Flame Transfer Function Research Articles

Influence of flame dynamics on the optimal control of combustion with uncertainties

ABSTRACTA non-linear optimal control system is developed for attenuating thermos-acoustic pressure oscillations in a combustion chamber where the unsteady flow field associated with the internal instability is modelled in terms of a finite set of assumed modes of the non-linear in-homogeneously driven pressure wave field. A distributed set of auxiliary fuel injectors are used to control the thermo-acoustic pressure field with pressure measurements at independent locations. The mathematical model of the thermo-acoustic pressure field with multiple fuel injectors is developed. The flame dynamics is also modelled and its states are included in the design of the controller. Extensive simulations are performed to reveal the features of the thermo-acoustic pressure field within the combustion chamber and qualitatively compared with published data. The controller is synthesized on the basis of a non-linear quadratic Gaussian approach as well as a non-linear H∞ controller approach. The performances of the two controllers are compared. The influence of the flame dynamics is assessed by comparing the closed-loop performance by including the lag effects of a simplified flame transfer function. In particular it is shown that the non-linear H∞ controller approach is well-suited for the control of the combustion chamber pressure field as it has the structure of comb or multiple-notch filter and can attenuate acoustic tones associated with the combustion instabilities.

Coupling heat transfer and large eddy simulation for combustion instability prediction in a swirl burner

Large eddy simulations (LES) of combustion instabilities are often performed with simplified thermal wall boundary conditions, typically adiabatic walls. However, wall temperatures directly affect the gas temperatures and therefore the sound speed field. They also control the flame itself, its stabilization characteristics and its response to acoustic waves, changing the flame transfer functions (FTFs) of many combustion chambers. This paper presents an example of LES of turbulent flames fully coupled to a heat conduction solver providing the temperature in the combustor walls. LES results obtained with the fully coupled approach are compared to experimental data and to LES performed with adiabatic walls for a swirled turbulent methane/air burner installed at Engler-Bunte-Institute, Karlsruhe Institute of Technology and German Aerospace Center (DLR) in Stuttgart. Results show that the fully coupled approach provides reasonable wall temperature estimations and that heat conduction in the combustor walls strongly affects both the mean state and the unstable modes of the combustor. The unstable thermoacoustic mode observed experimentally at 750 Hz is captured accurately by the coupled simulation but not by the adiabatic one, suggesting that coupling LES with heat conduction solvers within combustor walls may be necessary in other configurations in order to capture flame dynamics.

Response of a swirl flame to inertial waves

Acoustic waves passing through a swirler generate inertial waves in rotating flow. In the present study, the response of a premixed flame to an inertial wave is scrutinized, with emphasis on the fundamental fluid-dynamic and flame-kinematic interaction mechanism. The analysis relies on linearized reactive flow equations, with a two-part solution strategy implemented in a finite element framework: Firstly, the steady state, low-Mach number, Navier–Stokes equations with Arrhenius type one-step reaction mechanism are solved by Newton’s method. The flame impulse response is then computed by transient solution of the analytically linearized reactive flow equations in the time domain, with mean flow quantities provided by the steady-state solution. The corresponding flame transfer function is retrieved by fitting a finite impulse response model. This approach is validated against experiments for a perfectly premixed, lean, methane-air Bunsen flame, and then applied to a laminar swirling flame. This academic case serves to investigate in a generic manner the impact of an inertial wave on the flame response. The structure of the inertial wave is characterized by modal decomposition. It is shown that axial and radial velocity fluctuations related to the eigenmodes of the inertial wave dominate the flame front modulations. The dispersive nature of the eigenmodes plays an important role in the flame response.

Finite element analysis of self-excited instabilities in a lean premixed gas turbine combustor

The present study numerically simulates self-excited instabilities of hydrogen-blended natural gas flames in a lean premixed gas turbine combustor with variable chamber length. In order to effectively predict the thermoacoustic instability within the detailed geometry of the combustor, the Helmholtz equation is discretized with a Galerkin finite element method on a three-dimensional hybrid unstructured mesh. The unsteady heat release rate is modeled with an experimentally measured flame transfer function. The nonlinearity associated with the flame response term is handled with an iterative method, and the large-scale eigenvalue problem is solved by means of the shift-invert method of the ARPACK (ARnoldi PACKage) software. The present Helmholtz solver reproduces the experimentally observed instabilities in terms of the mode frequency and the chamber length range of self-excited pressure oscillations which are significantly affected by the hydrogen enrichment of natural gas fuel. The effects of the acoustic boundary condition and the flame response model on the predictive accuracy are also discussed.

The effect of an axial mean temperature gradient on communication between one-dimensional acoustic and entropy waves

This work performs a theoretical and numerical analysis of the communication between one-dimensional acoustic and entropy waves in a duct with a mean temperature gradient. Such a situation is highly relevant to combustor flows where the mean temperature drops axially due to heat losses. A duct containing a compact heating element followed by an axial temperature gradient and choked end is considered. The proposed jump conditions linking acoustic and entropy waves on either side of the flame show that the generated entropy wave is generally proportional to the mean temperature ratio across the flame and the ratio [Formula: see text], where [Formula: see text] is the flame transfer function. It is inversely proportional to the Mach number immediately downstream of the flame M2. The acoustic and entropy fields in the region of axial mean temperature gradient are calculated using four approaches: (1) using the full three linearised Euler equations as the reference; (2) using two linearised Euler equations in which the acoustic and entropy waves are assumed independent (thus allowing the extent of communication between the acoustic and entropy wave to be evaluated); (3) using a Helmholtz solver which neglects mean flow effects and (4) using a recently developed analytical solution. It is found that the communication between the acoustic and entropy waves is small at low Mach numbers; it rises with increasing Mach number and cannot be neglected when the mean Mach number downstream of the heating element exceeds 0.1. Predictions from the analytical method generally match those from the full three linearised Euler equations, and the Helmholtz solver accurately determines the acoustic field when [Formula: see text].

An analytical model based on the G-equation for the response of technically premixed flames to perturbations of equivalence ratio

A model for the response of technically premixed flames to equivalence ratio perturbations is proposed. The formulation, which is an extension of an analytical flame tracking model based on the linearized G-equation, considers the flame impulse response to a local, impulsive, infinitesimal perturbation that is transported by convection from the flame base towards the flame surface. It is shown that the contributions of laminar flame speed and heat of reaction to the impulse response exhibit a local behavior, i.e. the flame responds at the moment when and at the location where the equivalence ratio perturbation reaches the flame surface. The time lag of this process is related to a convective time scale, which corresponds to the convective transport of fuel from the base of the flame to the flame surface. On the contrary, the flame surface area contribution exhibits a non-local behavior: albeit fluctuations of the flame shape are generated locally due to a distortion of the kinematic balance between flame speed and the flow velocity, the resulting wrinkles in flame shape are then transported by convection towards the flame tip with the restorative time scale. The impact of radial non-uniformity in equivalence ratio perturbations on the flame impulse response is demonstrated by comparing the impulse responses for uniform and parabolic radial profiles. Considerable deviation in the phase of the flame transfer function, which is important for thermo-acoustic stability, is observed.

Uncertainty quantification and sensitivity analysis of thermoacoustic stability with non-intrusive polynomial chaos expansion

In this paper, non-intrusive polynomial chaos expansion (NIPCE) is used for forward uncertainty quantification and sensitivity analysis of thermoacoustic stability of two premixed flame configurations. The first configuration is a turbulent swirl combustor, modeled by the Helmholtz equation with an n−τ flame model. Uncertain input parameters are the gain and the time delay of the flame, as well as the magnitude and the phase of the outlet reflection coefficient. NIPCE is successfully validated against Monte Carlo simulation. It is observed that the first order expansion suffices to yield accurate results. The second configuration under investigation is a low order network model of a laminar slit burner, with the flame transfer function identified from weakly compressible CFD simulations of laminar reacting flow. Firstly the uncertainty and sensitivity of the growth rate due to three uncertain input parameters of the CFD model – i.e., flow velocity, burner plate temperature and equivalence ratio – are analyzed. A Monte Carlo simulation is no longer possible due to the computational cost of the CFD simulations. Secondly, two additional uncertain parameters are taken into account, i.e., the respective magnitudes of inlet and outlet reflection coefficients. This extension of the analysis does not entail a considerable increase in computational cost, since the additional parameters are included only in the low order network model. In both cases, the second order expansion is sufficient to model the uncertainties in growth rate.

Convective Scaling of Intrinsic Thermo-Acoustic Eigenfrequencies of a Premixed Swirl Combustor

Spectral distributions of the sound pressure level (SPL) observed in a premixed, swirl stabilized combustion test rig are scrutinized. Spectral peaks in the SPL for stable as well as unstable cases are interpreted with the help of a novel criterion for the resonance frequencies of the intrinsic thermo-acoustic (ITA) feedback loop. This criterion takes into the account the flow inertia of the burner and indicates that in the limit of very large flow inertia, ITA resonance should appear at frequencies where the phase of the flame transfer function (FTF) approaches −π/2. Conversely, in the limiting case of vanishing flow inertia, the new criterion agrees with previous results, which state that ITA modes may arise when the phase of the FTF is close to −π. Relying on the novel criterion, peaks in the SPL spectra are identified to correspond to either ITA or acoustic modes. Various combustor configurations are investigated over a range of operating conditions. It is found that in this particular combustor, ITA modes are prevalent and dominate the unstable cases. Remarkably, the ITA frequencies change significantly with the bulk flow velocity and the position of the swirler but are almost insensitive to changes in the length of the combustion chamber (CC). These observations imply that the resonance frequencies of the ITA feedback loop are governed by convective time scales. A scaling rule for ITA frequencies that relies on a model for the overall convective flame time lag shows good consistency for all operating conditions considered in this study.

Dynamic responses of anchored ducted flames to harmonic velocity forcing

This paper aims at developing a computationally inexpensive method to investigate the premixed flame instabilities. The kinematic G-equation is combined with a two-dimensional discrete vortex method, and the conformal mapping is applied to make calculations for complicated geometries more efficiently. The vortex dynamics and flame response to harmonic velocity forcing of an anchored ducted V-flame are investigated, and the effects of harmonic forcing, Reynolds number, and bluff body geometry are examined. Results show that the vortex structures, flow instability, and flame response are closely coupled with each other. The unsteady vortex structures generate instabilities at the flame base, and the convection of the flame wrinkles then influences the flame dynamics downstream. The flame heat release fluctuates with larger amplitude under low-frequency forcings, while the phase of the flame transfer function is quasi-linear with increasing forcing frequency. Both higher inflow velocity and sharper bluff body corners can result in more unsteady large-scale vortex structures and hence influence the flame responses.

Influence of flame-holder temperature on the acoustic flame transfer functions of a laminar flame

The occurrence of combustion instabilities in high-performance engines such as gas turbines is often affected by the thermal state of the engine. For example, strong bursts of pressure fluctuations may occur at cold start for operating conditions that are stable once the engine reaches thermal equilibrium. This observation raises the question of the influence of material temperature on the response of flames to acoustic perturbations. In this study, we assess the influence of the temperature of the flame holder for a laminar flame. Both experiments and numerical simulations show that the Flame Transfer Function (FTF) is strongly affected by the flame-holder temperature. The key factors driving the evolution of the FTF are the flame-root location as well as the modification of the flow, which affects its stability. In the case of the cooled flame-holder, the formation of a recirculation zone is identified as the main impact on the FTF.

Transient and limit cycle combustion dynamics analysis of turbulent premixed swirling flames

Premixed low swirling flames (methane–air and hydrogen–methane–air) are experimentally investigated for three different regimes. Stable, local transient to instability and limit cycle regimes corresponding to three distinct equivalence ratios are considered. Dynamic mode decomposition is applied to the hydrogen–air–methane flame to retrieve the modes frequencies, growth rates and spatial distributions for each regime. The results indicate that a vortical wave propagating along the flame front is associated with the transition from stability to instability. In addition, it is shown that a key effect on stability is the location of the non-oscillating (0 Hz) flame component. The phase-averaged unsteady motion of the flames over one cycle of oscillation shows the vortical wave rolling up the flame front. The Rayleigh index maps are formed to identify the region of driving and damping of the self-sustained oscillation, while the flame transfer function phase leads to the propagation mode of the perturbations along the flame front. The second mechanism identified concerns the swirl number fluctuation induced by the mode conversion. By utilizing hypotheses for the flow field and the flame structure, it is pointed out that those mechanisms are at work for both flames (methane–air and hydrogen–methane–air) and their effects on the unsteady heat release are determined. Both unsteady heat release contributions, the vortical wave induces flame surface fluctuations and swirl number oscillation induces unsteady turbulent burning velocity, are in phase opposition and of similar amplitudes.

부분 예혼합 가스터빈 연소기에서의 비연소 전달함수 계측으로부터의 화염전달함수 특성 파악

부분 예혼합 가스터빈 연소기에서의 비연소 전달함수 계측으로부터의 화염전달함수 특성 파악

Acoustic damping optimization of the injector based on dynamic mode decomposition in a subscale combustor

The acoustic tuning of a swirl coaxial jet injector mounted upstream a combustion chamber is investigated in the aspect of stabilization of unstable combustion. The injector, which has a primary function to mix the oxidizer injected through the central passage and the fuel injected through the peripheral holes, is designed to be used as a half-wave resonator. The least damped modes are extracted by applying Dynamic mode decomposition (DMD) and the injector length is tuned to damp the second longitudinal mode. Then, the sensitivity of the heat release perturbation to the velocity perturbation at the frequency of the second longitudinal mode is evaluated by flame transfer function calculated by DMD. The relation between these two quantities is achieved by combining two equations, that is, the Crocco’s model and the inhomogeneous wave equation, and enables us to compute Flame transfer function (FTF) at a specific mode. The gain field of FTF shows that the sensitivity of the heat release fluctuation to the inlet velocity fluctuation is minimal with the optimal injector length. The proposed approach for application of dynamic mode decomposition would be a valuable tool in tuning a resonator acoustically, computing efficiently flame transfer function, and quantifying the relative stability of a combustion chamber.

Application of a three-step approach for prediction of combustion instabilities in industrial gas turbine burners

Abstract Recently, because of environmental regulations, gas turbine manufacturers are restricted to produce machines that work in the lean combustion regime. Gas turbines operating in this regime are prone to combustion-driven acoustic oscillations referred as combustion instabilities. These oscillations could have such high amplitude that they can damage gas turbine hardware. In this study, the three-step approach for combustion instabilities prediction is applied to an industrial test rig. As the first step, the flame transfer function (FTF) of the burner is obtained performing unsteady computational fluid dynamics (CFD) simulations. As the second step, the obtained FTF is approximated with an analytical time-lag-distributed model. The third step is the time-domain simulations using a network model. The obtained results are compared against the experimental data. The obtained results show a good agreement with the experimental ones and the developed approach is able to predict thermoacoustic instabilities in gas turbines combustion chambers.

Two-step approach for pressure oscillations prediction in gas turbine combustion chambers

Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion-driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damage of combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. We have developed a two-step method to find a set of operating parameters under which gas turbines can be operated without going into self-excited pressure oscillations. As the first step, an unsteady Reynolds-averaged Navier–Stokes simulation with the flame speed closure model implemented in the OpenFOAM® environment is performed to obtain the flame transfer function of the combustion set-up. As the second step time-domain simulations employing low-order network model implemented in Simulink® are executed. In this work, we apply the proposed method to the Beschaufelter RingSpalt test rig developed at the Technische Universität München. The sensitivity of thermoacoustic stability to the length of a combustion chamber, flame position, gain and phase of flame transfer function and outlet reflection coefficient are studied.

An analytical study of the flame dynamics of a transversely forced asymmetric two-dimensional Bunsen flame

Combustion instabilities in annular combustors are of great interest because of their industrial relevance. Azimuthal acoustic modes, which involve transverse acoustic forcing to flames, have become a key process related to annular combustor instabilities. Transverse mean flow may be a factor that affects azimuthal oscillations. This paper provides an analytical model for a transversely forced two-dimensional Bunsen flame under transverse mean flow. The model is established using a low-amplitude perturbation assumption applied to a G-equation formulation. Forced flame displacement and flame transfer functions (FTFs) are calculated. The results are verified based on numerical solutions of the G-equation. Effects of frequency, transverse mean flow velocity and vertical mean flow velocity on the FTFs are discussed. The symmetric flame without transverse mean flow has a vanishing response to transverse acoustic forcing, while asymmetric flames, which are formed with transverse mean flow, have a bandpass response to transverse forcing. The response at very low and high forcing frequencies is small, with higher transfer function gains only in a certain frequency range. This bandpass response, which is inherently linked to the asymmetry of the flame, is an important factor to account for when considering the flame dynamics related to transverse acoustic effects.

Numerical analysis of the dynamic flame response of a spray flame for aero-engine applications

Incoming standards on NO x emissions are motivating many aero-engine manufacturers to adopt the lean burn combustion concept. One of the most critical issues affecting this kind of technology is the occurrence of thermo-acoustic instabilities that may compromise combustor life and integrity. Therefore the prediction of the thermo-acoustic behaviour of the system becomes of primary importance. In this paper, the complex interaction between the system acoustics and a turbulent spray flame for aero-engine applications is numerically studied. The dynamic flame response is computed exploiting reactive URANS simulations and system identification techniques. Great attention has been devoted to the impact of liquid fuel evolution and droplet dynamics. For this purpose, the GE Avio PERM (partially evaporating and rapid mixing) lean injection system has been analysed, focussing attention on the effect of several modelling parameters on the combustion and on the predicted flame response. A frequency analysis has also been set up and exploited to obtain even more insight on the dynamic flame response of the spray flame. The application is one of the few in the literature where the dynamic flame response of spray flames is numerically investigated, providing a description in terms of flame transfer function and detailed information on the physical phenomena.

The contribution of intrinsic thermoacoustic feedback to combustion noise and resonances of a confined turbulent premixed flame

The influence of Intrinsic Thermoacoustic (ITA) feedback on the combustion noise spectrum produced by a confined, turbulent, premixed, swirl flame is investigated. The analysis is based on the understanding that sound is generated by unsteady heat release resulting from turbulent fluctuations on the one hand, and from the response of the flame to incoming acoustic perturbations on the other. The former effect is described by a source term for combustion noise, i.e. a spectral distribution of unsteady heat release rate, the latter by the flame transfer function. Both quantities are identified from time series data for fluctuating velocity and heat release rate, generated with large eddy simulation of premix swirl burner. The combustion noise source term and the flame transfer function are then introduced in an acoustic network model of the test rig in order to compute the spectral distribution of the sound pressure level at a certain location in the combustion chamber. Results for the noise spectrum are in good agreement with experiment, showing a broadband component and well-defined peaks. The frequencies of the peaks correspond to either acoustic cavity or ITA resonances. The acoustic network model is used for parametric studies, where the acoustic reflection coefficient at the combustor exit is varied. Remarkably, it is found that the magnitude of the ITA peak increases with decreasing values of the acoustic reflection coefficient, and vice versa. Furthermore, the influence of combustion chamber length on resonance frequencies is explored. It is observed that the frequency of the ITA resonance is insensitive to combustor length. This behaviour is observed qualitatively also in experiments.

Theoretical analysis of the conical premixed flame response to upstream velocity disturbances considering flame speed development effects

The effect of upstream velocity perturbations on the response of a premixed flame was investigated in terms of the flame transfer function dependency on excitation frequency. In this study, the assumption of constant flame speed was extended and the effect of flame speed development was considered; i.e., the flame speed would grow with the time after ignition or with the distance from a flame-holder. In the present study, the kinematics of a conical flame was investigated by linearization of the front tracking equation of flame to uniform and convected fluctuations of the flow velocity and the response was compared with that of a V-shaped flame and the experimental data in the previous studies. The results show that the effect of flame speed development could influence a decreasing gain and increase the phase of the flame response to the uniform velocity oscillations in low and moderate frequencies. Comparing the variations in the gain of flame response upon normalized frequency, show that a conical flame has lower values than the V-flame. In other words, these flames might be less susceptible to combustion instabilities than the V-flames. Furthermore, the variations in phase of the V-flames responses, which show a quasi-linear behavior with normalized frequency, have higher values than the saturated behavior in phase of the conical flame responses. Also, considering that the flame speed development induces an increase in the gain and phase of the conical flame response to the convected velocity oscillations in certain frequencies; because the developed flame front has longer length in comparison to the flame front in constant flame speed model. Therefore, the flame length may be longer than convective wavelength and the heat release would be generated in different points of the flame; consequently the flow oscillations might exert a stronger impact on the unsteady heat release fluctuations.

High-Frequency Thermoacoustic Modulation Mechanisms in Swirl-Stabilized Gas Turbine Combustors—Part II: Modeling and Analysis

This paper deals with high-frequency (HF) thermoacoustic instabilities in swirl-stabilized gas turbine combustors. Driving mechanisms associated with periodic flame displacement and flame shape deformations are theoretically discussed, and corresponding flame transfer functions (FTF) are derived from first principles. These linear feedback models are then evaluated by means of a lab-scale swirl-stabilized combustor in combination with part one of this joint publication. For this purpose, the models are used to thermoacoustically characterize a complete set of operation points of this combustor facility. Specifically, growth rates of the first transversal modes are computed, and compared against experimentally obtained pressure amplitudes as an indicator for thermoacoustic stability. The characterization is based on a hybrid analysis approach relying on a frequency domain formulation of acoustic conservation equations, in which nonuniform temperature fields and distributed thermoacoustic source terms/flame transfer functions can be straightforwardly considered. The relative contribution of flame displacement and deformation driving mechanisms–i.e., their significance with respect to the total driving–is identified. Furthermore, promoting/inhibiting conditions for the occurrence of high frequency, transversal acoustic instabilities within swirl-stabilized gas turbine combustors are revealed.