Related papers: Simple Model of Propagating Flame Pulsations
We introduce a simple mathematical model for bushfires accounting for temperature diffusion in the presence of a combustion term which is activated above a given ignition state. The model also takes into consideration the effect of the…
In this paper we investigate the acceleration of the expansion of premixed spherical flames and evolution of the cellular patterns on their surfaces. An asymptotic model is used for the simulations and a spectral numerical algorithm is…
Flame propagation through a non-volatile solid-fuel suspension is studied using a simplified, time-dependent numerical model that considers the influence of both diffusional and kinetic rates on the particle combustion process. It is…
We extend a low Mach number hydrodynamics method developed for terrestrial combustion, to the study of thermonuclear flames in Type Ia supernovae. We discuss the differences between 2-D and 3-D Rayleigh-Taylor unstable flame simulations,…
We consider flame front propagation in channel geometries. The steady state solution in this problem is space dependent, and therefore the linear stability analysis is described by a partial integro-differential equation with a space…
A simple, semi-analytic representation is developed for nuclear burning in Type Ia supernovae in the special case where turbulent eddies completely disrupt the flame. The speed and width of the ``distributed'' flame front are derived. For…
We present a statistical model which shows the influence of turbulence on a thermonuclear flame propagating in C+O white dwarf matter. Based on a Monte Carlo description of turbulence, it provides a method for investigating the physics in…
We consider the competition of the different physical processes that can affect the evolution of a flame bubble in a Type Ia supernovae -- burning, turbulence and buoyancy. Even in the vigorously turbulent conditions of a convecting white…
Planar flames are intrinsically unstable in open domains due to the thermal expansion across the burning front--the Landau-Darrieus instability. This instability leads to wrinkling and growth of the flame surface, and corresponding…
The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity-free. Flames confined in channels with…
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…
In previous studies, we examined turbulence-flame interactions in carbon-burning thermonuclear flames in Type Ia supernovae. In this study, we consider turbulence-flame interactions in the trailing oxygen flames. The two aims of the paper…
We provide a mathematical analysis of a thermo-diffusive combustion model of lean spray flames, for which we prove the existence of travelling waves. In the high activation energy singular limit we show the existence of two distinct…
We continue to investigate two-dimensional laterally propagating flames in type I X-ray bursts using fully compressible hydrodynamics simulations. In the current study we relax previous approximations where we artificially boosted the…
The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate…
This paper presents a numerical investigation into the phenomenon of flame spread over thin circular ducts in normal gravity and microgravity environments. Flame spread over such geometry is of significant interest due to its relevance in…
In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…
In the present work, the discrete flame model [1] is augmented by introducing the thermal inertia of particles in the preheating zone. The effect of particle thermal inertia on flame speed, propagation limits, and near-limits dynamics of…
Critically understanding the `standard candle'-like behavior of Type Ia supernovae requires understanding their explosion mechanism. One family of models for Type Ia Supernovae begins with a deflagration in a Carbon-Oxygen white dwarf which…
The application of Type Ia supernovae (SNe Ia) as distance indicators in cosmology calls for a sound understanding of these objects. Recent years have seen a brisk development of astrophysical models which explain SNe Ia as thermonuclear…