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.     

Effect of geometrical parameters on thermo-acoustic instability of downward propagating flames in tubes

Experiments and theoretical analysis are presented to clarify the effect of geometrical parameters on thermo-acoustic instability of downward propagating flames in tubes. The experiments reveal that the longer tubes have higher instability compared to shorter tubes and the lower diameter tubes have higher instability compared to higher diameter tubes. The secondary instability leading to turbulent burning is found to be more sensitive to change in geometrical parameters compared to primary instability (oscillating flat flame). The secondary instability is re-stabilized for some intermediate burning velocity conditions even though lower and higher burning velocity conditions show secondary instability. The appearance of such re-stabilization is only observed for some specific lengths of the tube. Present experimental observations pertaining to the effect of geometrical parameters is found to be contradicting the theoretical predictions based on pressure coupling mechanism. To clear the underlying mechanism, analytical growth rate is computed considering velocity coupling mechanism. The computed growth rates correctly predict the effect of geometrical parameters on thermo-acoustic instability of downward propagating flames. This work provides further evidence to believe that the flame -acoustic coupling in downward propagating flames is due to flame area modulation (leading to heat release modulation) through action of acoustic acceleration.     

Flame propagation in gaseous nitrous oxide

The characteristics of the propagation of a nitrous oxide decomposition flame in a tube with an internal diameter of 70 mm were measured. It was demonstrated that the pattern of flame propagation and the extent of burnout are determined by the convective motion of the flame kernel because of a very slow burning of nitrous oxide. The laminar flame speed estimated from pressure oscillograms and calculated using thermal theory of flame propagation was found to be ～1 cm/s. The critical diameter of flame quenching in channels were measured to decrease from 10 to 4 mm as the pressure was increased from 15 to 20 atm. Because of the possibility of reignition of the fresh mixture behind the flame arrester by the outflowing combustion products, the channel should be significantly longer than 200 mm.     

Analysis of the influence of nanometric aluminium particle vaporisation on flame propagation in bulk powder media

The combustion of nanometric aluminium (Al) powder with an oxidiser such as molybdenum trioxide (MoO₃) is studied analytically. The analysis was performed to correlate individual Al particle gasification rates to macroscopic flame propagation rates observed in flame tube experiments. Examination of various characteristic times relevant to propagation of a deflagration reveals that particles below about 1.7 nm in diameter evaporate before appreciable chemical reactions occur. Experimental studies used Al particles greater than 1.7 nm in diameter such that a diffusion flame model was developed to better understand the combustion dynamics of multiphase Al particles greater than 1.7 nm diameter relative to experimentally measured macroscopic flame propagation rates. The diffusion flame model predicted orders of magnitude slower propagation rates than experimentally observed. These results imply that (1) another reaction mechanism is responsible for promoting reaction propagation and/or (2) modes other than diffusion play a more dominant role in flame propagation.     

Combustion dynamics of inverted conical flames

An inverted conical flame anchored on a central bluff-body in an unconfined burner configuration features a distinctive acoustic response. This configuration typifies more complex situations in which the thermo-acoustic instability is driven by the interaction of a flame with a convective vorticity mode. The axisymmetric geometry investigated in this article features a shear region between the reactive jet and the surrounding atmosphere. It exhibits self-sustained oscillations for certain operating conditions involving a powerful flame collapse phenomenon with sudden annihilation of flame surface area. This is caused by a strong interaction between the flame and vortices created in the outer jet shear layer, a process which determines the amplitude of heat release fluctuation and its time delay with respect to incident velocity perturbations. This process also generates an acoustic field that excites the burner and synchronizes the vortex shedding mechanism. The transfer functions between the velocity signal at the burner outlet and heat release are obtained experimentally for a set of flow velocities fluctuations levels. It is found that heat release fluctuations are a strong function of the incoming velocity perturbation amplitude and that the time delay between these two quantities is mainly determined by the convection of the large scale vortices formed in the jet shear layer. A model is formulated, which suitably describes the observed instabilities.     

Effects of imperfect premixing coupled with hydrodynamic instability on flame propagation

The problem of flame propagation in imperfectly premixed mixtures—mixtures of reactants with variable composition—is considered in this numerical study. We carry out two-dimensional direct numerical simulations of a flame propagating in a globally lean fuel-oxidizer mixture with imposed velocity and composition fluctuations of various intensities. The configuration adopted is that of a flame front interacting with spatially evolving fluctuations, and the characteristic scales of the domain and of the fluctuations imposed are significantly larger than the characteristic thickness of the flame, to account for important flame dynamics such as the hydrodynamic instability. One-step chemistry and Fick’s diffusion law are considered, along with unity Lewis number assumption for all the species. It is observed, in agreement with previous results, that relatively weak fluctuations in composition alone may lead to a large increase in flame length and burning rate. The hydrodynamic instability caused by gas expansion, catalyzed by the composition fluctuations interacting with the flame, is found to be responsible for the flame length enhancement. It is observed as well that the relative importance of this effect diminishes as the velocity fluctuations present become more intense, and that composition fluctuations have a small impact on flame length for these cases. It is additionally found that, with increasing intensity of composition fluctuations, there is eventually a reduction of burning rate per unit length of flame which leads, consequently, to a weak reduction of overall burning rate for the largest velocity fluctuation intensities covered by this study.     

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。     

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.     

Transition in the propagation mechanism during flame acceleration in porous media

The combustion of stoichiometric hydrogen-air at various initial pressures was investigated in a 7.62 cm square cross-section channel filled with 1.27 cm diameter beads. The flame time-of-arrival and pressure time history along the channel were obtained by ionization probes and piezoelectric pressure transducers. Flame acceleration was found to be very rapid, e.g. at an initial pressure of 45 kPa the flame achieves a velocity of over 600 m/s in roughly 0.3 m. It was determined that at this high speed a well defined planar shock wave precedes a thick reaction zone. It was also shown that there is a transition in the flame propagation mechanism, similar to that observed in an obstacle laden channel [G. Ciccarelli and C. Johansen, The role of shock-flame interactions on flame acceleration in an obstacle laden channel, Proc. 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems, Minsk, 2009]. By varying the initial pressure of the mixture, changes in the axial location of the transition between combustion propagation regimes was also observed. A soot foil technique was used to identify the transition in the propagation mechanism, as well as to provide information concerning the local flow field around the beads and the overall average flow direction.     

Influence of water mist on propagation and suppression of laminar premixed flame

The combustion of premixed gas mixtures containing micro droplets of water was studied using one-dimensional approximation. The dependencies of the burning velocity and flammability limits on the initial conditions and on the properties of liquid droplets were analyzed. Effects of droplet size and concentration of added liquid were studied. It was demonstrated that the droplets with smaller diameters are more effective in reducing the flame velocity. For droplets vaporizing in the reaction zone, the burning velocity is independent of droplet size, and it depends only on the concentration of added liquid. With further increase of the droplet diameter the droplets are passing through the reaction zone with completion of vaporization in the combustion products. It was demonstrated that for droplets above a certain size there are two stable stationary modes of flame propagation with transition of hysteresis type. The critical conditions of the transition are due to the appearance of the temperature maximum at the flame front and the temperature gradient with heat losses from the reaction zone to the products, as a result of droplet vaporization passing through the reaction zone. The critical conditions are similar to the critical conditions of the classical flammability limits of flame with the thermal mechanism of flame propagation. The maximum decrease in the burning velocity and decrease in the combustion temperature at the critical turning point corresponds to predictions of the classical theories of flammability limits of Zel'dovich and Spalding. The stability analysis of stationary modes of flame propagation in the presence of water mist showed the lack of oscillatory processes in the frames of the assumed model.     

多孔介质中甲烷预混气火焰传播特性实验研究

本文对甲烷预混气在多孔介质中的火焰传播特性进行了实验研究,在开口竖直管中充填多孔介质,通过改变预混气氧含量使火焰在不同多孔介质中传播并测量火焰传播速度。预混气中氧含量最高达到29％。实验结果表明:多孔介质中甲烷可燃预混气火焰传播速度大于其层流火焰传播速度,可达到5倍以上(当量比的甲烷-空气预混气);多孔介质当量孔直径越大,或预混气层流火焰速度越高,则预混气火焰传播速度越高;多孔介质中可燃混气的火焰传播界限变小,当量孔直径大的多孔介质其界限值较大。实验结果与Babkin提出的多孔介质中的火焰传播机理相符。     

Simulation of hydrodynamic phenomena attendant on the flame front propagation in a tube behind a piston

The propagation of a propane-air flame in a model internal combustion chamber, a tube with one or two pistons, is studied experimentally. Situations are simulated in which the flame front moves in a semiopen flat or cylindrical tube between two pistons or between a piston and the closed end of the tube. The time dependence of the flame front position and acceleration is obtained for the case of the variable tube length and combustible mixture volume. Self-oscillation conditions for the flame front and piston are determined. A relation between their amplitude-frequency characteristics is found. It is established that the piston paradox motion effect, i.e., the motion of the piston toward the flame front, depends on the length of the tube. It is demonstrated that the piston effect is related to the formation of a “tulip” flame. An explanation to the observed hydrodynamic phenomena is given.     

Reaction propagation modes in millimeter-scale tubes for ethylene/oxygen mixtures

Effects of tube diameter and equivalence ratio on reaction front propagations of ethylene/oxygen mixtures in capillary tubes were experimentally analyzed using high speed cinematography. The inner diameters of the tubes investigated were 0.5, 1, 2 and 3 mm. The flame was ignited at the center of the 1.5 m long smooth tube under ambient pressure and temperature before propagated towards the exits in the opposite directions. A total of five reaction propagation scenarios, including deflagration-to-detonation transition followed by steady detonation wave transmission (DDT/C–J detonation), oscillating flame, steady deflagration, galloping detonation and quenching flame, were identified. DDT/C–J detonation mode was observed for all tubes for equivalence ratios in the vicinity of stoichiometry. The velocity for the steady detonation wave propagation was approximately Chapman–Jouguet velocity for 1, 2, and 3 mm I.D. tubes; however, a velocity deficit of 5% was found for the case in 0.5 mm I.D. tube. For leaner mixtures, an oscillating flame mode was found for tubes with diameters of 1 to 3 mm, and the reaction front travelled in a steady deflagrative flame mode with velocities around 2–3 m/s when the mixture equivalence ratio becomes even leaner. Galloping detonation wave propagation was the dominant mode for the fuel lean regime in the 0.5 mm I.D. tube. For rich mixtures beyond the detonation limits, a fast flame followed by flame quenching was observed.     

Mechanism of combustion dynamics in a backward-facing step stabilized premixed flame

Combustion dynamics leading to thermoacoustic instability in a rearward-facing step stabilized premixed flame is experimentally examined with the objective of investigating the fluid dynamic mechanism that drives heat release rate fluctuations, and how it couples with the acoustic field. The field is probed visually, using linear photodiode arrays that capture the spatiotemporal distribution of CH* and OH*; an equivalence ratio monitor; and a number of pressure sensors. Results show resonance between the acoustic quarter wave mode of the combustion tunnel and a fluid dynamic mode of the wake. Under unstable conditions, the flame is convoluted around a large vortex that extends several step heights downstream. During a typical cycle, while the velocity is decreasing, the vortex grows, and the flame extends downstream around its outer edge. As the velocity reaches its minimum, becoming mostly negative, the vortex reaches its maximum size, and the flame collides with the upper wall; its leading edge folds, trapping reactants pockets, and its trailing edge propagates far upstream of the step. In the next phase, while the velocity is increasing, the heat release grows rapidly as trapped reactant’ pockets are consumed by flames converging towards their centers, and the upstream flame is dislodged back downstream. The heat release rate reaches its maximum halfway into the velocity rise period, leading the maximum velocity by about 90°. In this quarter-wave mode, the pressure leads the velocity by 90° as well, that is, it is in phase with the heat release rate. Numerical modeling results support this mechanism. Equivalence ratio contribution to the instability mechanism is shown to be minor, i.e., heat release dynamics are governed by the cyclical formation of the wake vortex and its interaction with the flame.     

Premixed flame oscillations in obstructed channels with both ends open

An initially laminar premixed flame front accelerates extremely fast and may even trigger a detonation when propagating in a semi-open obstructed channel (one end of the channel is closed; the flame is ignited at the closed end and moves towards the open one). However, industrial and laboratory conduits oftentimes have both ends open, or vented, with a flame ignited at one of these ends. The latter constitutes the focus of the present work. Specifically, premixed flame propagation through a comb-shaped array of obstacles, in-built in a channel with both ends open, is studied by means of computational simulation of the reacting flow equations with fully-compressible hydrodynamics and an Arrhenius chemical kinetics. The parametric study includes various blockage ratios and spacing as well as the thermal expansion ratios, with oscillations of the burning rate observed in the majority of the cases, which conceptually differs from fast flame acceleration in semi-open channels. Such a difference is devoted to the fact that while the entire flame-generated jet-flow is pushed towards a single exit in a semi-open channel, in a channel with two ends open, this jet-flow is distributed between the upstream and downstream flows, thereby moderating flame propagation. The flame oscillations are nonlinear in all cases where they are observed. The oscillation period grows with the blockage ratio but decreases with the thermal expansion. The present results also support the recent experiments, modeling and theory of flames in obstructed channels with both ends open, which all yielded steady or quasi-steady flame propagation prior to the onset of flame acceleration. Indeed, the present oscillations can be treated as the fluctuations around a quasi-steady solution.     

On the thermo-acoustic Fant equation

A ‘reduced complexity’ equation is derived to investigate combustion instabilities of a Rijke burner. The equation is nonlinear and furnishes limit cycle solutions for finite amplitude burner modes. It is a generalisation to combustion flows of the Fant equation used to investigate the production of voiced speech by unsteady throttling of flow by the vocal folds [G. Fant, Acoustic Theory of Speech Production. Mouton, The Hague, 1960]. In the thermo-acoustic problem the throttling occurs at the flame holder. The Fant equation governs the unsteady volume flow past the flame holder which, in turn, determines the acoustics of the entire system. The equation includes a fully determinate part that depends on the geometry of the flame holder and the thermo-acoustic system, and terms defined by integrals involving thermo-aerodynamic sources, such as a flame and vortex sound sources. These integrals provide a clear indication of what must be known about the flow to obtain a proper understanding of the dynamics of the thermo-acoustic system. Illustrative numerical results are presented for the linearised equation. This governs the growth rates of the natural acoustic modes, determined by system geometry, boundary conditions and mean temperature distribution, which are excited into instability by unsteady heat release from the flame and damped by large scale vorticity production and radiation losses into the environment. In addition, the equation supplies information about the ‘combustion modes’ excited by the local time-delay feedback dynamics of the flame.     

Heat recirculation effects on flame propagation and flame structure in a mesoscale tube

Heat recirculation effects on flame propagation and flame structure are theoretically and experimentally examined in a mesoscale tube as the simplest model of heat-recirculating burners. Solutions for steady propagation are obtained using a one-dimensional two-temperature approximation. The results show that the low heat diffusivities of common solid materials permit significant heat recirculation through the wall only for a slowly-propagating condition, otherwise the flame behaves almost like a freely-propagating nonadiabatic flame. This limited heat recirculation sharply pinches and stretches two well-known branches of the freely-propagating nonadiabatic flame, resulting in the appearance of two slow-propagation branches. On the upper slow-propagation branch flames can reach superadiabatic temperatures and on the lower one, which is stretched from the classical unstable lower branch, flames can be stable. As the tube inner diameter decreases, another burning regime appears where flames are barely sustained by the heat recirculation. Further reduction of the tube inner diameter makes no flame exist. It is also revealed that a flame in a mesoscale tube has two length scales, i.e. the conventional flame thickness and a convective preheat zone thickness, and that the latter should be much larger than the former for significant heat recirculation. It is theoretically predicted that a heat-recirculating, even superadiabatic, flame with positive propagation velocity against the gas flow can exist in a mesoscale tube. It is also found that a flame transition from one branch to another in a given tube is well described by only one dimensionless parameter. Finally, these theoretical results show good qualitative agreements with experiments, especially for the transition behaviours.     

Experimental investigation on the self-ignition of pressurized hydrogen released by the failure of a rupture disk through tubes

Hydrogen is expected to be used as a clean energy carrier. However, when high-pressure hydrogen is suddenly released into the air through tubes, self-ignition can occur by a diffusion ignition mechanism. In this paper, the phenomena of self-ignition and flame propagation during the sudden release of high-pressure hydrogen were investigated experimentally. Experimental results show that self-ignition can occur when bursting pressure is sufficiently high in spite of the shortness of the tube. For example, self-ignition was observed at a bursting pressure as high as 23.5 MPa with 50 mm long tube. When self-ignition successfully occurs, a hydrogen jet flame is produced by the ignition. The flame is then stabilized at the tube outlet. From photodiode signals and flame images, the propagation of a flame inside the tube is confirmed and the flame is detected near the rupture disk as the bursting pressure increases. When the tube length is not long enough to produce self-ignition, a hydrogen flame is observed in the only boundary layer at the end of tube and it quenches after the flame exits the tube. Consequently, the formation of a complete flame across the tube is important to initiate self-ignition, which sustains a diffusion flame after jetting out of the tube into the air. Also, in order to establish a complete flame across the tube, it is necessary to have sufficient length such that the mixing region is generated by multi-dimensional shock–shock interactions.     

Experimental research on flame revolution and precession of fire whirls

This paper presents the first experimental effort to explore the large scale 3-D flame instabilities of fire whirls, including the inclined flame revolution during the transition from a general pool fire to fire whirl, and the swirling flame precession in a quasi-steady fire whirl. The experimental medium-scale fire whirls were produced by a fixed-frame facility. Experimental observations indicate that flame revolution is an important flame instability during the formation of fire whirl, showing that the entire flame is inclined and revolves around the geometrical axis of symmetry with increasing angular velocity until the critical point, without the self-rotation of the flame. It is found that the inlet velocity fluctuates synchronously with the flame revolution. As soon as the fire whirl forms, the erect swirling flame starts to precess around the geometrical axis of symmetry. Analysis indicates that during flame precession the periodic fluctuations of inlet velocity disappear and a local annular external recirculation zone (ERZ) is produced outside the flame (vortex core), while the flow is upward inside. It is found that the inlet velocities are nearly constant within the continuous flame in order to maintain a stable generating eddy. A good linear correlation exists between the average inlet velocities and average ambient circulations for all fuel pan sizes. The precession frequency is relatively stable during one test. The frequencies of flame revolution and precession are both proportional to the average inlet velocity, and the corresponding Strouhal numbers are constants of 0.42 and 0.80, respectively. The flame revolves and precesses in the same direction as the self-rotation of the fire whirl flame in all tests. The flame revolution is related to the periodical fluctuations of inlet flow, while the flame precession is considered to be linked to the occurrence of ERZ in fire whirls.     

Violent folding of a flame front in a flame-acoustic resonance

The first direct numerical simulations of violent flame folding because of the flame-acoustic resonance are performed. Flame propagates in a tube from an open end to a closed one. Acoustic amplitude becomes extremely large when the acoustic mode between the flame and the closed tube end comes in resonance with intrinsic flame oscillations. The acoustic oscillations produce an effective acceleration field at the flame front leading to a strong Rayleigh-Taylor instability during every second half period of the oscillations. The Rayleigh-Taylor instability makes the flame front strongly corrugated with elongated jets of heavy fuel mixture penetrating the burnt gas and even with pockets of unburned matter separated from the flame front.