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The effects of flame stretch as well as that of thermal and molecular diffusion on the scenario of flame acceleration in channels are quantified by means of computational and analytical endeavors. The analytical formulation incorporates the internal transport flame properties into the theory of flame acceleration due to wall friction by means of the Markstein number, which characterizes the flame response to curvature and stretch. Being a positive or negative quantity and a function of the thermal-chemical combustion parameters, such as the thermal expansion ratio as well as the Lewis and Zeldovich numbers, the Markstein number either moderates or promotes flame acceleration. While the Markstein number may provide a substantial impact on the flame acceleration rate in narrow channels, this effect diminishes with increase in the channel width. The analytical formulation is accompanied by extensive computational simulations of the reacting flow equations, which clarify the impact of the Lewis number on flame acceleration. It is noted that for Lewis numbers below a certain critical value, at the initial stage of flame acceleration, a globally convex flame front splits into two or more finger-like segments, accompanied by a drastic increase in the flame front surface area and associated enhancement of flame acceleration. Later, however, these segments of the flame front meet, promptly consuming cavities and pockets, which substantially decreases the flame surface area and moderates acceleration. Eventually, this dynamics results in a single, globally convex flame, which keeps accelerating. Overall, the thermal-diffusive effects substantially facilitate flame acceleration, thereby advancing a potential deflagration-to-detonation transition.

Propagation of a premixed flame from a closed to an open end in micro-channels with smooth non-slip isothermal walls is considered in the context of flame extinction dynamics. Powerful exponential flame acceleration in micro-channels with adiabatic walls has been demonstrated at the initial quasi-isobaric stage of the process [Bychkov et al., Phys. Rev. E 72, 046307 (2005)]. In contrast to the previous studies, here we investigate flame propagation in channels with isothermal walls. The problem is solved by means of high-fidelity laminar numerical simulations of the complete set of the Navier–Stokes combustion equations. For most of the problem parameter sets chosen, we obtain initial flame acceleration after ignition at the closed channel end. This acceleration resembles qualitatively the adiabatic case, but it develops noticeably slower, in an approximately linear regime instead of the exponential one and persists only for a limited time interval. Subsequently, heat loss to the walls reduces the temperature and hence the volume of the burnt gas behind the flame front, which produces a reverse flow in the direction of the closed channel end. When the amount of the burnt gas becomes sufficiently large, the reverse flow stops the acceleration process and drives the flame backwards with modifications of the flame front shape from convex to concave. Eventually, the flame extinguishes. Qualitatively, the process obtained reproduces a possible combustion failure during deflagration-to-detonation transition observed in previous experiments. We investigate the key characteristics of initial flame acceleration such as the acceleration rate and the maximum speed of the flame tip.

While flame propagation through obstacles is often associated with turbulence and/or shocks, Bychkov et al. [V. Bychkov et al., Phys. Rev. Lett. 101, 164501 (2008)] have revealed a shockless, conceptually laminar mechanism of extremely fast flame acceleration in semiopen obstructed pipes (one end of a pipe is closed; a flame is ignited at the closed end and propagates towards the open one). The acceleration is devoted to a powerful jet flow produced by delayed combustion in the spaces between the obstacles, with turbulence playing only a supplementary role in this process. In the present work, this formulation is extended to pipes with both ends open in order to describe the recent experiments and modeling by Yanez et al. [J. Yanez et al., arXiv: 1208.6453] as well as the simulations by Middha and Hansen [P. Middha and O. R. Hansen, Process Safety Prog. 27, 192 (2008)]. It is demonstrated that flames accelerate strongly in open or vented obstructed pipes and the acceleration mechanism is similar to that in semiopen ones (shockless and laminar), although acceleration is weaker in open pipes. Starting with an inviscid approximation, we subsequently incorporate hydraulic resistance (viscous forces) into the analysis for the sake of comparing its role to that of a jet flow driving acceleration. It is shown that hydraulic resistance is actually not required to drive flame acceleration. In contrast, this is a supplementary effect, which moderates acceleration. On the other hand, viscous forces are nevertheless an important effect because they are responsible for the initial delay occurring before the flame acceleration onset, which is observed in the experiments and simulations. Accounting for this effect provides good agreement between the experiments, modeling, and the present theory.

We extend the existing theoretical model for determining the characteristic features of magnetic deflagration in nanomagnet crystals. For the first time, all energy levels are accounted for calculation of the the Zeeman energy, the deflagration velocity, and other parameters. It reduces the final temperature and significantly changes the propagation velocity of the spin-flipping front. We also consider the effect of a strong transverse magnetic field, and show that the latter significantly modifies the spin-state structure, leading to an uncertainty concerning the activation energy of the spin flipping. Our front velocity prediction for a crystal of Mn-12 acetate in a longitudinal magnetic field is in much better agreement with experimental data than the previous reduced-model results.

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.

To reveal the inner mechanism of gas explosion, the entire scenario of premixed flame front evolution within an accidental fire is prescribed. Specifically, "finger" flame shape, which is one of the key stages of flame evolution, is scrutinized with the situation of a methane-air explosion. A transition from a globally -spherical front to a finger-shaped one occurs when a flame starts approaching the passage walls. While this acceleration is extremely strong, it stops as soon as the flame touches the passage wall. This mechanism is Reynolds-independent; being equally relevant to micro channels and giant tunnels. The flame speed increases by an order of magnitude during this stage. To implement dusty environments, Seshadri formulation for the planar flame [Combustion and Flame 89 (7992) 333] is employed with a non-uniform distribution of inert dust gradients, specifically, linear, parabolic and hyperbolic spatial dust distribution gradients are incorporated into the "finger" flame shape. This study systematically investigates how the noncombustible dust distributions affect fire evolution, the flame shape, and propagation velocity.

The magnetic instability at the front of the spin avalanche in a crystal of molecular magnets is considered. This phenomenon reveals similar features with the Darrieus-Landau instability, inherent to classical combustion flame fronts. The instability growth rate and the cutoff wavelength are investigated with respect to the strength of the external magnetic field, both analytically in the limit of an infinitely thin front and numerically for finite-width fronts. The presence of quantum tunneling resonances is shown to increase the growth rate significantly, which may lead to a possible transition from deflagration to detonation regimes. Different orientations of the crystal easy axis are shown to exhibit opposite stability properties. In addition, we suggest experimental conditions that could evidence the instability and its influence on the magnetic deflagration velocity.

A conceptually laminar mechanism of extremely fast flame acceleration in obstructed channels, identified by Bychkov et al. ["Physical mechanism of ultrafast flame acceleration," Phys. Rev. Lett. 101, 164501 (2008)], is further studied by means of analytical endeavors and computational simulations of compressible hydrodynamic and combustion equations. Specifically, it is shown how the obstacles length, distance between the obstacles, channel width, and thermal boundary conditions at the walls modify flamepropagation through a comb-shaped array of parallel thin obstacles. Adiabatic and isothermal (cold and preheated) side walls are considered, obtaining minor difference between these cases, which opposes the unobstructed channel case, where adiabatic and isothermal walls provide qualitatively different regimes offlame propagation. Variations of the obstructed channel width also provide a minor influence on flamepropagation, justifying a scale-invariant nature of this acceleration mechanism. In contrast, the spacing between obstacles has a significant role, although it is weaker than that of the blockage ratio (defined as the fraction of the channel blocked by obstacles), which is the key parameter of the problem. Evolution of the burning velocity and the dependence of the flame acceleration rate on the blockage ratio are quantified. The critical blockage ratio, providing the limitations for the acceleration mechanism in channels with comb-shaped obstacles array, is found analytically and numerically, with good agreement between both approaches. Additionally, this comb-shaped obstacles-driven acceleration is compared to finger flameacceleration and to that produced by wall friction.

Flame dynamics in micro-pipes have been observed to be strongly affected by the wall boundary conditions. In this respect, two mechanisms of flame acceleration are related to the momentum transferred in these regions: 1) that associated with flame stretching produced by wall friction forces; and 2) when obstacles are placed at the walls, as a result of the delayed burning occurring between them, a jet-flow is formed, intensively promoting the flame spreading. Wall thermal conditions have usually been neglected, thus restricting the cases to adiabatic wall conditions. In contrast, in the present work, the effect of the boundary conditions on the flame propagation dynamics is investigated, computationally, with the effect of wall heat losses included in the consideration. In addition, the powerful flame acceleration attained in obstructed pipes is studied in relation to the obstacle size, which determines how different this mechanism is from the wall friction. A parametric study of two-dimensional (2D) channels and cylindrical tubes, of various radiuses, with one end open is performed. The walls are subjected to slip and non-slip, adiabatic and constant temperature conditions, with different fuel mixtures described by varying the thermal expansion coefficients. Results demonstrate that higher wall temperatures promote slower propagation as they reduce the thermal expansion rate, as a result of the post-cooling of the burn matter. In turn, smaller obstacle sizes generate weaker flame acceleration, although the mechanism is noticed to be stronger than the wall friction-driven, even for the smaller sizes considered.

A shockless, conceptually-laminar formulation on extremely fast flame acceleration in semi-open obstructed pipes [Physical Review Letters 101 (2008) 164501; Combust. Flame 157 (2010) 1012], Refs. [8-9] is extended to pipes with both ends open/vented. The acceleration is devoted to a powerful jet-flow produced by delayed combustion in the pockets between the obstacles, and it leads to a prompt deflagration-to-detonation transition event. Starting with inviscid approximation, the analysis subsequently incorporates the viscous forces (hydraulic resistance). The theory is validated by the recent experiments [http://arxiv.org/abs/1208.6453], Ref. [11]. It is shown that hydraulic resistance is not required to drive the flame acceleration. In contrast, this is a supplementary effect, which actually moderates the acceleration rate. On the other hand, hydraulic resistance plays an important role: it is responsible for the initial delay, before the flame acceleration onset, observed in the experiments. It is demonstrated that flames accelerate strongly in open/vented obstructed pipes, and the acceleration mechanism is qualitatively the same as that in the semi-open ones. However, because of the flame-generated flow distributed upward and downward of the flame front, the acceleration rate in open pipes is noticeably less than that in the semi-open ones.