlike impinging injectors. The liquid spray was modeled using Lagrangian approach, while the gas was regarded as Euler phase. Stress-blended eddy simulation and finite rate/eddy–dissipation model were adopted to simulate the turbulent combustion process. Consistent with the experiment results, this work successfully simulated the transformation of tangential combustion instability from standing mode to spinning mode. The mean pressure, amplitude and frequency of limit cycle oscillation were in good agreement with the experiment. There was a detailed analysis about the flow field, Rayleigh index, and driving mechanism of the combustion instability. It was found that the oscillation began with hot spots of heat release rate due to the interaction between the spray of impinging injectors and cooling fuel jet. More than that, cooling fuel jet also contributed to drive the oscillation. In the standing mode, injectors in the inner and outer rings drive the oscillation together, while the spinning mode is mainly driven by injectors in the outer ring. The pressure wave is subsonic and its Mach number is close to 1. It was shown that the pressure wave contained a complex structure divided into three parts. This led to the in-phase of the pressure along the axial direction and the double-peak characteristic of the downstream pressure signal. Besides, a positive feedback closed-loop system associated with periodic oxidizer/fuel ratio was believed to sustain the combustion instability. The oscillation can be maintained when pressure, heat release and oxidizer/fuel ratio are coupled together. The analysis results indicate that rotating detonation is an implication to tangential combustion instability.

Effect of the flame motion on azimuthal combustion instabilities

In the analysis of combustion instabilities in the annular combustors, especially for the azimuthal combustion modes, the flame motion is usually neglected and the flame is typically regarded as a discontinuity at rest. However, this simplicity may cause severe prediction errors for certain conditions. In this paper, the influence of the flame motion on the entropy, vortex, acoustic, and intrinsic modes in the annular combustion chamber is investigated by constructing an analytical model with the flame motion. Meantime, the influence of flame model parameters is also explored. The flame motion can affect both the frequency and growth rate of the entropy mode, but the growth rate is influenced more significantly. This effect can be damped or enlarged by the inlet Mach number depending on which parameter of flame model remains unchanged. The effect of the flame motion on vortex, acoustic, and intrinsic modes remains small when the inlet Mach number is very small. However, the increase of inlet Mach number can enlarge this effect.

Bifurcation analysis of combustion instability in a Rijke burner with an improved third-order saturated flame model

Bifurcation analysis of combustion instability in a Rijke burner with an improved third-order saturated flame model

Analysis of self-excited transverse combustion instability in a rectangular model rocket combustor

A methane/oxygen mixture is considered to be an appropriate propellant for many future rocket engines due to its practicality and low cost. To better understand the combustion instability in methane/oxygen-fed rocket engines, the spontaneous transverse combustion instability in a rectangular multi-element combustor (RMC) was analyzed both experimentally and numerically. Severe combustion instabilities occurred in the RMC during repeatable hot-fire tests. The physical mechanisms were systematically investigated through numerical simulations based on the stress-blended eddy simulation and flamelet-generated manifolds method with detailed chemical mechanisms (GRI Mech 3.0). The numerical results for the frequency spectrum and spatial modes agree well with the theoretical analysis and experimental data. The driven regions of the combustion instability were identified on both sides of the combustion chamber through a Rayleigh index analysis. The longitudinal pressure oscillations in the oxidizer post were found to be coupled with the transverse pressure waves in the combustion chamber and led to periodic oscillations of the mass flow rate of propellant. Moreover, the mixing was highly enhanced when the pressure wave interacted with walls of the combustion chamber. Therefore, a sudden release of heat occurred. The pressure oscillations were enhanced by pulsated heat release. A closed-loop system with positive feedback associated with periodic oscillations mass flow rate of the propellant, and sudden heat release, was believed to account for the present combustion instability.

Flame describing function and combustion instability analysis of non-premixed coaxial jet flames

This study examines the effect of nonlinear flame dynamics on combustion instabilities in coaxial jet flames. The flame describing function (FDF) was used to establish this nonlinearity experimentally. The FDF gain was approximately constant despite velocity oscillation changes. However, the phase difference caused constructive interference to be converted into destructive interference as the velocity oscillations increased. With a closed boundary and external forcing, the initial velocity oscillation is damped from 200 to 240 Hz and amplified from 260 to 340 Hz. In the damping frequency range, the magnitude of the initial velocity oscillation decreases as the combustion chamber length decreases. When the velocity oscillates between 260 and 340 Hz, the combustion length that shows the maximum velocity oscillation varies from 200 to 500 mm and also decreases as the forcing frequency increases. This can be related to the resonant frequency that increases as the combustion chamber length decreases. There is no damping or amplification with other excitation frequencies. The self-excited pressure oscillations also occurred at a similar frequency range, which can amplify the initial velocity oscillation, but only for a combustor length of 350 mm. The second resonant frequency calculated via low-order combustion instability simulation, OSCILOS, is within the pressure oscillation range. The growth rate computed via OSCILOS exhibited a negative value, except for a combustor length of 350 mm. The growth rate also became negative as the velocity oscillations increased from 0.15 to 0.2 m/s. This could be related to a phase difference change in the FDF. The phase difference of the FDF is varied at only 300 Hz, and changes from in-phase to out-of-phase as the velocity oscillation increases from 0.1 to 0.15 m/s. The results of this study emphasize the importance of the FDF for combustion instability analysis.

Effect of flame motion on longitudinal combustion instabilities

In the analysis of combustion instabilities, especially for the longitudinal modes, the flame typically is regarded as a discontinuity at rest and the flame motion is usually ignored. However, this may lead to errors in the prediction of combustion instabilities for certain conditions. This paper investigates the effect of flame motion on the longitudinal combustion instabilities in a simple ducted combustion chamber. An analytical model considering the flame motion is incorporated into the thermoacoustic system. The dispersion relation is established, and the eigenvalues of thermoacoustic system can be obtained by solving it. The present study considers the cases with and without entropy noise produced at the outlet boundary. The effect of flame motion on longitudinal combustion instabilities is evaluated by consider it and not. When there is no entropy noise, the effect of the flame motion remains small. However, when the entropy noise is considered, the flame motion can have a large effect on different longitudinal modes. Furthermore, the presence of the flame motion can dissipate the entropy wave generated from the flame and further the corresponding combustion instability for the present configuration.

Characterizing modal exponential growth behaviors of self-excited transverse and longitudinal thermoacoustic instabilities

Self-excited thermoacoustic instabilities as frequently observed in rocket motors, gas turbines, ramjets, and aeroengine afterburners are highly detrimental and undesirable for engine manufacturers. Conventionally, modal analysis of such combustion instability is conducted by examining the eigenfrequencies. In this work, thermoacoustic dynamics coupling studies are performed as an alternative approach to predict and characterize modal growth behaviors in the presence of transverse and longitudinal combustion instabilities. Unsteady heat release is assumed to depend on the temperature rate of change that results from the chemical reaction. Coupling the unsteady heat release model with traveling waves enables the modal growth rate of acoustic disturbances to be predicted, thus providing a platform to gain insights onto stability behaviors of the combustor. Both modal growth and total energy analyses of acoustic disturbances are performed by linearizing the unsteady heat release model and recasting it into the classical time-lag N−τ formulation with respect to the velocity potential function ϕ. It is shown from both analyses that the amplitude of any acoustic disturbances tends to increase exponentially with time, until the growth rate is limited by some dissipative process ζ. The chemical reaction rate increase with temperature is shown to be unstable with respect to acoustic wave motions. Furthermore, the maximum modal “growth rate” is determined in the absence of acoustic losses, i.e., ζ = 0. The derived maximum growth rate is experimentally confirmed to be greater than those practically measured ones from both Rijke tubes and swirling combustors. A phase drift is also experimentally observed. Finally, the effects of (1) the interaction index N, (2) the time-delay τ, (3) the ratio γ of the specific heats, and (4) the acoustic losses/damping ζ are examined via cases studies. They are found to vary the critical temperature rate of change of the chemical reaction or the critical frequency ωcri above which the combustion system becomes unstable.

Nonlinear combustion instability analysis of a bluff body burner based on the flame describing function

Lean premixed combustion is a common form of combustion organization in power equipment and propulsion systems. In order to understand the dynamic characteristics of lean premixed flame and predict and control its combustion instability, it is necessary to obtain its flame describing function (FDF). Based on the open source CFD toolbox, OpenFOAM, the dynamic K-equation model, and the finite rate Partially Stirred Reactor (PaSR) model were used to perform large eddy simulations (LES) of lean premixed combustion, and the response of the unsteady heat release rate to single-frequency harmonic disturbances was studied. The response of the unsteady heat release rate was characterized by the FDF, and the response of the unsteady heat release rate to the two-frequency harmonic disturbance was studied. The results show that the quantitative heat release rate response and flame dynamics have very proper accuracy. In the single-frequency harmonic disturbance, as the forcing frequency increases, the curling behavior of the flame surface and the instantaneous vortex structure change; the nonlinear kinematics effect is manifested by the entrainment of the vortex. At lower forcing frequencies, the heat release response changes linearly with the increase of forcing amplitude; at intermediate frequencies, the heat release response exhibits obvious nonlinear behavior; at high frequencies, the heat release response to amplitude changes decreases. The introduction of the second harmonic disturbance will significantly reduce the response range of the total heat release rate and make the combustion more stable.

Thermoacoustics of multi-burner combustors with plenum and chamber cross-talk

This paper presents a thermoacoustic model in the frequency domain for multi-burner combustors composed of multiple plenum-nozzle-chamber modules with cross-talk at both plenums and chambers. The thermoacoustic model is given as a multi-input-multi-output transfer function matrix from heat fluctuation input vector to velocity fluctuation output vector. The discrete rotational symmetry of a multi-burner combustor is exploited to obtain a simple, diagonal transfer function matrix. The resonance equation, whose roots are resonances, is given as a set of scalar equations. The explicit form of the resonance equation reveals how combustor and operating parameters influence the resonances, and which parameters are significant for the longitudinal-azimuthal coupling and the plenum-chamber coupling. The diagonalization also allows us to show constructively that every mode shape is a Bloch wave and those mode shapes can characterize all resonances in terms of longitudinal and azimuthal mode numbers. At a low frequency, the resonance equation can be approximated as biquadratic and quadratic equations for a typical combustor geometry and operating conditions. A bunch of low-frequency resonances, peculiar to multi-burner combustors with cross-talk, are interpreted as azimuthal Helmholtz modes in which plenums/chambers and cross-talk ducts serve as the cavities and necks, respectively. Our combustor model is combined with a diagonal flame transfer function matrix for combustion instability analysis and we develop a set of scalar stability equations whose roots determine combustion instability. This stability equation reveals how combustion instability depends on the combustor geometry and operating parameters. Several numerical examples are presented to validate our thermoacoustic model and theoretical findings.