Accelerating flames in tubes—an analysis

Flame acceleration in tubes is studied. A tube filled with flammable mixture is closed at one end and open to the atmosphere at its second end. When ignition takes place near the closed end, it is well-known from experiments that the flame may accelerate, oscillate and eventually reach considerable speeds. A one-dimensional analysis is presented, based upon the assumption that the flame front propagates at a speed that is small compared to the speed of sound. The analysis leads to a construction of the complete unsteady solution. Results from the analysis and from a numerical simulation are compared. They are similar enough to validate the analysis. The tube acoustics are set in motion by the expansion of the fluid due to ignition at the closed end. Subsequently, both spectrum and amplitude evolve because of the motion of the temperature interface, and because of forcing by the flame front, which the analysis precisely quantifies. Oscillations in the front position are strong enough to result in flow reversal. In addition, the induced periodic acoustic acceleration of the temperature and density interface will periodically make the flame front Rayleigh–Taylor unstable, which should result in the dramatic increase in the propagation speed seen in experiments.     

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.     

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.     

Effects of gas compressibility on the dynamics of premixed flames in long narrow adiabatic channels

We examine the dynamics of premixed flames in long, narrow, adiabatic channels focusing, in particular, on the effects of gas compressibility on the propagation. Recognising the importance of the boundary conditions, we examine and compare three cases: flame propagation in channels open at both ends, where the pressure must adjust to the ambient pressure at both ends and the expanding gas is allowed to leave the channel freely, and flame propagation in channels that remain closed at one of the two ends, where the burned/unburned gas remains trapped between the flame and one of the two walls. Earlier studies have shown that a flame accelerates when travelling down a narrow channel as a result of the combined effects of wall friction and thermal expansion. In the present work we show that compressibility effects enhance the transition to fast accelerating flames in channels open at both ends and in channels closed at the ignition end. In both situations, the accelerating flames could reach values that, depending on the effective Mach number, are as large as fifty times the laminar flame speed. In contrast, when the channel is closed at the far end, the acceleration is limited and the propagation speed is damped as the flame approaches the far boundary. Moreover, we show that, in channels closed at their ignition end, the flame in sufficiently long channels evolves into a steadily propagating compression-driven flame. The propagation speed of these flames depends exponentially on the constant-volume equilibrium temperature, which is higher than the (constant pressure) adiabatic flame temperature, and is therefore larger than for ordinary isobaric flames. Fast propagating compression waves cannot emerge in channels that remain open at their ignition end because of the reduced pressure forced by the open boundary.     

Strong flame acceleration and detonation limit of hydrogen-oxygen mixture at cryogenic temperature

A series of experiments were carried out in a closed tube at cryogenic temperature (77 K) for hydrogen-oxygen mixtures. Flame propagation speed and overpressure were measured by optical fibers and pressure sensors, respectively. The first and second shock waves were captured in the cryogenic experiments, although the shock waves always precede the flames in all cases indicating the absence of stable detonation. However, strong flame acceleration was observed for all situations, which is consistent with the prediction by expansion ratio and Zeldovich number. Besides, the tube diameter and length are also critical for flame acceleration to supersonic. All the flames in this work accelerate drastically reaching the C-J deflagration state. But at 0.4 atm, only fast flame is formed, while at higher initial pressures, the flame further accelerates to a galloping mode manifesting a near-limit detonation, which could be indicated by the stability parameter $\chi$.     

On the mechanism of the deflagration-to-detonation transition in a hydrogen-oxygen mixture

The flame acceleration and the physical mechanism underlying the deflagration-to-detonation transition (DDT) have been studied experimentally, theoretically, and using a two-dimensional gasdynamic model for a hydrogen-oxygen gas mixture by taking into account the chain chemical reaction kinetics for eight components. A flame accelerating in a tube is shown to generate shock waves that are formed directly at the flame front just before DDT occurred, producing a layer of compressed gas adjacent to the flame front. A mixture with a density higher than that of the initial gas enters the flame front, is heated, and enters into reaction. As a result, a high-amplitude pressure peak is formed at the flame front. An increase in pressure and density at the leading edge of the flame front accelerates the chemical reaction, causing amplification of the compression wave and an exponentially rapid growth of the pressure peak, which “drags” the flame behind. A high-amplitude compression wave produces a strong shock immediately ahead of the reaction zone, generating a detonation wave. The theory and numerical simulations of the flame acceleration and the new physical mechanism of DDT are in complete agreement with the experimentally observed flame acceleration, shock formation, and DDT in a hydrogen-oxygen gas mixture.     

Dynamic response of turbulent swirling flames to acoustic perturbations

The dynamic response of a turbulent, perfectly premixed flame, stabilized by means of an aerodynamic flameholder, to an upstream acoustic perturbation of the approaching flow is investigated by means of experimental and analytical tools, and simulated through a large eddy simulation of the reacting flow. It is found that the main contribution to the unsteady heat release rate is due to the fluctuation in area of the flame front, which in turn is strongly influenced by the corresponding response of the flow field to the acoustic perturbation. Numerical data show that perturbing a swirling flow that undergoes vortex breakdown results in a strong displacement of the breakdown position along its axis, while its outer part only weakly responds to the perturbation. This results in a translational motion of the flame's anchoring point, which ultimately leads to an unsteady variation of the flame area and, therefore, of the amount of heat released. This unsteady heat release mechanism can be described in a way similar to that used for characterizing the dynamic behaviour of ducted flames, stabilized by means of a bluff-body flameholder; differently from these models, however, the anchoring point of the flame can now fluctuate freely in space, and the time delay of the system is no longer identified with the travelling time of a perturbation of the flame element along it, but is now associated with the oscillation of the breakdown position. Controlling the interaction between breakdown and acoustics should allow for obtaining optimal flame dynamics, so as to limit and possibly avoid the occurrence of strong pulsation peaks whenever the combustion device is operated in an acoustically closed system.     

Combustion driven oscillations

Combustion driven oscillations can occur when a turbulent flame is enclosed in a tube or cavity. Interaction between heat fluctuations and the internal standing wave field at one of the natural frequencies of the air column produces strong organ pipe tones. The sound power emitted by this thermal-acoustic interaction depends on the impedance either side of the combustion zone and on a transfer function defining the response of the flame to sound wave disturbances. If this power exceeds the rate at which energy is dissipated at the cavity boundaries then there is a growth of the internal pressure field and an increase in the radiated sound. Plane wave theory is used to calculate the flame transfer function and adjacent impedances for a simple gas fired tube assembly. The predicted instability frequencies are then compared with experimental data. The results indicate that the flame transfer function plays a dominant role in determining the acoustic stability of the cavity and that insufficient data is available for accurately predicting unsteady flame front behaviour.     

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.     

Studies of the dynamics of autoignition assisted outwardly propagating spherical cool and double flames under shock-tube conditions

The initiation, propagation, and transition of the autoignition assisted spherical cool flame and double flame are studied numerically and experimentally using n-heptane/air/He mixtures under shock-tube experimental conditions over a wide range of temperatures. The primary goal of the current study is to understand the effects of the ignition Damkohler number, ignition energy, flame curvature, and autoignition-induced flow compression on the propagation of spherical flames to ensure the proper interpretation of shock-tube flame speed measurements at engine-relevant conditions. The results show that at high ignition Damkohler number, there are three different flame regimes, cool flame, double flame, and hot flame. The cool flame speed accelerates dramatically with the increase of ignition Damkohler number. In addition, it is found that the change of flame regime, low-temperature autoignition, flame stretch, and autoignition-induced flow compression result in a complicated non-linear dependence of flame speed on stretch. The results also reveal that the spherical cool flame has much lower Markstein length compared to the hot flame at T > 600 K. Moreover, it is found that both the autoignition assisted cool flame and the trailing hot flame front in the double flame can propagate much faster that the hot flame alone at the same mixture conditions, leading to a nonlinear dependence of flame speed on the mixture initial temperature. The simulated flame trajectories and the flame speed dependence on temperature agree qualitatively well with the shock-tube experiments. A quantitative criterion to ensure the accurate speed measurement of the cool and hot flame is proposed. The present study provides important physical insight and guidance for the flame speed measurement using a shock-tube at engine relevant conditions.     

Symmetry breaking modelling for azimuthal combustion dynamics

Annular combustors can exhibit azimuthal thermoacoustic instabilities, which can rotate as a spinning wave at the speed of sound in the azimuthal direction, oscillate as a standing wave with pressure nodes fixed in space, or be a linear combination of these. These oscillations happen if a positive feedback loop between acoustics and the response of the flames to the acoustics in the annulus occurs. This paper discusses how two different explicit symmetry breaking mechanisms affect the dynamics of these waves. We first show how small differences between the flame responses lead to one strong topological change in the dynamical system phase space, making the system prefer orientation angles at two azimuthal locations, one opposite of the other in the annulus, as found in the experiments. This symmetry breaking is modelled by directly perturbing the flame responses around the annulus with some scatter, to represent the effect of manufacturing tolerances of the burners. We then consider recent experimental evidence that the heat release rate of the flames depends on the spinning direction (clockwise or anticlockwise) when the system is spinning. In particular we model one experiment in which the flame response is found to be stronger when the wave rotates in the anticlockwise direction. We show that the statistics of the resulting model are qualitatively very similar to the experimental results showing a preference for spinning states in the anticlockwise direction.     

Effects of heat loss and viscosity friction at walls on flame acceleration and deflagration to detonation transition

The coupled effect of wall heat loss and viscosity friction on flame propagation and deflagration to detonation transition(DDT) in micro-scale channel is investigated by high-resolution numerical simulations.The results show that when the heat loss at walls is considered, the oscillating flame presents a reciprocating motion of the flame front.The channel width and Boit number are varied to understand the effect of heat loss on the oscillating flame and DDT.It is found that the oscillating propagation is determined by the competition between wall heat loss and viscous friction.The flame retreat is led by the adverse pressure gradient caused by thermal contraction, while it is inhibited by the viscous effects of wall friction and flame boundary layer.The adverse pressure gradient formed in front of a flame, caused by the heat loss and thermal contraction, is the main reason for the flame retreat.Furthermore, the oscillating flame can develop to a detonation due to the pressure rise by thermal expansion and wall friction.The transition to detonation depends non-monotonically on the channel width.     

Flame acceleration in long narrow open channels

We study the propagation of premixed flames in long but finite channels, when the mixture is ignited at one end and both ends remain open and exposed to atmospheric pressure. Thermal expansion produces a continuous flow of burned gas directed away from the flame and towards the end of the channel where ignition took place. Owing to viscous drag, the flow is retarded at the walls and accelerated in the center, producing a pressure gradient that pushes the unburned gas ahead of the flame towards the other end of the channel. As a result the flame accelerates when it travels from end to end of the channel. The total travel time depends on the length of the channel and is proportional to γ^?1ln(1 + γ), where γ is the heat release parameter.     

Formation of the preheated zone ahead of a propagating flame and the mechanism underlying the deflagration-to-detonation transition

The Letter presents analytical, numerical and experimental studies of the mechanism underlying the deflagration-to-detonation transition (DDT). Insight into how, when, and where DDT occurs is obtained by analyzing analytically and by means of multidimensional numerical simulations dynamics of a flame accelerating in a tube with no-slip walls. It is shown that the deflagration-to-detonation transition exhibits three separate stages of evolution corroborating majority experimental observations. During the first stage flame accelerates and generates shocks far ahead of the flame front. During the second stage the flame slows down, shocks are formed in the immediate proximity of the flame front and the preheated zone ahead of the flame front is created. The third stage is self-restructuring of the steep temperature profile within the flame, formation of a reactivity gradient and the actual formation of the detonation wave itself. The mechanism for the detonation wave formation, given an appropriate formation of the preheated zone, seems to be universal and involves a reactivity gradient formed from the initially steep flame temperature profile in the presence of the preheated zone. The developed theory and numerical simulations are found to be well consistent with extensive experiments of the DDT in hydrogen-oxygen and ethylene-oxygen mixtures in tubes with smooth and rough walls.     

Numerical study of premixed flame dynamics in a closed tube: Effect of wall boundary condition

Numerical simulations were conducted to study the dynamics of premixed flames propagating in a closed tube by solving the fully compressible reactive Navier–Stokes equations using a high-order numerical method on a dynamically adapting grid. A simplified chemical-diffusive model was used to describe the reactions and energy release in a stoichiometric hydrogen-air mixture. The influence of wall boundary condition on the flame dynamics was explored by considering three different types of condition on the walls: adiabatic no-slip, adiabatic free-slip, and isothermal. The calculations show that the wall boundary condition has a significant effect on the generation and amplification of pressure waves and consequently on the flame dynamics. In the early stages of flame propagation, the flame behaves in a similar manner for different boundary conditions, that is, the flame develops a tulip shape that further evolves into a distorted tulip flame (DTF) through Rayleigh-Taylor instability arising from acoustic-flame interaction. Significant differences, however, arise after DTF formation in the late stages, especially when the primary acoustic wave is amplified to form a shock wave in the adiabatic free-slip and isothermal cases. The shock-flame interactions facilitate the formation of a series of increasingly corrugated flames by triggering the Richtmyer–Meshkov instabilities. The way how the lateral flame fronts touch the tube sidewalls to generate the primary acoustics and the heat conduction through the tube sidewalls play an important role in the generation and amplification of the pressure waves.     

半开口管道中的氢/空气火焰加速和压力发展过程

本文研究了氢／空气预混火焰在半开口管道中的火焰加速现象和压力发展过程．结果表明,重复布置的障碍物对火焰速度和压力提升产生显著的影响．火焰传播状态随着氢气当量比的变化而发生改变,在氢气当量比约为０．３４时,火焰速度出现第一次跃变;随着氢气当量比进一步提高,火焰速度发生第二次跃变,即由爆燃转为爆轰．发生爆轰时氢气当量比的范围随着阻塞比的不同而发生变化．     

DNS analysis of boundary layer flashback in turbulent flow with wall-normal pressure gradient

The presence of swirl in combustion systems produces a marked change in their boundary layer flashback behaviour. Two aspects of swirling flow are investigated in this study: the effect of the swirl-generated wall-normal pressure gradient, and the effect of misalignment between the mean flow direction and the direction of flame propagation. The analysis employs Direct Numerical Simulation (DNS) of fuel-lean premixed hydrogen-air flames in turbulent planar channel flow with friction Reynolds number of 180. The effect of swirl on the flashback process is investigated by imposing a wall-normal pressure gradient profile. Analysis of the DNS data shows how the resulting differences in flow field and flame topology contribute to the differences in the overall flashback speed. Misalignment of the flow and propagation directions leads to asymmetry in the flame shape statistics as streaks of high velocity fluid in the boundary layer cleave into the flame front at an angle, yielding an increase in flame surface density away from the wall. Swirl has a stabilising effect on the turbulent flame front during flashback along the centre-body of a swirling annular flow due to the density stratification across the flame front, and produces a reduction in turbulent consumption speed. However the swirl also sets up a hydrostatic pressure difference that drives the flame forward, and the net effect is that the flashback speed is increased. The dominance of hydrostatic effects motivates development of relatively simple modelling for the effect of swirl on flashback speed. A model accounting for the inviscid momentum balance and for confinement effects is presented which adequately describes the effect of swirl on flashback speed observed in previous experimental studies.     

Inward-propagating cylindrical flames under different ignition conditions

Inward-propagating cylindrical flames are studied numerically by high-resolution simulations using a one-step Arrhenius kinetics. Emphasis is placed on the effect of shock waves on the flame propagation by setting initial ignition conditions with and without shock wave. It is found that without initial shock wave, the inward-propagating flame propagates initially at a constant speed, while in the later stage of the propagation, it shows a small-amplitude oscillatory motion. When the shock wave initially introduced is medium, a large-amplitude oscillatory motion is caused by the interaction of shock waves with the inward-propagating flame. Moreover, autoignition occurs at the center and develops outwardly into a cellular flame. However, as the introduced shock wave is strong, autoignition created at the center evolves outwardly a cellular detonation.     

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.     

Flame patterns of acoustic wave and flame interaction in a cylindrical tube

In this short paper, flame and acoustic wave interactions under laboratory conditions have been reported. The test rig consists of a cylindrical Perspex tube and a fuel tube (burner) positioned along the central axis of the tube. The acoustic characteristics of the rig are measured. The flame instability with and without acoustic excitation has been investigated. A high shutter speed colour camera has been applied to capture many interesting unstable flame patterns. It has been found that strong flame instability only occurs at particular frequencies. The position of the burner inside the cylindrical tube also has an effect on flame instability.