Linear response of stretch-affected premixed flames to flow oscillations

The linear response of 2D wedge-shaped premixed flames to harmonic velocity disturbances was studied, allowing for the influence of flame stretch manifested as variations in the local flame speed along the wrinkled flame front. Results obtained from analyzing the G-equation show that the flame response is mainly characterized by a Markstein number , which measures the curvature effect of the wrinkles, and a Strouhal number, Stf, defined as the angular frequency of the disturbance normalized by the time taken for the disturbance to propagate the flame length. Flame stretch is found to become important when the disturbance frequency satisfies , i.e. . Specifically, for disturbance frequencies below this order, stretch effects are small and the flame responds as an unstretched one. When the disturbance frequencies are of this order, the transfer function, defined as the ratio of the normalized fluctuation of the heat release rate to that of the velocity, is contributed mostly from fluctuations of the flame surface area, which is now affected by stretch. Finally, as the disturbance frequency increases to , i.e. , the direct contribution from the stretch-affected flame speed fluctuation to the transfer function becomes comparable to that of the flame surface area. The present study phenomenologically explains the experimentally observed filtering effect in which the flame wrinkles developed at the flame base decay along the flame surface for large frequency disturbances as well as for thermal-diffusively stable and weakly unstable mixtures.     

Experimental study on premixed combustion of spherically propagating methanol-air-nitrogen flames

The outward propagation and development of surface instability of the spark-ignited spherical premixed flames for methanol-air-nitrogen mixtures were experimentally studied by using a constant volume combustion chamber and a high-speed schlieren photography system. The laminar burning velocities, the mass burning fluxes, and the Markstein lengths were obtained at different equivalence ratios, dilution ratios, initial temperatures, and pressures. The laminar burning velocities and the mass burning fluxes give a similar curve versus the equivalence ratios. They increase with the increase of initial temperature and decrease with the increase of dilution ratio. The laminar burning velocity decreases with elevating the initial pressure, while the mass burning flux increases with the increase of the initial pressure. Markstein length decreases slightly with the increase of initial temperature for the rich mixtures. High initial pressure corresponds to low Markstein length. Markstein length increases with the increase of dilution ratio, which is more obvious when the mixture becomes leaner. Equivalence ratio has a slight impact on the development of the diffusive-thermal cellular structure at elevated initial pressures. The initial pressure has a significant influence on the occurrence of the flame front cellular structure. At the elevated pressures, the cracks on the flame surface branch and develop into the cell structure. These cells are bounded by cracks emitting a bright light, which may indicate soot formation. For very lean mixture combustion, the buoyancy effect and cooling effect from the spark electrodes have a significant impact on the flame propagation. The hydrodynamic instability, inhibited with the increase of initial temperature around the stoichiometric equivalence ratio, is enhanced with the increase of initial pressure and suppressed by mixture dilution.     

Onset of cellular instabilities in spherically propagating hydrogen-air premixed laminar flames

Using high-speed Schlieren and Shadow photography, the instabilities of outwardly propagating spherical hydrogen-air flames have been studied in a constant volume combustion bomb. Combustion under different equivalence ratios (0.2 ∼ 1.0), temperatures (298 K ∼ 423 K) and pressures (1.0 bar ∼ 10.0 bar) is visualized. The results show that flames experience both unequal diffusion and/or hydrodynamic instabilities at different stages of propagation. The critical flame radius for such instabilities is measured and correlated to the variations of equivalence ratio, temperature and pressure. Analysis revealed that equivalence ratio affects unequal diffusion instability via varying the Lewis number, Le$Le$; increased temperature can delay both types of instabilities in the majority of tests by promoting combustion rate and changing density ratio; pressure variation has minor effect on unequal diffusion instability but is responsible for enhancing hydrodynamic instability, particularly for stoichiometric and near-stoichiometric flames.     

Lewis number effect on the propagation of premixed flames in narrow adiabatic channels: Symmetric and non-symmetric flames and their linear stability analysis

The propagation of premixed flames with different Lewis numbers in a planar channel subject to a Poiseuille flow is considered within the diffusive-thermal model for steady and time-dependent cases. It was found that, depending on the Lewis number and the flow rate, symmetric and non-symmetric flames are possible. The existence of multiple steady solutions in cases of the low Lewis number is demonstrated. The time-dependent simulations carried out for high Lewis number flames also showed the symmetric and non-symmetric oscillatory solutions.Linear stability analysis of two-dimensional steady-states was performed using a practical method developed in the paper and applied to calculate the main eigenvalue. It was shown that for symmetric flames with a low Lewis number the increase in the flow rate leads to a loss of stability with subsequent formation of non-symmetric solutions. For flames with a high Lewis number the Poiseuille flow produces a stabilization effect. The results of the stability analysis were successfully compared with the results of direct numerical simulations.     

Upstream flow dynamics of a laminar premixed conical flame submitted to acoustic modulations

This study is concerned with the response of conical flames to acoustic modulations. It deals with the dynamics of the velocity field in the fresh gases feeding the flame. Experiments are carried out to determine the gain and phase shift between the excitation signal and the axial velocity signal. This information, combined with PIV data, is used to identify the propagation mode in the fresh stream. Experiments indicate that three ranges can be defined based on a Strouhal number St involving the burner diameter and the upstream flow velocity. When this number is sufficiently low (St?1), the response consists in a convective wave featuring a phase velocity close to that of the mean flow. As St is augmented (1?St?Stc), where Stc depends on the flame geometry, the phase difference between the velocity oscillation and the imposed signal nearly vanishes in a finite region adjacent to the burner exhaust indicating that the perturbation propagates at the speed of sound. Further away from the burner, velocity perturbations exhibit convective features again. In the third frequency range, corresponding to higher modulation frequencies (St?Stc), velocity perturbations are dominated by acoustics in most of the experimental domain. It is shown that this behavior results from the upstream influence of the flame wrinkling. The region of influence may be deduced by considering the velocity potential associated with the flame motion. When this perturbation potential takes large values, the flow is dominated by the convective wave. This suitably reproduces experimental observations.     

Response dynamics of bluff-body stabilized conical premixed turbulent flames with spatial mixture gradients

Response of bluff-body stabilized conical turbulent premixed flames was experimentally studied for a range of excitation frequencies (10-400 Hz), mean flow velocities (5, 10 and 15 m/s) and three different spatial mixture distributions (uniform, inner and outer enrichment). Upstream excitation was provided by a loudspeaker producing velocity oscillation amplitudes of about 8% of the mean flow velocity. Flame response was detected by a photomultiplier observing the CH^∗ emission from the flame. The studied turbulent flames exhibited transfer function characteristics of a low-pass filter with a cutoff Strouhal number between 0.08 and 0.12. The amplification factors at low frequencies ranged from 2 to 20 and generally increased for mean flow velocities from 5 to 15 m/s. The highest levels of amplification were found for the outer mixture enrichment followed in decreasing order by uniform and inner mixture gradient cases. The high levels of flame response for the outer enrichment case were attributed to the enhanced flame-vortex interaction in outer jet shear layer. At high excitation levels (u^′/Um≈0.3) for where non-linear flame response is expected, the flame exhibited a reduced amplitude response in the frequency range between 40 and 100 Hz for the uniform and outer equivalence ratio gradient cases and no discernible effect for the inner equivalence ratio gradient. In all cases, transfer function phase was found to vary linearly with excitation frequency. Finally, a relationship between the amplitude characteristics of the bluff-body wake transfer function and flame blowoff equivalence ratio was presented.     

Propagation of symmetric and non-symmetric premixed flames in narrow channels: Influence of conductive heat-losses

Two-dimensional symmetric and non-symmetric premixed flames propagating in a narrow channel subject to a Poiseuille flow are investigated within the context of a diffusive-thermal model. Attention is focussed on the impact of the flame-wall heat exchange on the structure and stability of flames. It is found that an increase in the heat-losses leads to a discontinuity of the steady-state response curves: for Le < 1 the flame extinguishes inside a finite interval of flow rate values while for Le > 1 the flame cannot exist for flow rates larger or smaller than some critical values.     

Extinction of laminar partially premixed flames

Flame extinction represents one of the classical phenomena in combustion science. It is important to a variety of combustion systems in transportation and power generation applications. Flame extinguishment studies are also motivated from the consideration of fire safety and suppression. Such studies have generally considered non-premixed and premixed flames, although fires can often originate in a partially premixed mode, i.e., fuel and oxidizer are partially premixed as they are transported to the reaction zone. Several recent investigations have considered this scenario and focused on the extinction of partially premixed flames (PPFs). Such flames have been described as hybrid flames possessing characteristics of both premixed and non-premixed flames. This paper provides a review of studies dealing with the extinction of PPFs, which represent a broad family of flames, including double, triple (tribrachial), and edge flames. Theoretical, numerical and experimental studies dealing with the extinction of such flames in coflow and counterflow configurations are discussed. Since these flames contain both premixed and non-premixed burning zones, a brief review of the dilution-induced extinction of premixed and non-premixed flames is also provided. For the coflow configuration, processes associated with flame liftoff and blowout are described. Since lifted non-premixed jet flames often contain a partially premixed or an edge-flame structure prior to blowout, the review also considers such flames. While the perspective of this review is broad focusing on the fundamental aspects of flame extinction and blowout, results mostly consider flame extinction caused by the addition of a flame suppressant, with relevance to fire suppression on earth and in space environment. With respect to the latter, the effect of gravity on the extinction of PPFs is discussed. Future research needs are identified.     

Diffusive-thermal instability of premixed tubular flames

A systematic study of the diffusive-thermal instability of premixed tubular flames is carried out. The problem becomes amenable to a complete analysis in the frame of the diffusive-thermal approximation when a simplified flow field and the flame-sheet combustion model are used. The dispersion relation determining the growth rate of instability is obtained in an analytical form which therefore analyzed numerically. Stability diagrams showing stable and unstable states, in particular those manifesting the cellular flames, are presented.     

The influence of reactant temperature on the dynamics of bluff body stabilized premixed flames

The impact of increased reactant temperature on the dynamics of bluff-body stabilized premixed flows is investigated using numerical simulation. A two-dimensional triangular bluff body is considered. Flow compressibility is assumed to exist at the low Mach number limit and combustion is fast and robust such that a flamesheet representation is assumed to apply. In this formulation, reactant temperature variations are represented via corresponding temperature ratio and flame speed variations. The Lagrangian, Transport Element Method is used to provide the numerical solutions. Results indicate that as reactant temperature increases, the fluid dynamics transition from a low amplitude, broadband, coarsely symmetric (about the bluff-body centerline) behavior, to a high amplitude, tonal and asymmetric one that bears similarities to the corresponding non-reacting flow. The reasons for this are that as the reactant temperature increases, (i) the temperature ratio across the flame is reduced, thus reducing combustion exothermicity, and (ii) the flame speed increases causing the flame to propagate away from the bluff-body wake. In both cases the ability of the two main combustion-driven fluid dynamical processes, namely volumetric expansion and baroclinic generation to impact the bluff body generated vorticity is reduced. Reduction in baroclinic generation enables to wake to survive futher downsteam and makes the flow susceptible to the wake instability. As reactant temperature is increased the location of the onset of the instability moves upstream. At very high reactant temperatures even the near field symmetrizing effect of volumetric expansion is overwhelmed and asymmetric vortex shedding is witnessed at the bluff body. Even in this regime, the flow differs from the non-reacting flow in that it is susceptible to bifurcations in vortex shedding behavior that are linked to local flame-vortex interactions. Results also show that in the general case, knowledge of the fluid dynamics alone is not sufficient to characterize the flame dynamics, as the flame position in relation to the vorticity field is critical to the unsteady flame response. Specifically, the flame exhibits a similar transition from a broadband to a tonal response but the amplitude is not monotonically increasing. Rather it experiences a regime of decreasing response for intermediate reactant temperatures where the flame propagation away from the wake appears to dominate the increase in fluid dynamical induced oscillations due to the enhancement of the asymmetric mode.     

Nonlinear combustion instability analysis based on the flame describing function applied to turbulent premixed swirling flames

Instability analysis of swirling flames is of importance in the design of advanced combustor concepts for aircraft propulsion and powerplant for electricity production. Thermoacoustic instabilities are analyzed here by making use of a nonlinear representation of flame dynamics based on a describing function. In this framework, the flame response is determined as a function of frequency and amplitude of perturbations impinging on the combustion region. This model is adapted to the case of confined swirling flames comprising an upstream manifold, an injection unit equipped with a swirler and a cylindrical flame tube. The flame describing function is experimentally determined and is combined with an acoustic transfer matrix representation of the system to provide growth rates and oscillation frequencies as a function of perturbation amplitude. These data can be used to determine regions of instability, frequency shifts with respect to the acoustic eigenfrequencies and they also yield amplitude levels when self-sustained oscillations of the system have reached a limit cycle. This equilibrium is obtained when the amplitude dependent growth rate equals the damping rate in the system. This requires an independent determination of this last quantity which is here based on measurements of the combustor resonance response curve, together with numerical estimates of the flame contribution to the system response. The geometrical parameters of the upstream manifold and flame tube are varied and the corresponding operating regimes are compared with those predicted with the FDF framework. The present demonstration of the FDF framework in a generic configuration indicates that this can be used in more general situations of technological interest.     

Self-induced instabilities of premixed flames in a multiple injection configuration

This article presents an experimental study of self-sustained instabilities of an ensemble of premixed flames anchored on perforated plates. A theoretical analysis based on experimental results is developed in order to model the acoustic-flame coupling. In the unconfined configuration envisaged in this study, the coupling occurs with the upstream cavity. Experiments carried out on this multipoint injection configuration concern the acoustic response of the system and the influence of the perforated plate impedance, the emission of sound by the flames and the combustion transfer function. The thickness of the perforated plate is an important parameter that modifies the resonant frequencies and the ranges of instability. Instability bands determined by the model are in good agreement with experimental data, providing a suitable explanation of the mode hopping process characterizing such configurations.     

Identification of combustion intermediates in isomeric fuel-rich premixed butanol-oxygen flames at low pressure

Laminar premixed low-pressure flames fueled by either one of the four isomers of butanol were investigated by a molecular-beam photoionization mass spectrometer using vacuum ultraviolet (VUV) synchrotron radiation as the ionization source. The photoionization efficiency (PIE) spectra of most flame intermediates were measured between 7.75 and 11.00 eV. By comparing the resulting PIE spectra to known ionization energies (IEs) or known PIE spectra of pure substances, most hydrocarbon and oxygenated combustion intermediates, including some radicals, in the mass range from m/z=15 to 106 were assigned and identified in the four butanol flames. The results show that the higher-mass oxygenated species in butanol flames are strongly affected by the fuel structure, while many hydrocarbon isomers appear almost independent of the fuel structure. The respective dissociation mechanisms of the fuels, including complex fission, simple fission, and H-atom abstraction, are in good agreement with previous results from nonpremixed butanol flames.     

Dynamics of premixed hydrogen/air flames in microchannels

The stabilization and dynamics of lean (φ=0.5) premixed hydrogen/air atmospheric-pressure flames in planar microchannels of prescribed wall temperature are investigated with respect to the inflow velocity and channel height (0.3 to 1.0 mm) using direct numerical simulation with detailed chemistry and transport. Rich dynamics starting from periodic ignition and extinction of the flame and further transitioning to symmetric V-shaped flames, asymmetric flames, oscillating and pulsating flames, and finally again to asymmetric flames are observed as the inlet velocity is increased. The richest behavior is observed for the 1.0-mm-height channel. For narrower channels, some of the dynamics are suppressed. The asymmetric flames, in particular, vanish for channel heights roughly less than twice the laminar flame thickness. Stability maps delineating the regions of the different flame types in the inlet velocity/channel height parameter space are constructed.     

Dynamics of premixed flames in a narrow channel with a step-wise wall temperature

The effect of channel height, inflow velocity and wall temperature on the dynamics and stability of unity Lewis number premixed flames in channels with specified wall temperature is investigated with steady and transient numerical simulations using a two-dimensional thermo-diffusive model. The simplified model is capable of capturing many of the transitions and the combustion modes observed experimentally and in direct numerical simulations in micro- and meso-scale channels, and indicates that the thermal flame/wall interaction is the mechanism leading to the observed flame instabilities. Finally, an ad-hoc one-dimensional model based on the flame-sheet approximation is tested in its capacity to reproduce some of the flame dynamics of the two-dimensional thermo-diffusive model.     

Excitation of thermoacoustic oscillations by small premixed flames

Experiments have been carried out in which very small lean premixed flames closely representative of those formed by modern multiport domestic gas burners have been subjected to controlled acoustic perturbation. PLIF from CH has been used to visualise the flame response and the heat-release-rate fluctuations have been evaluated directly from the flame images. It is shown that small laminar flames can amplify the effects of acoustic velocity fluctuations by mechanisms that do not involve resonant heat loss to the burner and that the fluctuations in flame-front area are not adequately characterised by a Strouhal number alone. The measured transfer function is compared with the predictions of various analytical formulations and a new model of the flame oscillation is proposed which applies specifically to situations in which the design of the burner renders the flame base immobile.     

The effect of hydrogen enrichment on the forced response of CH4/H2/Air laminar flames

Hydrogen-enrichment of conventional natural gas mixtures is an actively-explored strategy for reducing pollutant emissions from combustion. This study investigates the effect of hydrogen enrichment on the unsteady flame response to perturbations, with a view to understanding the implications for thermoacoustic stability. The Level Set Approach for kinematically tracking the flame front was applied to a laminar conical premixed methane/hydrogen/air flame subjected to 2D incompressible velocity perturbations. For hydrogen enrichment levels ranging from 0% to 80% by volume, the resulting unsteady heat release rate of the flame was used to generate the Flame Describing Functions (FDFs). This was performed across a range of perturbation frequencies and levels at ambient pressure. The mean heat release rate of the flame was fixed at $\overline{\stackrel{?}{Q}}$$=2.69\text{k}\text{W}$ and the equivalence ratio was set to ? = 1.08 for all hydrogen enrichment levels. Hydrogen-enrichment was found to shift the FDF gain drop-off to higher frequencies, which will increase propensity to thermoacoustic instability. It also reduced the effective flame time delay. Sensitivity analyses at ? = 0.8 revealed that the changes in FDF were driven predominantly by the flame burning speed, and were insensitive to changes in Markstein length.     

Numerical investigation on combustion characteristics of laminar premixed n-heptane/air flames at elevated initial temperature and pressure

Freely-propagating laminar premixed n-heptane/air flames were modeled using the Lawrence Livermore National Laboratory (LLNL) v3.1 n-heptane mechanism and the PREMIX code. Numerical calculations were conducted for unburned mixture temperature range of 298–423 K, at elevated pressures 1–10 atm and equivalent ratio 0.6–1.6, and the changes of laminar burning velocity (LBV), adiabatic flame temperature (AFT), heat release rate (HRR), and concentration profiles of important intermediate species were obtained. The results show that the overall results of LBVs of n-heptane at different elevated temperatures, pressures, and equivalence ratios are in good agreement with available experimental results. However, at the initial temperature 353 K, the calculated values of LBVs at pressure 1 atm and the 10 atm deviate significantly from the experimental results. The sensitivity analysis shows that, similar to many other hydrocarbon fuels, the most sensitive reaction in the oxidation of n-heptane responsible for the rise of flame temperature promoting heat release is R1 H + O₂<=>O + OH, and the reaction that has the greatest influence on heat release is R8 H₂O + M<=>H + OH + M. In addition, when the initial temperature is 353, 398 and 423 K, the mole fractions of H, OH, and O increase rapidly around the flame front, while the mole fractions of C₁C₃ dramatically decreases, reflecting the intense consumption of the intermediate products at the reaction zone.     

Transient response of premixed methane flames

The response of premixed methane-air flames to transient strain and local variations in equivalence ratio is studied during isolated interactions between a line-vortex pair and a V-flame. The temporal evolution of OH and CH is measured with planar laser-induced fluorescence for N₂-diluted flames with equivalence ratios ranging from 0.8 to 1.2. One-dimensional laminar flame calculations are used to simulate the flame response to unsteady strain and variations in reactant composition. When the reactant composition of the vortex pair and the V-flame are identical, the measurements and predictions show that the peak mole fractions of OH and CH decay monotonically in lean, stoichiometric, and rich flames. We also investigate the effects of a vortex pair with a leaner composition than the V-flame. In a stoichiometric flame, the leaner vortex enhances the decay of both OH and CH. In a rich flame, we observe an abrupt increase in OH-LIF signal and a disappearance of CH-LIF signal that are consistent with a previous experimental investigation. Our results indicate that the previously observed OH burst and CH breakage were caused by a difference in the equivalence ratios of the vortex pair and the main reactant flow. A numerical study shows that N₂ dilution enhances the response of premixed flames to unsteady strain and variations in stoichiometry. Reaction-path and sensitivity analyses indicate that the peak OH and CH mole fractions exhibit significant sensitivity to the main branching reaction, H + O₂ ↔ OH + O. The sensitivity of OH and CH to this and other reactions is enhanced by N₂ dilution. As a result, N₂-diluted flames provide a good test case for studying the reliability of chemical kinetic and transport models.     

Impact of exothermicity on steady and linearized response of a premixed ducted flame

Thermoacoustic instabilities arise in power generation devices such as gas turbines and aero-engines when acoustic modes couple with unsteady heat released due to combustion in a positive feedback loop. This work focuses on the development of a reduced order model for understanding flame dynamics in the case of flameholder-stabilized premixed combustion in a duct—a situation typical in many of these applications. Similar to earlier studies in reduced order modeling of this flow, we employ a G-equation formulation to obtain kinematical representation of the premixed flame and ignore the impact of the unsteady (vortical) fluid dynamics downstream of the flameholder. Unlike those studies, however, we retain the impact of combustion exothermicity in the form of a density jump and associated volume generation at the flame front as well as the steady portion of the baroclinic vortical effect. The reduced order model yields analytical solutions for the flame location and for linear transfer functions between imposed (acoustic) perturbation and combustion heat release. We validate these solutions against numerical simulations and other results in literature. The role of expansion (dilatation) and baroclinic aspects of exothermic effects are discussed in detail. Results show that for realistic density ratios across the flame, the flow is accelerated in the streamwise direction on account of combustion exothermicity and the effects of confinement. This not only alters the flame location but also changes the linearized dynamics of the flame and brings into question conclusions drawn from similar analyses in which exothermicity effects were neglected. This is discussed in the context of modeling and controlling thermoacoustic instabilities.