On the Dynamics of Equations Describing Gasless Combustion in Condensed Systems

Dimitriou, Pavlos; Puszynski, Jan A.; Hlaváček, Vladimír

doi:10.1080/00102208908924071

Cited by 42 publications

(17 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is also observed that sufficiently far from the stability threshold the oscillations may undergo period doubling. A similar effect has been recently reported for gasless systems where a whole sequence of period doublings was found (Dimitriou et al, 1989;Bayliss and Matkowsky, 1990). Note that in contrast to the premixed gas flames in gasless systems where Le = co, the flame speed -R, is always positive (Matkowsky and Sivashinsky, 1978).…”

Section: Introductionsupporting

confidence: 60%

Negative Burning Speed in Oscillatory Premixed Gas Combustion

Brailovsky

Sivashinsky

1993

Combustion Science and Technology

View full text Add to dashboard Cite

show abstract

Section: Introductionsupporting

confidence: 60%

Negative Burning Speed in Oscillatory Premixed Gas Combustion

Brailovsky

Sivashinsky

1993

Combustion Science and Technology

View full text Add to dashboard Cite

show abstract

“…We note that chaotic and quasi-periodic combustion had previously been found for diffusional thermal instabilities in the cellular regime either from long wavelength approximations leading to the Kuramoto-Sivashinsky equation (Hyman and Nicolaenko, 1986;Michelson and Sivashinsky, 1977 or directly from the equations of the diffusional thermal model (Bayliss and Matkowsky, 1992). Chaotic dynamics, including a transition to chaos via successive period doublings, has also been found in condensed phase combustion Dimitrou, Puszynski and Hlavacek, 1989). In this paper we demonstrate that apparently chaotic combustion can occur for gaseous combustion near the extinction point when the full interaction between the flow field and the transport processes is taken into account and that this transition is unrelated to the formation of cells.…”

Section: Introductionmentioning

confidence: 95%

Pulsating and Chaotic Dynamics near the Extinction Limit

Bayliss

Leaf²,

Matkowsky³

1992

GCST

View full text Add to dashboard Cite

We numerically solve the problem of a premixed flame in the region between two concentric cylinders, in which the combustible mixture is fed in through the inner cylinder, and combustion products are removed through the outer cylinder and through the sides. We employ a model which accounts for the full coupling between fluid and transport elfects and chemical reactions. The model accounts for heat loss through both the outer and inner cylindrical walls. We find thai as heal loss is increased or as the inflow velocity is decreased, a transition from stationary to pulsating combustion occurs prior to extinction. For certain parameter ranges a transition to apparently chaotic dynamics occurs via a period doubling cascade.

show abstract

“…All the models discussed in this literature review exhibit the same spectrum of dynamics as experiments. Specifically, we refer to computed solutions of (i) the reaction-diffusion system governed by the full Arrhenius kinetics (e.g., [5]), (ii) the reaction-diffusion system with Arrhenius kinetics with a cutoff (e.g., [1]), and models that use point-source kinetics like (iii) the free-interface ("two-sided") model with constant heat diffusivity (e.g., [9]), as well as (iv) the freeboundary ("one-sided") model, in which heat transfer behind the flame front (in the burned matter) is qualitatively unimportant (e.g., [9]). Simulations on all these models show the same dynamical behaviors as one pushes the bifurcation parameters deeper into the instability regions.…”

Section: Introductionmentioning

confidence: 99%

Weakly Nonlinear and Numerical Analyses of Dynamics in a Solid Combustion Model

Gross

Yu²

2005

SIAM J. Appl. Math.

View full text Add to dashboard Cite

Abstract. This paper contains qualitative and quantitative comparisons between a weakly nonlinear analysis and direct numerical simulations of a free-boundary problem. The former involves modulating the most linearly unstable mode, taking a small perturbation of the neutrally stable value νc of a parameter ν related to the activation energy. Analogously, we perform the direct numerical computations near the marginally unstable value, namely, ν = νc − 2 , where is rather small.We delineate the role of a different parameter σ (related to the Arrhenius kinetics) in the combustion dynamics when ν = νc − 2 . In particular, the numerics show that varying σ produces a period-doubling scenario when lies approximately between 0.08 and 0.12. We describe the σ intervals within which complex dynamics occur for various values of and for ν fixed at νc − 2 . When drops to approximately 0.06, the asymptotic and numerical solutions agree well for all physical values of σ.

show abstract

On the Dynamics of Equations Describing Gasless Combustion in Condensed Systems

Cited by 42 publications

References 11 publications

Negative Burning Speed in Oscillatory Premixed Gas Combustion

Negative Burning Speed in Oscillatory Premixed Gas Combustion

Pulsating and Chaotic Dynamics near the Extinction Limit

Weakly Nonlinear and Numerical Analyses of Dynamics in a Solid Combustion Model

Contact Info

Product

Resources

About