Pattern formation in 2D continuum and discrete chemically reactive media

The spatio-temporal instabilities of a solid-gas combustion front and its resulting pattern formation are examined in the framework of thermal-mass diffusional instabilities, in the case of homogenous and heterogeneous media. In our numerical simulations, by employing a novel adaptive mesh refinement algorithm, we achieve experimentally relevant system sizes. To our knowledge, this is the first work where these methods are applied to a new class of solid-gas combustion models.We introduce a unified mathematical model called “master model” to describe the combustion of metal fuel particles in an oxidizer gas, based on the physical parameters of the problem (i.e. order of the chemical reaction (n = 0, 1), the ignition temperature Tign, and the Lewis number Le, defined as the ratio of thermal to mass diffusivity), and for different limits of oxidizer mass diffusivity, with continuous and random reactant fuel distributions.Our numerical findings for a combustion front in the continuum limit show that a front develops a cellular structure for a specific ignition temperature Tign, and below a critical Lewis number Lec. The linear regime of these morphologies is investigated numerically and found to agree well with the dispersion relation predicted analytically by Brailovsky et al.. The effect of system size and Lewis number on the linear regime were also addressed. For Lewis numbers Le close to the critical value Lec, the transition from linear to non-linear (i.e. late time) is prolonged. This regime is characterized by the appearance of shallow-cell structures, and those morphologies can be described qualitatively based on the growth modes available in the linear regime. For this reason, this regime is called “quasi-linear” regime. By lowering the Lewis number values below Le~0.4, the morphology of the front changes significantly and becomes complex, featuring non-symmetric deep cells and overhangs. The dendritic patterns simulated in this work are similar to those observed in experiments of flame propagation over a bed of nano-aluminum powder burning with a counter-flowing oxidizer conducted by Malchi et al.We further studied the linear regime of cellular combustion fronts under heat dissipation conditions. Our numerical results show that the growth rate of high k modes, in the presence of heat dissipation, can effectively be described by the same modes as in the adiabatic condition, but with their amplification rate increased. The dynamics of a combustion front propagating in random media, assuming zero-order kinetics n=0 and for a small Lewis number Le=0.3, were also studied numerically. These numerical findings suggest that the destabilizing effect of the random medium, is qualitatively analogous to lowering the Lewis number in the continuum limit. It leads to an increased stability range of modes and an increased growth rate. The late-time dynamics of cellular pattern formation in random media is also investigated. The results indicate that for both uniform and non-uniform random particle distributions, modifying the area fraction of the medium occupied by metal particles (denoted by s) alters the cell depth (i.e. max-to-min distance of cells). On the other hand, changing the number density Ns reshapes the morphology. Our numerical analysis for the effect of the Lewis number on the late-time dynamics show that even in the long run, the effect of a random distribution of particles is analogous to low-Lewis numbers in the continuum limit.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.