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The natural eigen-modes of a combustion system are a strong function of its geometric design, temperature profile, and boundary conditions. Many practical systems have multiple, closely-spaced natural mode frequencies. While several prior studies have noted the nonlinear interactions that occur when multiple, linearly unstable modes are present, the nature of these interactions for closely-spaced modes has not been analytically treated. This paper treats this problem theoretically by utilizing a Galerkin expansion of the Euler equations, and the method of averaging to derive a set of amplitude equations for the modal amplitudes. In cases where the frequency spacing is large, many of the oscillatory terms have short time-scales and average out. However, in the case of closely-spaced modes, terms oscillating at the frequency difference between the closely-spaced frequencies correspond to long time-scales and, thus, remain after the averaging process. Results show that frequency spacing between the modes has significant impacts on limit-cycle amplitudes and their stability, even in the case of a static non-linearity. In addition, the conditions under which both modes can co-exist are a strong function of the frequency spacing. There are also certain conditions where one mode is completely suppressed by the other, even if both modes have positive linear growth rates; non-intuitively, the mode that is suppressed could be the one with the larger growth rate. The conditions under which one mode is suppressed are also a strong function of the frequency spacing parameter. Finally, for conditions in which one mode is suppressed, the limit cycle amplitude of the other mode is independent of the frequency spacing. Taken together these results show the difficulty in experimentally inferring the linear stability/instability of (non-dominant) combustor modes based upon “steady state” data taken during limit cycle conditions. [ABSTRACT FROM AUTHOR]

Direct numerical simulations (DNS) with detailed chemical kinetics and chemical explosive mode analysis (CEMA) are performed to investigate the effect of operating pressure and hydrogen–methane blending on laminar wrinkled flames at reheat combustion conditions. Building upon previous three-dimensional DNS datasets of reheat hydrogen flames, the present work considers two-dimensional configurations that render computationally-feasible simulations of high-pressure combustion and significantly more complex hydrocarbon chemistry. A geometrically-simplified representation of the reheat combustor is adopted and the thermodynamic states considered in the simulations are carefully chosen to mimic gas turbine operation conditions, which are constrained to achieve a target flame position and flame temperature. The two-dimensional DNS results are first assessed against the available three-dimensional data and then analyzed to extract the main trends exhibited by the reheat combustion process with respect to the fraction of the fuel consumed by spontaneous ignition and flame propagation, for increasing pressures and hydrogen fractions. Due to significant differences in the characteristic features of the velocity and thermal boundary layers between the three-dimensional and the two-dimensional configurations, a different global flame shape is observed (V-shaped flame vs W-shape flame) together with a ∼ 10 % bias in the fraction of fuel consumed by spontaneous ignition. Crucially, results from the scaling studies reveal very clear trends with a significant decrease in the fuel consumption by spontaneous ignition for increasing pressures and hydrogen fractions, at the conditions investigated. Finally, this study highlights the important role that first-principle direct numerical simulations, even when conducted in computationally affordable two-dimensional simplified geometrical configurations, can play in obtaining detailed insights and quantitative trends useful for the characterization of complex reactive flows. Novelty and significance The reheat burners of the two-stage sequential gas turbine combustors are designed to stabilize flames primarily due to spontaneous ignition. However, prior numerical simulations revealed the presence of an additional assisted-ignition mode aided by recirculation zones. In this study, we used practically feasible two-dimensional direct numerical simulations of premixed hydrogen–air mixtures under lean conditions to quantify the roles of the two flame stabilization modes at different operating pressures. Achieving fundamental understanding of the effect of pressure and hydrogen fraction on flame stabilization is crucial to the development of two-stage sequential combustion and the present two-dimensional calculations provide important new insights. We show that at high pressures, both modes consume fuel to a similar extent. We also investigated the effect of methane blending on flame stabilization. This study also discusses how two-dimensional direct numerical simulations can be leveraged in the design optimization of reheat burners at low technology readiness levels. [ABSTRACT FROM AUTHOR]

Direct Numerical Simulations (DNS) are performed to investigate the process of spontaneous ignition of hydrogen flames at laminar, turbulent, adiabatic and non-adiabatic conditions. Mixtures of hydrogen and vitiated air at temperatures representing gas-turbine reheat combustion are considered. Adiabatic spontaneous ignition processes are investigated first, providing a quantitative characterization of stable and unstable flames. Results indicate that, in hydrogen reheat combustion, compressibility effects play a key role in flame stability and that unstable ignition and combustion are consistently encountered for reactant temperatures close to the mixture's characteristic crossover temperature. Furthermore, it is also found that the characterization of the adiabatic processes is also valid in the presence of non-adiabaticity due to wall heat-loss. Finally, a quantitative characterization of the instantaneous fuel consumption rate within the reaction front is obtained and of its ability, at auto-ignitive conditions, to advance against the approaching turbulent flow of the reactants, for a range of different turbulence intensities, temperatures and pressure levels. [ABSTRACT FROM AUTHOR]

Numerical simulations of laminar premixed flames burning hydrogen and methane in spontaneous ignition mode are performed by harmonically exciting the reactants' temperature at the domain inlet. The results are compared to an analytical model representing the same reactive flow configuration. The model provides a simplified but nevertheless accurate representation of reheat combustion taking place in sequential gas turbine combustors. An analytic expression for autoignition flames transfer functions to entropy waves is derived and used to extend transfer function models from the literature. For validation purposes, results from fully compressible Direct Numerical Simulations (DNS), including a complete representation of the fluctuating acoustic and entropic fields of the reactive flow, are analyzed and compared to incompressible Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations that only take into account the fluctuating entropic field. Methane flames are found to be more sensitive to entropic forcing than hydrogen flames, featuring nonlinear phenomena even for low excitation amplitudes. In the linear regime, all flames behave as predicted by the analytical model and the URANS simulations are found to correctly predict the fluctuating entropic field. The transition from linear to nonlinear flame response is described in detail and its physical mechanisms are explained. Comparisons with results available in the literature show good prediction capabilities, both in terms of flame describing function and integrated heat release rate. Limitations of the proposed analytical model with respect to real combustion systems are discussed and a simple correction is proposed. [ABSTRACT FROM AUTHOR]

Reheat flames are mainly stabilized by autoignition processes. In this paper their unsteady response to temperature fluctuations is investigated. To this end, a simple one dimensional duct is considered as an analytic surrogate model of a reheat combustion chamber. A chemistry-based correlation for the autoignition delay time is used to predict the flame position. In order to analyze the flame response to temperature fluctuations, the inlet boundary condition is harmonically excited. Depending on the amplitude and frequency of excitation, nonlinear phenomena are observed, in particular the co-existence of multiple flame fronts at different axial locations. The analytic formulation of the problem allows us to predict the onset of nonlinearities and to evaluate maps separating the linear from the nonlinear behavior, as function of the system parameters. Amplitude and frequency thresholds triggering different nonlinear properties of the system are identified. Verification of the obtained results for different excitation states is made by comparison to previously conducted Large Eddy Simulations of a simplified reheat combustor geometry represented by a backward-facing step. The simplified model is able to correctly predict the appearance of nonlinear phenomena as observed in the simulations suggesting that the governing factors are well represented. [ABSTRACT FROM AUTHOR]

This paper concerns the influence of the phase of the heat release response on thermoacoustic systems. We focus on one pair of degenerate azimuthal acoustic modes, with frequency ω 0 . The same results apply for an axial acoustic mode. We show how the value ϕ 0 and the slope − τ of the flame phase at the frequency ω 0 affects the boundary of stability, the frequency and amplitude of oscillation, and the phase ϕ qp between heat release rate and acoustic pressure. This effect depends on ϕ 0 and on the nondimensional number τω 0 , which can be quickly calculated. We find for example that systems with large values of τω 0 are more prone to oscillate, i.e. they are more likely to have larger growth rates, and that at very large values of τω 0 the value ϕ 0 of the flame phase at ω 0 does not play a role in determining the system’s stability. Moreover for a fixed flame gain, a flame whose phase changes rapidly with frequency is more likely to excite an acoustic mode. We propose ranges for typical values of nondimensional acoustic damping rates, frequency shifts and growth rates based on a literature review. We study the system in the nonlinear regime by applying the method of averaging and of multiple scales. We show how to account in the time domain for a varying frequency of oscillation as a function of amplitude, and validate these results with extensive numerical simulations for the parameters in the proposed ranges. We show that the frequency of oscillation ω B and the flame phase ϕ qp at the limit cycle match the respective values on the boundary of stability. We find good agreement between the model and thermoacoustic experiments, both in terms of the ratio ω B / ω 0 and of the phase ϕ qp , and provide an interpretation of the transition between different thermoacoustic states of an experiment. We discuss the effect of neglecting the component of heat release rate not in phase with the pressure p as assumed in previous studies. We show that this component should not be neglected when making a prediction of the system’s stability and amplitudes, but we present some evidence that it may be neglected when identifying a system that is unstable and is already oscillating [ABSTRACT FROM AUTHOR]

Features of the flame transfer function (FTF) are characterized for turbulent, non-swirled, bluff body stabilized "M" flames for different hydrogen and methane blends including pure hydrogen flames. An increase in the cut-off frequency of the FTF is observed for increasing hydrogen concentration. Modulations in the form of peaks and troughs in the gain and the phase were also observed and are shown to be caused by the interaction of two different flow disturbances, acoustic and convective, originating upstream of the flame. The first mechanism is due to the acoustic velocity fluctuations imposed at the base of the flame. A Strouhal number scaling based on the flame height and bulk velocity is shown to collapse the phase slopes and the cut-off frequencies. The second mechanism is shown to be due to vortex shedding from the grub screws used to align the bluff body in the inlet pipe. The associated convective time-delay is used to define a second Strouhal number which collapses the modulations in the gain and phase. A model is developed that separately considers the impulse response of each mechanism and is interpreted as a distribution of time lags between velocity fluctuations and the unsteady heat release rate. The distributed time lag (DTL) model consists of two distributions that are shown to capture all the features of the FTFs. The distributions show that the acoustic and convective mechanisms behave as a low pass filter and band pass filter, respectively. This results in a band of frequencies where they interact through superposition driving fluctuations of heat release rate. Similar interactions are shown to exist in the forced cold flow revealing that they are of hydrodynamic origin. Further, the band of frequencies are shown to be centered around the natural shedding frequency of the grub screws appearing as peaks in the unforced energy spectra of the velocity at the dump plane. Finally, a generalized model which takes as an input the bulk velocity, flame height and a geometric parameter is derived assuming a linear dependency of the DTL parameters. The model is shown to predict the behavior of the FTFs relatively well and can potentially be used to analyse regions in the operating conditions map which have not been experimentally tested. [ABSTRACT FROM AUTHOR]

To maximise power density practical gas turbine combustion systems have several injectors which can lead to complex interactions between flames. However, our knowledge about the effect of flame-flame interactions on the flame response, the essential element to predict the stability of a combustor, is still limited. The present study investigates the effect of hydrogen enrichment, flame-flame interaction, confinement, and asymmetries on the linear and non-linear acoustic response of three premixed flames in a simple can combustor. A parametric study of the linear response, characterised by the flame transfer function (FTF), is performed for swirling and non-swirling flames. Flame-flame interactions were achieved by changing the injector spacing and the level of hydrogen enrichment by power from 10 to 50%. It was found that the latter had the most significant effect on the flame response. Asymmetry effects were investigated by changing one of the flames by using a different bluff-body to alter both the flame shape and flow field. The global flame response showed that the asymmetric cases can be reconstructed using a superposition of the two symmetric cases where all three bluff-bodies and flames are the same. Overall, the linear response characterised by the flame transfer function (FTF) showed that the effect of increasing the level of hydrogen enrichment is more pronounced than the effect of the injector spacing. Increasing hydrogen enrichment results in more compact flames which minimises flame-flame interactions. More compact flames increase the cut-off frequency which can lead to self-excited modes at higher frequencies. Finally, the non-linear response was characterised by measuring the flame describing function (FDF) at a frequency close to a self-excited mode of the combustor for different injector spacings and levels of hydrogen enrichment. It is shown that increasing the hydrogen enrichment leads to higher saturation amplitude whereas the effect of injector spacing has a comparably smaller effect. [ABSTRACT FROM AUTHOR]