Exploring a critical diameter for thermo-acoustic instability of downward propagating flames in tubes

Thermo-acoustic oscillations are observed when a flame ignited at open end of a tube propagates towards the closed end due to interaction between unsteady heat release rate fluctuations from flame and acoustic fluctuations. In our past work, it was found that thermo-acoustic instability increases with decreasing diameter from 7.0 cm to 3.0 cm. A recent study in flame propagation in Hele–Shaw cells showed that thermo-acoustic instability is not observed for plate separation less than or equal to 0.4 cm. Thermoacoustic instabilities cannot be observed in very narrow tubes due to excessive damping from the wall. This opens up the possibility of a critical diameter where thermo-acoustic instability would be maximum. In this work we perform flame propagation experiments with diameter of combustion tube in the range 0.5 cm to 3 cm for a fixed length of 70.2 cm. It was found that thermo-acoustic parametric instability begins at lowest laminar burning velocity when the diameter is around 1.0 cm. This diameter is termed as critical diameter. Critical diameter is found to be independent of Lewis number of mixtures. Existence of a critical diameter is thus proved experimentally. Growth rates of primary instability increase with decreasing diameter and show a maximum around the critical diameter and decrease with further decrease in tube diameter. But, growth rates of secondary instability as well as maximum pressure fluctuation amplitude decreases continuously with decreasing diameter. Mechanisms responsible for these observations and existence of a critical diameter are clarified.     

Numerical studies of curved stationary flames in wide tubes

The nonlinear problem of the propagation of curved stationary flames in tubes of different widths is studied by means of direct numerical simulation of the complete system of hydrodynamic equations including thermal conduction, viscosity, fuel diffusion and chemical kinetics. While only a planar flame can propagate in a narrow tube of width smaller than half of the cut–off wavelength determined by the linear theory of the hydrodynamic instability of a flame front, in wider tubes stationary curved flames propagate with velocities considerably larger than the corresponding velocity of a planar flame. It is shown that only simple ‘single-hump’ slanted stationary flames are possible in wide tubes, and ‘multi–hump’ flames are possible in wide tubes only as a nonstationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes and the secondary Landau–Darrieus instability are investigated. The dependence of the velocity of the stationary flame on the tube width is studied. The analytical theory describes the flame reasonably well when the tube width does not exceed some critical value. The dynamics of the flame in wider tubes is shown to be governed by a large–scale stability mechanism resulting in a highly slanted flame front. In wide tubes, the skirt of the slanted flame remains smooth with the length of the skirt and the flame velocity increasing progressively with the increase of the tube width above the second critical value. Results of the analytical theory and numerical simulations are discussed and compared with the experimental data for laminar flames in wide tubes.     

Computational investigations of the coupling between transient flame dynamics and thermo-acoustic instability in a self-excited resonance combustor

Combustion instability due to thermo-acoustic interactions is a critical combustion problem that requires a thorough understanding because of its adverse impact on stable and reliable operation of combustors in high-speed propulsion devices like gas turbines and rockets. This work conducts computational investigations of the coupling between the transient flame dynamics such as the ignition delay and local extinction and the thermo-acoustic instability developed in a self-excited resonance combustor to gain deep insights into the mechanisms of thermo-acoustic instability. A 2D modelling framework that employs different flamelet models (the steady flamelet model and the flamelet/progress variable approach) is developed to enable the examination of the effect of the transient flame dynamics caused by the strong coupling of the turbulent mixing and finite-rate chemical kinetics on the occurrence of thermo-acoustic instability. The models are validated by using the available experimental data for the pressure signal. Parametric studies are performed to examine the effect of the occurrence of the transient flame dynamics, the effect of artificial amplification of the Damköhler number, and the effect of neglecting mixture fraction fluctuations on the predictions of the thermo-acoustic instability. The parametric studies reveal that the occurrence of transient flame dynamics has a strong influence on the onset of the thermo-acoustic instability. Further analysis is then conducted to localise the effect of a particular flame dynamic event, the ignition delay, on the thermo-acoustic instability. The reverse effect of the occurrence of the thermo-acoustic instability on the transient flame dynamics in the combustor is also investigated by examining the temporal evolution of the local flame events in conjunction with the pressure wave propagation. The above observed two-way coupling between the transient flame dynamics (the ignition delay) and the thermo-acoustic instability provides a plausible mechanism of the self-excited and sustained thermo-acoustic instability observed in the combustor despite the fact that the results are obtained from 2D simulations. The same analysis is expected to be extensible to fully 3D simulations.     

Numerical studies of flames in wide tubes: stability limits of curved stationary flames

Flame dynamics in wide tubes with ideally adiabatical and slip walls is studied by means of direct numerical simulations of the complete set of hydrodynamical equations including thermal conduction, fuel diffusion, viscosity, and chemical kinetics. Stability limits of curved stationary flames in wide tubes and the hydrodynamic instability of these flames (the secondary Darrieus-Landau instability) are investigated. The stability limits found in the present numerical simulations are in a very good agreement with the previous theoretical predictions. It is obtained that close to the stability limits the secondary Darrieus-Landau instability results in an extra cusp at the flame front. It is shown that the curved flames subject to the secondary Darrieus-Landau instability propagate with velocity considerably larger than the velocity of the stationary flames.     

Nonlinear equation for curved nonstationary flames and flame stability

A time-dependent nonlinear equation for a nonstationary curved flame front of an arbitrary expansion coefficient is derived under the assumptions of a small but finite flame thickness and weak nonlinearity. On the basis of the derived equation, stability of two-dimensional curved stationary flames propagating in tubes with ideally adiabatic and slip walls is studied. The stability analysis shows that curved stationary flames become unstable for sufficiently wide tubes. The obtained stability limits are in a good agreement with the results of numerical simulations of flame dynamics and with semiqualitative stability analysis of curved stationary flames. Possible outcomes of the obtained instability at the nonlinear stage are discussed. The instability may result in extra wrinkles at a flame front close to the stability limits and in self-turbulization of the flame far from the limits. The self-turbulization can also be interpreted as a fractal structure. The fractal dimension of a flame front and velocity of a self-turbulized flame are evaluated.     

Stability of inclined planar flames as a local approximation of weakly curved flames

To evaluate the effect of vorticity usually generated by curved flames on the flame stability, laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it shows more unstable characteristics due to not only the decrease of the stabilizing effect of gravity but also the increase of the destabilizing effect of rotational flow. Unlike the planar flame propagating downward with the right angle to the upstream flow, the obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable wave depends on the Lewis number as well as the flame angle and, especially for unity Lewis number, it is the same with tangential velocity at the reaction zone. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.     

Characteristics of microjet methane diffusion flames

Characteristics of microjet methane diffusion flames stabilized on top of the vertically oriented, stainless-steel tubes with an inner diameter ranging from 186 to 778 μ m are investigated experimentally, theoretically and numerically. Of particular interest are the flame shape, flame length and quenching limit, as they may be related to the minimum size and power of the devices in which such flames would be used for future micro-power generation. Experimental measurements of the flame shape, flame length and quenching velocity are compared with theoretical predictions as well as detailed numerical simulations. Comparisons of the theoretical predictions with measured results show that only Roper's model can satisfactorily predict the flame height and quenching velocity of microjet methane flames. Detailed numerical simulations, using skeletal chemical kinetic mechanism, of the flames stabilized at the tip of d = 186, 324 and 529 μ m tubes are performed to investigate the flame structures and the effects of burner materials on the standoff distance near extinction limit. The computed flame shape and flame length for the d = 186 μm flame are in excellent agreement with experimental results. Numerical predictions of the flame structures strongly suggest that the flame burns in a diffusion mode near the extinction limit. The calculated OH mass fraction isopleths indicate that different tube materials have a minor effect on the standoff distance, but influence the quenching gap between the flame and the tube.     

Velocity of weakly turbulent flames of finite thickness

The velocity increase of a weakly turbulent flame of finite thickness is investigated using analytical theory developed in previous papers. The obtained velocity increase depends on the flow parameters: on the turbulent intensity, on the turbulent spectrum and on the characteristic length scale. It also depends on the thermal and chemical properties of the burning matter: thermal expansion, the Markstein number and the temperature dependence of transport coefficients. It is shown that the influence of the finite flame thickness is especially strong close to the resonance point, when the wavelength of the turbulent harmonic is equal to the cut off wavelength of the Darrieus–Landau instability. The velocity increase is almost independent of the Prandtl number. On the contrary, the Markstein number is one of the most important parameters controlling the velocity increase. The relative role of the external turbulence and the Darrieus–Landau instability for the velocity increase is studied for different parameters of the flow and the burning matter. The velocity increase for turbulent flames in methane and propane fuel mixtures is calculated for different values of the equivalence ratio. The present theoretical results are compared with previous experiments on turbulent flames. In order to perform the comparison, the theoretical results of the present paper are extrapolated to the case of a strongly corrugated flame front using the ideas of self-similar flame dynamics. The obtained theoretical results are in a reasonable agreement with the experimental data, taking into account the uncertainties of both the theory and the experiments. It is shown that in many experiments on turbulent flames the Darrieus–Landau instability is more important for the flame velocity than the external turbulence.     

The response of turbulent premixed flames to normal acoustic excitation

To model the thermo-acoustic excitation of flames in practical combustion systems, it is necessary to know how a turbulent flame front responds to an incident acoustic wave. This will depend partly on the way in which the burning velocity responds to the wave. In this investigation, the response of CH₄/air and CH₄/H₂/air mixtures has been observed in a novel flame stabilisation configuration, in which the premixture of fuel and air is made to decelerate under controlled conditions in a wide-angle diffuser. Control is provided by an annular wall-jet of air and by turbulence generators at the inlet. Ignition from the outlet of the diffuser allows an approximately flat flame to propagate downwards and stabilise at a height that depends on the turbulent burning velocity. When the flow is excited acoustically, the ensemble-averaged height oscillates. The fluctuations in flow velocity and flame height are monitored by phase-locked particle image velocimetry and OH-planar laser induced fluorescence, respectively. The flame stabilised against a lower incident velocity as the acoustic amplitude increased. In addition, at the lowest frequency of 52 Hz, the fluctuations in turbulent burning velocity (as represented by the displacement speed) were out-of-phase with the acoustic velocity. Thus, the rate of displacement of the flame front relative to the flow slowed as the flow accelerated, and so the flame movement was bigger than it would have been if the burning velocity had not responded to the acoustic fluctuation. With an increase in frequency to 119 Hz, the relative flame movement became even larger, although the phase-difference was reduced, so the effect on burning velocity was less dramatic. The addition of hydrogen to the methane, so as to maintain the laminar burning velocity at a lower equivalence ratio, suppressed the response at low amplitude, but at a higher amplitude, the effect was reversed.     

On laminar premixed flame propagating into autoigniting mixtures under engine-relevant conditions

Usually premixed flame propagation and laminar burning velocity are studied for mixtures at normal or elevated temperatures and pressures, under which the ignition delay time of the premixture is much larger than the flame resistance time. However, in spark-ignition engines and spark-assisted compression ignition engines, the end-gas in the front of premixed flame is at the state that autoignition might happen before the mixture is consumed by the premixed flame. In this study, laminar premixed flames propagating into an autoigniting dimethyl ether/air mixture are simulated considering detailed chemistry and transport. The emphasis is on the laminar burning velocity of autoigniting mixtures under engine-relevant conditions. Two types of premixed flames are considered: one is the premixed planar flame propagating into an autoigniting DME/air without confinement; and the other is premixed spherical flame propagating inside a closed chamber, for which four stages are identified. Due to the confinement, the unburned mixture is compressed to high temperature and pressure close to or under engine-relevant conditions. The laminar burning velocity is determined from the constant-volume propagating spherical flame method as well as PREMIX. The laminar burning velocities of autoigniting DME/air mixture at different temperatures, pressures, and autoignition progresses are obtained. It is shown that the first-stage and second-stage autoignition can significantly accelerate the flame propagation and thereby greatly increase the laminar burning velocity. When the first-stage autoignition occurs in the unburned mixture, the isentropic compression assumption does not hold and thereby the traditional method cannot be used to calculate the laminar burning velocity. A modified method without using the isentropic compression assumption is proposed. It is shown to work well for autoigniting mixtures. Besides, a power law correlation is obtained based on all the laminar burning velocity data. It works well for mixtures before autoignition while improvement is still needed for mixtures after autoignition.     

Measurement of unstable burning velocities of iso-octane–air mixtures at high pressure and the derivation of laminar burning velocities

A new technique is reported for measuring burning velocities at high pressures in the final stages of two inwardly propagating flame kernels in an explosion bomb. The flames were initiated at diametrically opposite spark electrodes, close to the wall, in quiescent mixtures. Measurements of pressure and flame kernel propagation speeds by high-speed photography showed the burning velocities to be elevated above the corresponding laminar burning velocities as a result of the developing flame instabilities. The enhancement increased with increase in pressure and decreased with increase in Markstein number. When the Markstein number was negative, instabilities could be appreciable, as could the enhancement. For the iso-octane–air mixtures investigated, where the mixtures had well-characterised Markstein numbers or critical Peclet numbers at the relevant pressures and temperatures, it was possible to explain the enhancement quantitatively by the spherical explosion flame instability theory of Bechtold and Matalon, provided the critical Peclet number was that observed experimentally, and allowance was made for the changing pressure. With this theoretical procedure, it was possible to derive values of laminar burning velocity from the measured values of burning velocity over a wide range of equivalence ratios, pressures, and temperatures. The values became less reliable at the higher temperatures and pressures as the data on Markstein and critical Peclet numbers became less certain. It was found that with iso-octane as the fuel the laminar burning velocity decreased during isentropic compression.     

Autoignition delay modulation by high-frequency thermoacoustic oscillations in reheat flames

This paper investigates the sensitivity of the autoignition delay in reheat flames to acoustic pulsations associated with high-frequency transverse thermoacoustic oscillations. A reduced order model for the response of purely autoignition-stabilised flames to acoustic disturbances is compared with experimental observations. The experiments identified periodic flame motion associated with high-amplitude transverse limit-cycle oscillations in an atmospheric pressure reheat combustor. This flame motion was assumed to be the result of a superposition of two flame-acoustic coupling mechanisms: autoignition delay modulation by the oscillating acoustic field and displacement and deformation of the flame by the acoustic velocity. The reduced order model coupled to reaction kinetics calculations reveals that a significant portion of the observed flame motion can be attributed to autoignition delay modulation. The ignition position responds instantaneously to the acoustic pressure at the time of ignition, as observed experimentally. The model also provides insight into the importance of the history of acoustic disturbances experienced by the fuel-air mixture prior to ignition. Due to the high-frequency nature of the instability, a fluid particle can experience multiple oscillation cycles before ignition. The ignition delay responds in-phase with the net-acoustic perturbation experienced by a fluid particle between injection and ignition. These findings shed light on the underlying mechanisms of the flame motion observed in experiments and provide useful insight into the importance of autoignition delay modulation as a driving mechanism of high-frequency thermoacoustic instabilities in reheat flames.     

Stabilization, propagation and instability of tribrachial triple flames

A tribrachial (or triple) flame is one kind of edge flame that can be encountered in nonpremixed mixing layers, consisting of a lean and a rich premixed flame wing together with a trailing diffusion flame all extending from a single point. The flame could play an important role on the characteristics of various flame behaviors including lifted flames in jets, flame propagation in two-dimensional mixing layers, and autoignition fronts. The structure of tribrachial flame suggests that the edge is located along the stoichiometric contour in a mixing layer due to the coexistence of all three different types of flames. Since the edge has a premixed nature, it has unique propagation characteristics. In this review, the propagation speed of tribrachial flames will be discussed for flames propagating in mixing layers, including the effects of concentration gradient, velocity gradient, and burnt gas expansion. Based on the tribrachial edge structure observed experimentally in laminar lifted flames in jets, the flame stabilization characteristics including liftoff height, reattachment, and blowout behaviors and their buoyancy-induced instability will be explained. Various effects on liftoff heights in both free and coflow jets including jet velocity, the Schmidt number of fuel, nozzle diameter, partial premixing of air to fuel, and inert dilution to fuel are discussed. Implications of edge flames in the modeling of turbulent nonpremixed flames and the stabilization of turbulent lifted flames in jets are covered.     

Influence of micro-explosions on the stability of laminar premixed water-in-fuel emulsion spray flames

A model is presented for a one-dimensional laminar premixed flame, propagating into a rich, off-stoichiometric, fresh homogenous mixture of water-in-fuel emulsion spray, air and inert gas. Due to its relatively large latent heat of vaporisation, the water vapour acts to cool the flame that is sustained by the prior release of fuel vapour. To simplify the inherent complexity that characterises the analytic solution of multi-phase combustion processes, the analysis is restricted to fuel-rich laminar premixed water-in-fuel flames, and assumes a single-step global chemical reaction mechanism. The main purpose is to investigate the steady-state burning velocity and burnt temperature as functions of parameters such as initial water content in the emulsified droplet and total liquid droplet loading. In particular, the influence of micro-explosion of the spray’s droplets on the flame’s characteristics is highlighted for the first time. Steady-state analytical solutions are obtained and the sensitivity of the flame temperature and the flame propagating velocity to the initial water content of the micro-exploding emulsion droplets is established. A linear stability analysis is also performed and reveals the manner in which the micro-explosions influence the neutral stability boundaries of both cellular and pulsating instabilities.     

High-speed visualization of flame propagation in explosions

Flow visualization data is presented to describe the structure of flames propagating in methane-air explosions in semi-confined enclosures. The role of turbulence is well established as a mechanism for increasing burning velocity by fragmenting the flame front and increasing the surface area of flames propagating in explosions. This area increase enhances the burning rate and increases the resultant explosion overpressure. In real situations, such as those found in complex process plant areas offshore, the acceleration of a flame front results from a complex interaction between the moving flame front and the local blockage caused by presence of equipment. It is clear that any localised increase in flame burn rate and overpressure would have important implications for any adjacent plant and equipment and may lead to an escalation process internal to the overall event. To obtain the information required to quantify the role of obstacles, it is necessary to apply a range of sophisticated laser-based, optical diagnostic techniques. This paper describes the application of high-speed, laser-sheet flow visualization and digital imaging to record the temporal development of the flame structure in explosions. Data is presented to describe the interaction of the propagating flame with a range of obstacles for both homogeneous and stratified mixtures. The presented image sequences show the importance of turbulent flow structures in the wake of obstacles for controlling the mixing of a stratified concentration field and the subsequent flame propagation through the wake. The data quantifies the flame speed, shape and area for a range of obstacle shapes.     

Resonance of a turbulent flame in a high-frequency acoustic wave

Resonance of a weakly turbulent flame in a high-frequency acoustic wave is obtained. Because of the resonance, an acoustic wave may increase noticeably the amplitude of flame wrinkles, and the respective increase in propagation velocity of the turbulent flame front becomes larger by a factor of 10-20. The effect of resonance is especially important for turbulent flames with realistic thermal expansion propagating in a closed burning chamber, which may account for considerable scattering of experimental results on turbulent flame velocity.     

稀甲烷/氢气预混湍流传播火焰实验研究

本文采用定容湍流燃烧弹获取了稀甲烷/氢气/空气在强湍流条件下的火焰发展历程,研究了湍流火焰在负马克斯坦数条件下的传播特性.结果表明,湍流火焰呈现自相似传播特性,即使在强湍流条件下,湍流传播火焰仍然会受到不稳定性的影响.并且随着马克斯坦数的减小,不稳定性对湍流传播火焰的影响增强。同时,本文获得一种新的湍流燃烧速度拟合公式,包含了负马克斯坦数条件下不稳定性对湍流燃烧速度的影响。     

A dynamical system approach for solving the steady structure of high speed deflagrations

High-speed deflagrations have burning velocities much higher than laminar ones, and compressible effects become important. In the present paper, we study the structure of such high speed deflagrations in the thickened flame limit for a one-step Arrhenius rate law, whereby the transport coefficients are increased to give rise to buring velocities of finite Mach number. We study their steady structure and compare with the laminar low-Mach classical structure. The singular nature of both the fresh and burned gases conditions in the compressible regime, i.e., for large values of flame propagation Mach number, which are both saddle points, precludes the application of simple shooting methods to obtain their structure. The steps leading to the flame structure borrow techniques used to treat mathematical features commonly found in the study of dynamical systems (phase portrait of the flame structure equations system, eigenvalue decomposition of its linearized version), that can also be used to further comment on the nature of high-speed flames. The method proposed permits to determine the structure of deflagrations propagating up to speeds of aproximately 0.95 of the CJ-deflagration burning velocity, for a wide range of gas parameters commonly found in the field of numerical simulation of accelerating flames and their transitions to detonations. We comment on how the increasing role of compressibility modifies the structure of the laminar flame.     

Effects of Lewis number,density ratio and gravity on burning velocity and conditional statistics in stagnating turbulent premixed flames

DNS is performed to analyse the effects of Lewis number (Le), density ratio and gravity in stagnating turbulent premixed flames. The results show good agreement with those of Lee and Huh (Combustion and Flame, Vol. 159, 2012, pp. 1576–1591) with respect to the turbulent burning velocity, S_T, in terms of turbulent diffusivity, flamelet thickness, mean curvature and displacement speed at the leading edge. In all four stagnating flames studied, a mean tangential strain rate resulting in a mean flamelet thickness smaller than the unstretched laminar flame thickness leads to an increase in S_T. A flame cusp of positive curvature involves a superadiabatic burned gas temperature due to diffusive–thermal instability for an Le less than unity. Wrinkling tends to be suppressed at a larger density ratio, not enhanced by hydrodynamic instability, in the stagnating flow configuration. Turbulence is produced, resulting in highly anisotropic turbulence with heavier unburned gas accelerating through a flame brush by Rayleigh–Taylor instability. Results are also provided on brush thickness, flame surface density and conditional velocities in burned and unburned gas and on flame surfaces to represent the internal brush structures for all four test flames.     

Effect of non-zero relative velocity on the flame speed of two-phase laminar flames

A numerical study of one-dimensional n-heptane/air spray flames is presented. The objective is to evaluate the flame propagation speed in the case where droplets evaporate inside the reaction zone with possibly non-zero relative velocity. A Direct Numerical Simulation approach for the gaseous phase is coupled to a discrete particle Lagrangian formalism for the dispersed phase. A global two-step n-heptane/air chemical mechanism is used. The effects of initial droplet diameter, overall equivalence ratio, liquid loading and relative velocity between gaseous and liquid phases on the laminar spray flame speed and structure are studied. For lean premixed cases, it is found that the laminar flame speed decreases with increasing initial droplet diameter and relative velocity. On the contrary, rich premixed cases show a range of diameters for which the flame speed is enhanced compared to the corresponding purely gaseous flame. Finally, spray flames controlled by evaporation always have lower flame speeds. To highlight the controlling parameters of spray flame speed, approximate analytical expressions are proposed, which give the correct trends of the spray flame propagation speed behavior for both lean and rich mixtures.