Irina Brailovsky

Hydraulic resistance as a mechanism for deflagration-to-detonation transition

A one-dimensional model for premixed gas combustion in a rough tube (or in an inert porous matrix) accounting for the hydraulic resistance and molecular transport is considered. It is shown that the hydraulic resistance causes a gradual precompression and preheating of the unburned gas adjacent to the advancing deflagration which leads (after an extended induction period) to a localized thermal explosion triggering an abrupt transition from deflagration to detonation. The paper is an extension of a previous study of the problem, based on a reaction-diffusion-acoustics model, over a fully nonlinear formulation allowing for steepening of compression waves and formation of the shocks.

On combustion waves driven by diffusion of pressure

In gas filled porous media the local elevation of pressure slowly diffuses to the adjacent layers of gas inducing the rise in temperature there. In the case of explosive gases this mechanism may lead to the formation of a self-sustaining combustion wave propagating at a constant speed. It is argued that the barodiffusion may be responsible for the occurrence of the so-called high velocity regime often observed in filtration combustion It is shown that the high velocity regime may emanate from the low velocity regime controlled by the sysiems thermal diffusivity. It is suggested that the effect may be related to the classical problem of deflagration-to-detonation transition in narrow pipes.

Momentum loss as a mechanism for deflagration-to-detonation transition

A reduced model for premixed gas filtration combustion where the nonlinear effects are discarded everywhere but in the reaction rate term and where the only accounted for effect of the porous medium is its resistance to the gas flow is explored. While ruling out formation of shock waves the model appears rich enough to cover detonation-like phenomenon with barodiffusion acting as a driving agency. It is shown that depending on the initial conditions this creeping detonation mode is evoked either immediately or emerges after some time delay as a product of an abrupt transition from the low-velocity deflagration. The transition is triggered by a localized thermal explosion in the extended (friction-induced) preheat zone gradually formed ahead of the advancing deflagration.

Galloping and spinning modes of subsonic detonation

A reduced model for a pressure-driven subsonic combustion wave spreading through an inert porous medium (subsonic detonation) is derived. It is shown that the associated planar travelling wave solution may lose its stability assuming a galloping or spinning structure as occurs in supersonic free-space detonation. The problem of subsonic detonation is found to be dynamically akin to the problem of gasless combustion known for its rich pattern-forming dynamics.

Effects of momentum and heat losses on the multiplicity of detonation regimes

Abstract Employing Zeldovich’s (1940) quasi-one-dimensional formulation the multiplicity of detonation regimes occasionally observed in obstacle-laden systems is explored. The paper is an extension of the previously studied adiabatic version of the problem where, in addition to the well-known sub-CJ quasi-detonation, the low-speed supersonic as well as subsonic detonation regimes were identified. It is shown that the hysteresic loop associated with non-uniqueness of detonation regimes may be located entirely within the supersonic domain, the situation often encountered in experiments. By adopting a one-step bimolecular kinetics the well known dependency of the transition on the initial pressure is explained. The incorporation of heat losses, apart from bringing up detonability limits, strongly affects the low-speed regimes. The latter are found to occur only in the systems where the Reynolds analogy is strongly violated (rough tubes, porous media), and do not arise in smooth-walled tubes. The disparity between detonability and flammability limits is discussed.

Combustion waves in hydraulically resisted systems

The effects of hydraulic resistance on the burning of confined/obstacle-laden gaseous and gas-permeable solid explosives are discussed on the basis of recent research. Hydraulic resistance is found to induce a new powerful mechanism for the reaction spread (diffusion of pressure) allowing for both fast subsonic as well as supersonic propagation. Hydraulic resistance appears to be of relevance also for the multiplicity of detonation regimes as well as for the transitions from slow conductive to fast convective, choked or detonative burning. A quasi-one-dimensional Fanno-type model for premixed gas combustion in an obstructed channel open at the ignition end is discussed. It is shown that, similar to the closed-end case studied earlier, the hydraulic resistance causes a gradual precompression and preheating of the unburned gas adjacent to the advancing deflagration, which leads (after an extended induction period) to a localized autoignition that triggers an abrupt transition from deflagrative to detonative combustion. In line with the experimental observations, the ignition at the open end greatly encumbers the transition (compared with the closed-end case), and the deflagration practically does not accelerate up to the very transition point. Shchelkins effect, that ignition at a small distance from the closed end of a tube facilitates the transition, is described.

On stationary and travelling flame balls

The current work discusses a tractable one-dimensional model describing the relation between stationary and propagating flame balls that have recently been identified in direct numerical simulations of near-limit low-Lewis-number premixed flames.

On Deflagration-to-Detonation Transition

Abstract A reduced model for the reactive gas flow in a tube is proposed, where the nonlinear effects are discarded everywhere but in the reaction rate term. While ruling out the formation of shock-waves the model transpires to be rich enough to cover detonation-like phenomena with the sound waves acting as a driving agency. It is shown that depending on the ignition conditions, the detonation wave is evoked either immediately or gradually emanates from the low velocity deflagration by virtue of friction between the burning gas and the tube walls. At sufficiently strong friction the normal near-sonic detonation is found to undergo a hysteresic transition to a low speed quasi-detonation dominated by dissipative effects.

On Hydrodynamic Instability of Stretched Flames

Abstract The recent result on the diffusive instability of a planar premixed gas flame sustained in the stagnation-point flow are carried over on the hydrodynamic (Darrieus-Landau) instability. Similar to the former case the planar flame of the infinite aspect length-scale is unconditionally stable for any flow induced stretch however small. Yet in finite geometries occuring in numerical and laboratory experiments the flame may well become unstable provided the imposed stretch is weak enough. It is argued that the effect may be related to the formation of a non-steady multiple cusp structure often observed in large-scale flames.

On quenching of the reaction wave moving through spatially periodic shear flow

Abstract Abstract–A one-dimensional model describing a self-sustaining reaction wave moving through a unidirectional periodic flow field is proposed and studied numerically. In the case of zero diffusivity of the deficient reactant the reaction wave undergoes partial extinction, as a result of which a considerable portion of the original premixture remains unconsumed. For long-wavelength fields within a certain range of the flow intensities the system exhibits a peculiar nonuniqueness of possible propagation regimes. The transition from one regime to another occurs in a manner of hysteresis.