Prediction Of Thermoacoustic Instabilities Research Articles

Identification of flame transfer function and mechanism analysis of the influence of boundary impedance characteristics on thermoacoustic instability

Thermoacoustic instability is a common problem in the operation of modern gas turbines. The prediction of thermoacoustic instability and the clarification of its mechanism are the research focus and difficulty in the gas turbine industry. As a response function of flame to acoustic disturbance, flame transfer function is a key parameter in the study of thermoacoustic instability. In this paper, based on the scaled adaptive simulation (SAS) model combined with the eddy dissipation concept (EDC) combustion model, the time-domain flow field data are processed by the system identification method, and the results of flame transfer function extraction are in good agreement with the experimental values. Then, the detailed derivation process of the low-order thermoacoustic network model (LOTAN) is given to capture the behavior characteristics of the acoustic wave in the thermoacoustic system. On this basis, the effects of acoustic boundary conditions and hysteresis time on the thermoacoustic instability of the combustion system are analyzed, and the relationship between the mode shape, pressure, vibration velocity phase, and thermoacoustic instability is explored. It is found that the phase relationship between pressure and vibration mode can be used to determine the thermoacoustic instability of the system. This is of great practical significance for determining the thermoacoustic instability of the system and clarifying the internal mechanism of its generation and provides theoretical support for the subsequent thermoacoustic instability control.

Lattice-Boltzmann modeling of the quiet and unstable PRECCINSTA burner modes

Recent studies have shown that Lattice-Boltzmann methods are indeed very promising in the field of reactive flows. More work is required, however, to demonstrate its ability to tackle complex reacting cases, as no study – to the authors’ knowledge – involves simultaneously high Reynolds flows (for which the collision kernel needs specific care), complex geometries (for which models are required at the wall boundaries), and non-uniform grids (where non-conform meshes need to be addressed).The present study intends to fill that gap, by investigating the well-known PRECCINSTA burner, including (i) characteristic boundary conditions, (ii) classical turbulent combustion modeling, (iii) multi-level grid refinements. Combining these elements, numerical simulations of the PRECCINSTA burner are carried out, both for the quiet (φ=0.83) and unstable regimes (φ=0.7). In both regimes, results are consistent with those obtained with classical (Navier–Stokes) solvers, but at a much lower cost. In particular, it is the first time that successful prediction of thermoacoustic instabilities in a complex burner is shown in the framework of Lattice-Boltzmann methods.

Prediction of acoustic pressure of thermoacoustic combustion instability based on Elman neural network

Accurate prediction of thermoacoustic instability is a prerequisite for thermoacoustic control to avoid the damage of combustion chamber, however, this problem has not been completely solved yet. This paper proposes a data-driven method based on the Elman neural network (ENN) to predict the value of acoustic pressure of combustion instability. As a comparison, a model based on support vector machine (SVM) was built. It is proved that ENN has better prediction performance with a certain predicted time horizon compared to the SVM method. What is more, the prediction model based on ENN can adapt to time-varying characteristics of the transition scenario which is characterized by amplitude modulation, multiple frequencies, and irregular bursts. ENN model still maintains enough prediction accuracy for various input training sets, indicating that ENN can fully mine the features of data and has a strong feature extraction ability in combustion oscillation prediction. Hence, it is demonstrated that ENN is a promising prediction tool for thermoacoustic instability under various combustion conditions. These findings are of great significance for the accurate prediction and control of thermoacoustic instability.

Early warning detection of thermoacoustic instability using three-dimensional complexity-entropy causality space

Detection and prediction of thermoacoustic instabilities are major challenges in the development and operation of combustion systems. In this paper, we introduce a tool for categorizing dynamical states and detecting early warning signals of thermoacoustic instability in a combustor. This tool, named complexity-entropy causality space (CECS), exploits the permutation entropy and Jensen–Shannon complexity of both the pressure and heat release rate signal. We identify the early warning stage of thermoacoustic instability in both the experimental and numerical system by applying k-medoids clustering in CECS. This study constitutes the development and demonstration of a novel framework that can accurately detect the onset of impending thermoacoustic instabilities.

Comparison of strongly and weakly nonlinear flame models applied to thermoacoustic instability

Weakly nonlinear flame (or heater) dynamic models, only accounting for heat release rate disturbances from the flame (or heater) at forcing frequencies and omitting harmonic terms due to nonlinear mechanisms, are widely used in low-order tools for the analysis and prediction of thermoacoustic instabilities, because they have a numerical cost much cheaper than tools based on Navier–Stokes equations, and are easier to develop and validate. However, these models may lead to errors under certain conditions. The present work considers a Rijke tube model combustor, in which a classical third-order model is used to describe the flame dynamic response to the oncoming flow disturbance. We call this model the strongly nonlinear flame model. The weakly nonlinear flame model is then introduced. The wave-based approach is adopted as a low-order tool. The weakly and strongly nonlinear flame models are embedded in the low-order tool to reproduce the thermoacoustic instability of the model combustor. The natural frequency and growth rate of thermoacoustic instability are then determined by mode extracted methods. The differences between the results predicted by using the weakly and strongly nonlinear flame models are compared for a set of operating conditions, in order to find the conditions under which the weakly nonlinear flame model works. Short-time Fourier transform is adopted to analyze the extracted frequencies and growth rates of four selected cases. When the dominant acoustic mode strength is much stronger than the remaining modes, the weakly nonlinear models perform well. However, these models fail to capture the mode frequency and growth rate when multiple unstable modes are present.

Transfer learning of deep neural networks for predicting thermoacoustic instabilities in combustion systems

The intermittent nature of operation and unpredictable availability of renewable sources of energy (e.g., wind and solar) would require the combustors in fossil-fuel power plants, sharing the same grid, to operate with large turn-down ratios. This brings in new challenges of suppressing high-amplitude pressure oscillations (e.g., thermoacoustic instabilities (TAI)) in combustors. These pressure oscillations are usually self-sustained, as they occur within a feedback loop, and may induce severe thermomechanical stresses in structural components of combustors, which often lead to performance degradation and even system failures. Thus, prediction of thermoacoustic instabilities is a critical issue for both design and operation of combustion systems. From this perspective, it is important to identify operating conditions which can potentially lead to thermoacoustic instabilities. In this regard, data-driven approaches have shown considerable success in predicting the instability map as a function of operating conditions. However, often the available data are limited to learn such a relationship efficiently in a data-driven approach for a practical combustion system. In this work, a proof-of-concept demonstration of transfer learning is provided, whereby a deep neural network trained on relatively inexpensive experiments in an electrically heated Rijke tube has been adapted to predict the unstable operating conditions for a swirl-stabilized lean-premixed laboratory scaled combustor, for which data are expensive to obtain. The operating spaces and underlying flow physics of these two combustion systems are different, and hence this work presents a strong case of using transfer learning as a potential data-driven solution for transferring knowledge across domains. The results show that the knowledge transfer from the electrically heated Rijke tube apparatus helps in formulating an accurate data-driven surrogate model for predicting the unstable operating conditions in the swirl-stabilized combustor, even though the available data are significantly less for the latter.

A Gaussian-process-based framework for high-dimensional uncertainty quantification analysis in thermoacoustic instability predictions

When combining a flame model with acoustic tools to predict thermoacoustic instability, uncertainties embedded in the flame model and acoustic system parameters propagate through the thermoacoustic model, inducing variations in calculation results. Therefore, uncertainty quantification (UQ) analysis is essential for delivering a reliable prediction of thermoacoustic instability. The present paper proposes a general, surrogate-based framework to efficiently perform UQ analysis in thermoacoustic instability predictions that (1) can handle large variational ranges and flexible statistical descriptions of the uncertain parameters, (2) takes into account uncertainties from both acoustic system parameters and high-dimensional flame response models (e.g. the finite impulse response model (FIR), the flame describing function (FDF), etc.), (3) quantifies uncertainties in modal frequency and linear growth rate for linear thermoacoustic analysis, or (4) quantifies uncertainties in limit cycle frequency and amplitude for nonlinear thermoacoustic analysis. The framework is built upon Gaussian process (GP) surrogate models. An active learning strategy from the machine learning community has been adopted to significantly enhance the efficiency of GP model training, thus achieving a significant reduction in computational cost. The effectiveness of the proposed UQ framework is demonstrated by two case studies: one linear case with an uncertain FIR model and acoustic system parameters, and one nonlinear case with an uncertain FDF dataset and acoustic system parameters. Compared with reference Monte Carlo simulations, the case studies reveal UQ analyses that are, respectively, 20 and 15 times faster, but nevertheless highly accurate. The proposed GP-based framework also forms an efficient foundation on which to address other types of studies, in which repetitive thermoacoustic calculations are required, such as parametric investigations, sensitivity analyses, nonlinear bifurcation studies and robust design.

Data-driven Detection and Early Prediction of Thermoacoustic Instability in a Multi-nozzle Combustor

ABSTRACT Thermoacoustic instability (TAI) is a critical issue in modern lean-burn gas-turbine combustors, which is induced by a strong coupling between the resonant combustor acoustics and fluctuations in the heat release rate. This instability may lead to high-amplitude pressure waves that generate undesirable noise levels as well as fatigue stresses in mechanical structures of the combustor. The intense pressure fluctuations due to TAI may also cause large flow perturbations and possibly flow reversal that may lead to flame oscillations, flame liftoff, and even flame blow-out. Hence, there is a strong need for exercising control actions in a timely fashion to mitigate the TAI phenomena. Anomaly detection is an essential prerequisite to the design of a good controller and such a detector must be able to reliably predict a forthcoming TAI. To detect and predict the onset of a TAI from an ensemble of pressure time series, this paper investigates three data-driven methods: Fast Fourier transform (FFT), symbolic time series analysis (STSA), and hidden Markov modeling (HMM). The main focus of the paper is to make a comparative evaluation of these three anomaly detection methods for classification of the current regime of operation into stable and unstable categories as well as for real-time identification of precursors to impending instabilities with short-length time series of measured variables (e.g., pressure oscillations). The results, generated on experimental data from a multi-nozzle combustor apparatus, have been compared to evaluate the performance of FFT, STSA, and HMM methods for TAI analysis.

Experimental analysis on mechanism and prediction of thermo-acoustic instability of supercritical RP-3 fuel flowing in a vertical upward channel

This article presented an experimental investigation of thermo-acoustic instability of RP-3 (Rocket Propellant 3) aviation kerosene under supercritical pressures in a vertical upward circular channel. The oscillation characteristics of measured parameters were studied. The mechanisms and characteristics of unstable flow and heat transfer were analyzed. The effects of operating parameters, including the inlet fluid temperature, inlet fluid pressure, mass flow rate, and heat flux, on flow and heat transfer instabilities were discussed. The investigation on boundary between stable and unstable conditions under various operating parameters was performed, and two new empirical correlations for critical heat flux prediction were obtained. Results indicate that the coupling relation between the inside-wall temperature, outlet fluid temperature, and inlet-outlet pressure drop is found. The instability of pseudo-film boiling leads to this unstable phenomenon. The critical heat flux increases as the inlet fluid pressure rises, while increases first and then decreases with the increasing Reynolds number of inlet fluid. The proposed correlations work reasonably well in predicting the onset of thermo-acoustic instability.

Effects of liquid fuel/wall interaction on thermoacoustic instabilities in swirling spray flames

Computational prediction of thermoacoustic instabilities arising in gas turbine and aero-engine combustors still remains a challenge especially if fuel is injected in a liquid spray form. This study shows that, in LES of such a combustor, the treatment of the liquid fuel film created on the walls of the injection system affects the mean flame weakly, but modifies the flame dynamics strongly. The configuration used for this work is the experimental setup SICCA-spray available at EM2C laboratory in Paris. First steady spray flame measurements are used to validate the LES Euler-Lagrange approach. Two modelling strategies for the interaction between the liquid fuel and the injector walls are tested with a negligible impact on the flame shape and structure. In the second part the same comparison is applied to another operating condition where a self-sustained thermo-acoustic limit-cycle is experimentally observed. In that case resonant coupling is achieved with LES, confirming the adequacy of the approach but only when the film layer is taken into account. Indeed, contrarily to the stable configuration, the difference between the two Lagrangian boundary conditions is shown to have a major impact on the feedback mechanism leading to the thermoacoustic oscillation.

Large-Eddy-Simulation Modeling of the Flame Describing Function of a Lean-Premixed Swirl-Stabilized Flame

The prediction of thermo-acoustic instabilities is of paramount importance for gas-turbine combustion systems to meet the emission and efficiency targets. To predict the frequencies and amplitudes of pressure oscillations, and as a consequence, their impact on engine reliability, the nonlinear behavior of the system should be studied. An atmospheric lean-premixed combustor has been numerically investigated for validation purposes. A decoupled approach, separating the acoustic behavior and the nonlinear flame response, which is represented in this work by the flame describing function, has been used. As the first step, the flame describing function calculation from large-eddy simulations has been validated, including the effects of flame stretch and heat loss into the turbulence combustion model. Then, frequency-domain calculations using a three-dimensional Helmholtz solver have been carried out, and results have been validated against experimental measurements and a self-excited large-eddy simulation.

A novel modal expansion method for low-order modeling of thermoacoustic instabilities in complex geometries

This work proposes an improvement to existing methods based on modal expansions used for the prediction of thermoacoustic instabilities in zero Mach number flow conditions. Whereas the orthogonal basis made of the acoustic eigenmodes of the domain bounded by rigid walls is classically used, an alternative method based on a modal expansion onto an over-complete set of acoustic eigenmodes is proposed. This allows avoiding the misrepresentation of the acoustic velocity field often observed near non rigid-wall boundaries. A Low Order Model network utilizing a state-space framework is then built upon this novel type of modal expansion. Several test cases, going from non reacting ducts to a complex geometry with combustion, are studied to assess the potential of the approach. The methodology not only successfully mitigates the misrepresentation in the acoustic field in the presence of non-rigid-wall boundaries, but it also drastically improves the convergence speed. The modularity of the method and its ability to handle complex geometries are illustrated by considering a configuration featuring an annular chamber, an annular plenum, as well as multiple burners. This novel technique is expected to bring worthy improvements to existing Low Order Models using modal expansions for the prediction of combustion instabilities.

Intrinsic thermoacoustic modes and their interplay with acoustic modes in a Rijke burner

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.

Dynamic Data-Driven Design of Lean Premixed Combustors for Thermoacoustically Stable Operations

Prediction of thermoacoustic instabilities is a critical issue for both design and operation of combustion systems. Sustained high-amplitude pressure and temperature oscillations may cause stresses in structural components of the combustor, leading to thermomechanical damage. Therefore, the design of combustion systems must take into account the dynamic characteristics of thermoacoustic instabilities in the combustor. From this perspective, there needs to be a procedure, in the design process, to recognize the operating conditions (or parameters) that could lead to such thermoacoustic instabilities. However, often the available experimental data are limited and may not provide a complete map of the stability region(s) over the entire range of operations. To address this issue, a Bayesian nonparametric method has been adopted in this paper. By making use of limited experimental data, the proposed design method determines a mapping from a set of operating conditions to that of stability regions in the combustion system. This map is designed to be capable of (i) predicting the system response of the combustor at operating conditions at which experimental data are unavailable and (ii) statistically quantifying the uncertainties in the estimated parameters. With the ensemble of information thus gained about the system response at different operating points, the key design parameters of the combustor system can be identified; such a design would be statistically significant for satisfying the system specifications. The proposed method has been validated with experimental data of pressure time-series from a laboratory-scale lean-premixed swirl-stabilized combustor apparatus.

A Green’s function approach to the rapid prediction of thermoacoustic instabilities in combustors

The prediction of thermoacoustic instabilities is fundamental for combustion systems such as domestic burners and industrial gas turbine engines. High-amplitude pressure oscillations cause thermal and mechanical stress to the equipment, leading to premature wear or even critical damage. In this paper we present a new approach to produce nonlinear (i.e. amplitude-dependent) stability maps of a combustion system as a function of various parameters. Our approach is based on the tailored Green’s function of the combustion system, which we calculate analytically. To this end, we assume that the combustor is one-dimensional, and we describe its boundary conditions through reflection coefficients. The heat release is modelled by a generalised $n{\it\tau}$ law. This includes a direct-feedback term in addition to the usual time-lag term; moreover, its parameters (time lag, coupling coefficients) depend on the oscillation amplitude. The model provides new insight into the physical mechanism of the feedback between heat release rate and acoustic perturbations. It predicts the key nonlinear features of the thermoacoustic feedback, such as limit cycles, bistability and hysteresis. It also explains the frequency shift in the acoustic modes.

Response of a swirl-stabilized flame to simultaneous perturbations in equivalence ratio and velocity at high oscillation amplitudes

The flame describing function is a valuable tool for the limit-cycle prediction of thermoacoustic instabilities, which are frequently observed in modern gas turbines. In these applications, flames are of lean partially premixed type, and their unsteady response originates from a combination of mechanisms related to perturbations in velocity and equivalence ratio. The interference between these two mechanisms at high forcing amplitudes is the focus of the present study. Well-defined variations of the degree of unmixedness of a practically relevant swirl flame are analyzed to obtain the nonlinear response of the flame to equivalence ratio fluctuations. A lean premixed swirl-stabilized flame is investigated experimentally at atmospheric conditions for a Reynolds number of approximately 35,000. The flow field and the flame dynamics are investigated for perfectly and partially premixed conditions at various frequencies and excitation amplitudes using high-speed particle image velocimetry and OH*-chemiluminescence imaging. The multi microphone method is applied at different degrees of unmixedness of fuel and air to obtain the nonlinear flame response. By a change in the fuel split between two injection positions the unmixedness is controlled. The nonlinear flame response of the different partially premixed flames and the corresponding premixed flame are analyzed in this study. A decomposition approach is applied to emphasize the trends caused by the contribution of the equivalence ratio perturbations to the flame describing function. Flow field measurements indicate that the flow field dynamics are very similar for the investigated premixed and partially premixed flames. The results of the flame describing function decomposition support the assumption of a superposition of equivalence ratio perturbations and velocity fluctuations effects at low and high forcing amplitudes for most of the investigated frequencies. The decomposition reveals a saturation of the equivalence ratio contribution to the flame response already at small acoustic forcing amplitudes. A conceptual reasoning is presented with the help of a simplified flame model, which explains the observed saturation in the response of partially premixed flames. Increased mixing at high forcing amplitudes is proposed as a new saturation mechanism. Especially at small and intermediate forcing amplitudes as well as higher frequencies, increased turbulence production and changes in the mean flow field lead to an increase of the damping of equivalence ratio fluctuations. An experimentally observed growth of the turbulent shear stresses with increasing acoustic forcing amplitude supports this explanation.

Nonlinear Instability Analysis for Partially Premixed Swirl Flames

Limit-cycle prediction of thermoacoustic instabilities for unstable practical gas turbine combustion systems is still a challenge for the gas turbine industry. The nonlinear stability analysis is especially demanding for highly turbulent swirling flames with significant equivalence ratio fluctuations. In the present study, a partially premixed swirl-stabilized flame at a Reynolds number of approximately 35,000 is investigated. An experimentally obtained flame describing function (FDF) is used for the determination of the thermoacoustic oscillation frequency and amplitude. Damping is obtained directly from measurements. The multi-microphone method is used to determine the amplitude dependent transfer function of the flame as well as the transfer function of the burner and the acoustic response of the boundary conditions. Solving the thermoacoustic modeling framework, with the measured transfer functions incorporated, yields frequency and amplitude of the self-excited limit cycle oscillation. The error between model and experimental results is thoroughly assessed. Measurements were made for various lengths of the combustion chamber exhaust gas tube to verify the results for different frequencies and amplitudes. Good agreement is found for the entire range of combustor lengths investigated. A sensitivity analysis of the linear flame transfer function to several operational parameters is provided allowing for an assessment of the limits of the nonlinear stability analysis approach. Furthermore, the effect of amplitude dependent damping is addressed.

Assessment of Flame Transfer Function Formulations for the Thermoacoustic Analysis of Lean Burn Aero-engine Combustors

The numerical analysis of thermoacoustic instability in lean burn aero-engines requires proper Flame Transfer Functions (FTF) able to describe the complex physical phenomena characterizing the coupling between heat release rate fluctuations and the acoustic field which is further complicated by the use of liquid fuel together with advanced injection systems. In this work simple FTF formulations have been applied to the thermoacoustic analysis of a tubular combustor equipped with a PERM (Partially Evaporating and Rapid Mixing) injection system with the main aim of assessing their capabilities in the prediction of thermoacoustic instabilities in lean burn aero-engine combustors.

Temperature Response of an Acoustically Forced Turbulent Lean Premixed Flame: A Quantitative Experimental Determination

Temperature measurements have been taken on an acoustically forced lean premixed turbulent bluff-body stabilized flame. The burner used in this study is a test-bed to investigate thermoacoustic instability in gas-turbine engines at the University of Cambridge. Numerous experiments have been performed on the burner, one of which used two-line OH planar laser induced fluorescence to measure temperature. Here, we employ vibrational coherent anti-Stokes Raman scattering (CARS) of nitrogen as an alternative to measure temperature, circumventing the limitations of the former method. The use of nitrogen CARS avoids the problem of probing regions of the flame with low OH concentrations that resulted in erroneous temperature. Such an application of CARS showed that the results from previous efforts were systematically biased up to 47% close to the bluff-body. We also critically review the limitations of CARS used in our experiments, pertaining to spatial resolution and associated biasing further downstream from the bluff-body. Using the more accurate results from this work, more up-to-date computational fluid dynamical (CFD) models of the burner can be validated, with the aim of improved understanding and prediction of thermoacoustic instability in gas turbines.

Prediction of thermoacoustic instability in Rijke tube using CFD-CAA numerical method

The coupling between the emitted energy and the acoustic energy in a thermal system, e.g. combustor, may result in system instability accompanying severe vibration. In this study, the limit curve for thermo-acoustic instability is numerically obtained by using the CFD- CAA combined method. The response function for pulsating release of heat in the Rijke tube and the distribution of mean density in the tube are computed accurately by the CFD analysis and used as inputs to CAA predictions. To verify the accuracy of the prediction method, the thermo-acoustics inside the horizontal, one meter long Rijke tube of square cross-section, which has the heating part at the location of one quarter length, is simulated. The predicted instability curve agrees well with the experimental one except the low flow- rate region of ReDo < 1.