Multizone combustion of condensed systems

Мержанов, А. Г.; Rumanov, É. N.; Khaikin, B. I.

doi:10.1007/bf01200543

Cited by 11 publications

(7 citation statements)

References 1 publication

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“…These patterns arise when, in certain ranges of parameters, uniformly traveling modes of propagation become unstable, and undergo a transition to self-oscillatory regimes. Such transitions have been observed in experiments for both the condensed phase and the premixed gaseous combustion [20,22]. Similar instabilities have been observed in the process of rapid solidification of thin films initiated by a laser beam (see [23]), and laser-induced evaporation of solid materials [15].…”

Section: Introductionsupporting

confidence: 60%

Finite-dimensional dynamical system modeling thermal instabilities

Frankel¹,

Kovačič²,

Roytburd³

et al. 2000

Physica D: Nonlinear Phenomena

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We describe a three-dimensional dynamical system, which is obtained as a pseudo-spectral approximation to a free boundary problem modeling solid combustion and rapid solidification, and is capable of generating its major dynamical patterns. These patterns include a Hopf bifurcation followed by a sequence of secondary period doubling and a transition to chaos, reverse sequences, and sequences followed by Shilnikov type trajectories. A computer-assisted bifurcation analysis uncovers some novel mechanisms of stability exchange. The most striking of them is an infinite period bifurcation which resembles the classical Shilnikov bifurcation, but instead of a funnel-shaped spiral along which the period is continually increasing, the continuation produced a series of isolas. Each isola is a closed branch of solutions of roughly the same period, and with the same number of oscillations. The isolas corresponding to consecutive numbers of low amplitude oscillations about the equilibrium are adjacent to each other, and appear to accumulate on a saddle-focus homoclinic connection of Shilnikov type.

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Section: Introductionsupporting

confidence: 60%

Finite-dimensional dynamical system modeling thermal instabilities

Frankel¹,

Kovačič²,

Roytburd³

et al. 2000

Physica D: Nonlinear Phenomena

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“…Earlier. oscillatory and spinning flames had been observed only in gasless combustion of condensed systems (Merzhanov et al 1973). In these systems, the diffusivity of the fuel is zero (Le = oo) and the instability region is easily reached.…”

Section: Oscillatory and Spinning Dames Analysis Of The Full Dispmentioning

confidence: 99%

Instabilities, Pattern Formation, and Turbulence in Flames

Sivashinsky¹

1983

Annu. Rev. Fluid Mech.

715

313

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“…Such propagation modes were first found experimentally [30], [44] and studied theoretically [19], [27], [28], [51], [52] in combustion, and then for polymerization processes [7], [50], [55]. The theoretical analysis of the problem usually involves the investigation of the thermal instability; however, if the reactants are in a liquid phase, the hydrodynamical perturbations can also influence the stability of the front.…”

mentioning

confidence: 99%