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.     

Chemical-diffusive models for flame acceleration and transition-to-detonation: genetic algorithm and optimisation procedure

This paper presents a general approach for developing an automated, fast and flexible procedure to determine the reaction parameters for a simplified chemical-diffusive model to simulate flame acceleration and deflagration-to-detonation transition (DDT) in a stoichiometric methane–air mixture. The procedure uses a combination of a genetic algorithm and Nelder-Mead optimisation scheme to find the optimal reaction parameters for a reaction rate based on an Arrhenius form for conversion of reactants to products. The model finds six optimal reaction parameters that reproduce six flame and detonation properties. Results show that the reaction parameters closely reproduce their intended flame and detonation properties. The laminar flame profile computed using the reaction parameters in a 1D Navier-Stokes code matches the profile obtained when using a detailed chemical reaction mechanism. The optimal reaction parameters are then used in a 2D simulation of flame acceleration and DDT in an obstacle-laden channel containing stoichiometric methane–air, and the results show that the computation closely follows the transition-to-detonation observed in experiments. This automated procedure for finding parameters for a proposed reaction model makes it possible to simulate the behaviour of flames and detonations in large, complex scenarios, which would otherwise be an incalculable problem.     

The rate of expansion of spherical flames

In this paper we investigate the acceleration of the expansion of premixed spherical flames and evolution of the cellular patterns on their surfaces. An asymptotic model is used for the simulations and a spectral numerical algorithm is employed to study flames over large time intervals. Numerous numerical experiments indicate that for large enough time the acceleration of a two-dimensional expanding flame slows down but the expansion rate is still able to reach values significantly exceeding the burning rate of an exactly circular flame. The importance of the effect of forcing was also confirmed and the validity of simulations of sectors of circular flame fronts was studied in order to justify prospective use of the Fourier spectral model for three-dimensional spherical flames.     

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 $\chi$.     

An experimental investigation on self-acceleration of cellular spherical flames

The cells that continuously develop over the flame surface of an expanding spherical flame increase its area and thereby the global propagation rate, resulting in the possibility of self-acceleration. The present study examines whether this self-acceleration could be self-similar, and, if so, whether it could also be self-turbulizing. Extensive experiments at elevated pressures and thereby reduced laminar flame thicknesses and enhanced propensity to exhibit Darrieus-Landau instability were conducted for hydrogen/air mixtures over an extensive range of equivalence ratios. The results demonstrate the strong possibility of self-similar flame acceleration, weak influence of the system pressure and diffusional-thermal instability, and a corresponding moderate spread in the power-law acceleration exponent.     

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.     

氢氧爆轰波在激波管中的成长机制研究

 针对气相爆轰波成长机制研究,采用压力传感器和高速摄影技术,测试了氢氧混合气体在点火后的火焰波、前驱冲击波以及爆轰波的成长变化过程,计算了冲击波过程参数和气体状态参数,分析了火焰加速机制。实验结果表明,APX-RS型高速摄影系统可用于拍摄气相爆轰波的成长历程;氢氧爆轰波的产生是由于湍流火焰和冲击波的相互正反馈作用,导致反应区内多处发生局部爆炸,爆炸波与冲击波相互耦合,最终成长为定常爆轰波。     

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.     

Enhanced DDT mechanism from shock-flame interactions in thin channels

We show experimentally and numerically that when a weak shock interacts with a finger flame in a narrow channel, an extremely efficient mechanism for deflagration to detonation transition occurs. This is demonstrated in a 19-mm-thick channel in hydrogen-air mixtures at pressures below 0.2 atm and weak shocks of Mach numbers 1.5 to 2. The mechanism relies primarily on the straining of the flame shape into an elongated alligator flame maintained by the anchoring mechanism of Gamezo in a bifurcated lambda shock due to boundary layers. The mechanism can increase the flame surface area by more than two orders of magnitude without any turbulence on the flame time scale. The resulting alligator-shaped flame is shown to saturate near the Chapman–Jouguet condition and further slowly accelerate until its burning velocity reaches the sound speed in the shocked unburned gas. At this state, the lead shock and further adiabatic compression of the gas in the induction zone gives rise to auto-ignition and very rapid transition to detonation through merging of numerous spontaneous flames from ignition spots. The entire acceleration can occur on a time scale comparable to the laminar flame time.     

Effect of the plasma location on the deflagration-to-detonation transition of a hydrogen–air flame enhanced by nanosecond repetitively pulsed discharges

This work presents a method for using nanosecond repetitively pulsed (NRP) plasma discharges for accelerating a propagating flame such that the deflagration-to-detonation transition occurs. A strategy is developed for bringing the location of the plasma near the tube wall and, thus, reducing the presence of the electrodes in the combustion tube as well as presenting a configuration in which cooling of the electrodes is viable for practical applications. Time-of-flight measurements were used in combination with energy deposition measurements and high-speed OH*-chemiluminescence imagery to investigate the flame acceleration process. For stoichiometric hydrogen–air flames, successful transition to detonation was achieved by applying a burst of 110 pulses at 100 kHz, with energies as low as 10 mJ per pulse. This was also achieved when plasma discharges were applied in the vicinity of the wall. Two enhancement mechanisms for flame acceleration were identified. The essential role of shock–flame interaction was established as being the main mechanism for flame acceleration when the discharges are located near the wall. This work presents an effective alternative that allows for NRP discharges to be applied near the wall while successfully maintaining a promising success rate for detonation transition.     

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.     

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.     

Flame acceleration process and detonation transition in a channel with roughness elements on a wall

We experimentally investigated the effect of small roughness elements, which could be regarded as the wall roughness, on flame acceleration and deflagration-to-detonation transition (DDT). Our previous experiments (Maeda et al., 2019) using the sandpaper-like irregular roughness indicated that the flame acceleration and the associated DDT were greatly enhanced by the roughness. In this study, CH* chemiluminescence imaging as well as schlieren imaging was conducted in parallel with pressure measurements using an ethylene-oxygen combustion in the channel (486 mm long, 10 mm square cross-section) with the regular roughness (square pyramid elements with a base length and a height of 1 mm) in order to directly link the interference between the flow-field affected by the roughness and the propagating flame surface resulting the enhancement of chemical reactions, whereas the schlieren imaging alone could not allow to discuss the chemical reaction field in the previous study. After the leading shock wave was formed by the initial finger flame acceleration process, multiple interactions were observed on the flame front with the flow-field and pressure disturbances of the unreacted gas near the roughness elements. The results provided clear evidence that the roughness emphasized the effect of boundary layer, and the region where the disturbance layer and the flame were interacting coincided with the strong chemical reaction in the chemiluminescence image, indicating increase of the flame surface area caused by the turbulence on the flame front, which was also validated by the rough estimation of the burning velocity. The detonation onset was observed at the flame surface near the wall with the roughness elements. The possible factors of the final detonation transition were deduced to be the hot spot formation based on the multiple interactions of pressure waves with the roughness elements and entrainment of the unreacted gas of the highly turbulent flame front.     

Experimental observations of flame acceleration and transition to detonation following shock-flame interaction

Observations are presented from experiments where laminar flame bubbles were perturbed successively by incident and reflected shock waves. Significant flame acceleration was observed in many instances, with the flame closely coupled to the reflected shock wave. The coupled waves are interpreted using a generalized Hugoniot analysis. As the incident shock velocity increased, detonation emerged near the highly convolved reaction zone. Prior to detonation the external visual attributes of the combustion fronts appear identical to turbulent combustion. However, they cannot be due to classical isotropic turbulence. The overall conclusion is that the observed enhancement of combustion is driven by chemi-acoustic interactions and related gas-dynamic effects. An analysis of the prevailing thermodynamic states suggests that thermal auto-ignition chemistry could also play a significant role prior to the onset of detonation.     

A DNS study of the physical mechanisms associated with density ratio influence on turbulent burning velocity in premixed flames

Data obtained in 3D direct numerical simulations of statistically planar, 1D weakly turbulent flames characterised by different density ratios σ are analysed to study the influence of thermal expansion on flame surface area and burning rate. Results show that, on the one hand, the pressure gradient induced within a flame brush owing to heat release in flamelets significantly accelerates the unburned gas that deeply intrudes into the combustion products in the form of an unburned mixture finger, thus causing large-scale oscillations of the burning rate and flame brush thickness. Under the conditions of the present simulations, the contribution of this mechanism to the creation of the flame surface area is substantial and is increased by σ, thus implying an increase in the burning rate by σ. On the other hand, the total flame surface areas simulated at σ = 7.53 and 2.5 are approximately equal. The apparent inconsistency between these results implies the existence of another thermal expansion effect that reduces the influence of σ on the flame surface area and burning rate. Investigation of the issue shows that the flow acceleration by the combustion-induced pressure gradient not only creates the flame surface area by pushing the finger tip into the products, but also mitigates wrinkling of the flame surface (the side surface of the finger) by turbulent eddies. The latter effect is attributed to the high-speed (at σ = 7.53) axial flow of the unburned gas, which is induced by the axial pressure gradient within the flame brush (and the finger). This axial flow acceleration reduces the residence time of a turbulent eddy in an unburned zone of the flame brush (e.g. within the finger). Therefore, the capability of the eddy for wrinkling the flamelet surface (e.g. the side finger surface) is weakened owing to a shorter residence time.     

Towards a predictive scenario of a burning accident in a mining passage

To reveal the inner mechanisms of a combustion accident in a coalmine, the key stages and characteristics of premixed flame front evolution such as the flame shapes, propagation speeds, acceleration rates, run-up distances and flame-generated velocity profiles are scrutinised. The theories of globally spherical, expanding flames and of finger-flame acceleration are combined into a general analytical formulation. Two-dimensional and cylindrical mining passages are studied, with noticeably stronger acceleration found in the cylindrical geometry. The entire acceleration scenario may promote the total burning rate by up to two orders of magnitude, to a near-sonic value. Starting with gaseous combustion, the analysis is subsequently extended to gaseous-dusty environments. Specifically, combustible dust (e.g. coal), inert dust (e.g. sand), and their combination are considered, and the influence of the size and concentration of the dust particles is quantified. In particular, small particles influence flame propagation more than large ones, and flame acceleration increases with the concentration of a combustible dust, until the concentration attains a certain limit.     

Flame acceleration in a narrow channel with flow compressibility and diverging or converging walls

We study the effects of non-parallel (diverging or converging) channel walls on flame propagation and acceleration in planar and cylindrical narrow channels, closed at the ignition end and open at the other, accounting for thermal expansion in both the zero Mach number and weakly compressible flow limits. For parallel channel walls, previous work has shown that thermal expansion induces an axial flow in the channel, which can significantly increase the propagation speed and acceleration of the flame. In this study, we consider examples of diverging/converging linear walls, although our asymptotic analysis is also valid for curved walls. The slope of the channel walls is chosen so that the magnitude of the thermal-expansion induced flow through the channel obtained for parallel walls is modified at leading-order, thereby influencing the leading-order flame propagation. For zero Mach number flows, the effect of the diverging/converging channel walls is moderate. However, for weakly compressible flows, the non-parallel walls directly affect the rate at which pressure diffuses through the channel, significantly inhibiting flame acceleration for diverging walls, whereas the flame acceleration process is enhanced for converging walls. We consider several values of the compressibility factor and channel wall slopes. We also show that the effect of a cylindrical channel geometry can act to significantly enhance flame acceleration relative to planar channels. The study reveals several new physical insights on how non-parallel channel walls can influence the ability of flames to accelerate by modifying the flow and pressure distribution induced by thermal expansion.     

Oscillatory flame propagation: Coupling with the acoustic field

An analysis is presented of flame acceleration in a tube filled with flammable mixture, closed at one end and open to the atmosphere at its second end. Ignition takes place near the closed end; experiments then show that the flame accelerates, slows down and moves back, accelerates again, and may eventually reach considerable speeds. The one-dimensional analysis is based upon the assumption that the flame front propagates at a speed that is small compared to the speed of sound, and that depends upon the temperature and pressure perturbation due to acoustics that it encounters. A complete unsteady solution is constructed. 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 itself depends upon the effect of acoustics on the state of the fluid that it encounters. Oscillations in the front position are stronger than in a previous study in which the flame propagation speed was taken to be constant. With the additional feedback now included, it is strong enough to result in strong flow reversal.     

Numerical simulations of flame propagation and DDT in obstructed channels filled with hydrogen–air mixture

We study flame acceleration and deflagration-to-detonation transition (DDT) in channels with obstacles using 2D and 3D reactive Navier–Stokes numerical simulations. The energy release rate for the stoichiometric H₂–air mixture is modeled by a one-step Arrhenius kinetics. Computations show that at initial stages, the flame and flow acceleration is caused by thermal expansion of hot combustion products. At later stages, shock–flame interactions, Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instabilities, and flame–vortex interactions in obstacle wakes become responsible for the increase of the flame surface area, the energy-release rate, and, eventually, the shock strength. Computations performed for different channel widths d with the distance between obstacles d and the constant blockage ratio 0.5 reproduce the main regimes observed in experiments: choking flames, quasi-detonations, and detonations. For quasi-detonations, both the initial DDT and succeeding detonation reignitions occur when the Mach stem, created by the reflection of the leading shock from the bottom wall, collides with an obstacle. As the size of the system increases, the time to DDT and the distance to DDT increase linearly with d². We also observe an intermediate regime of fast flame propagation in which local detonations periodically appear behind the leading shock, but do not reach it.     

Phenomenological model of the unstable stage of a vacuum spark discharge

A model of the unstable stage of a spark discharge in vacuum is proposed, which describes all typical manifestations of this stage, including current spikes in the diode, an increase in the potential at the cathode flame front, collective acceleration of ions in vacuum and plasma diodes, change in the cathode erosion mechanism, and the emergence of electron microbeams with a high current density at the anode. It is shown that these processes are associated with the formation of a charged electron layer of a spatially inhomogeneous plasma at the cathode flame boundary at the unstable stage of the spark discharge in vacuum. The emergence of this layer is associated with a limited emissive ability of the plasma at the cathode flame front during its expansion in vacuum. This leads to disruption of the plasma (field-induced emission of electron from the boundary region of the flame) and the formation of a short-lived charged plasma, viz., high-density ion cluster at the cathode flame boundary. The estimates obtained using this model are in good agreement with the experimental data on physical processes at the unstable stage of a vacuum spark discharge.