Pulsating and Chaotic Dynamics near the Extinction Limit

Abstract

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.

Adaptive numerical simulation of pulsating planar flames for large Lewis and Zeldovich ranges

“…7, right side). These pulsating flames and their transition to chaos have also been observed in previous numerical simulations [16,1].…”

Low Mach Number Modeling of Type I X‐Ray Burst Deflagrations

“…Other approaches (e.g., Majda & Sethian 1985;Bayliss et al 1992) solve the energy equation, employing the continuity equation as a constraint. We adopt the latter approach.…”

“…However, at present only the LMNA can successfully model the compressibility effects and significant lateral fluctuations in temperature and density that characterize deflagrations, as well as offer substantial increases in time step and avoid acoustic boundary complications. While the LMNA is routinely used to model terrestrial combustion (e.g., Bayliss et al 1992;McGrattan et al 2004), only recently have efforts begun to adapt it to the astrophysical setting. Alternative astrophysical LMNA models have been recently developed by Bell et al (2004a) and Almgren et al (2006aAlmgren et al ( , 2006b.…”

Orbital instability and prediction of a Bunsen flame tip motion with burner rotation

“…Recently several experimental and numerical studies have been conducted to study chaotic flame motions which arise in Bunsen flames subjected to acoustic forcing [1], pulse combustion [2], engine combustion [3], cellular flames [4], flame extinction [5][6][7], and soot formation [8]. These studies apply linear analysis and fast Fourier transforms (FFT); they also apply methods based on the deterministic chaos theory.…”