Dimensional scaling of flame propagation in discrete particulate clouds

Abstract

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 sources are not resolved and the heat release is assumed spatially uniform, is solved via conventional finite difference techniques. Second, a discrete source model, wherein the heat diffusion from individual sources is modeled via superposition of the Green's function of each source, is employed to examine the influence of the random, discrete nature of the media. Heat transfer to cold, isothermal walls and to a layer of inert gas surrounding the reactive medium are considered as the loss mechanisms. Both cylindrical and rectangular (slab) geometries of the reactive medium are considered, and the flame speed is measured as a function of the diameter and thickness of the domains, respectively. In the continuum model with inert gas confinement, a universal scaling of critical diameter to critical thickness near 2:1 is found. In the discrete source model, as the time scale of heat release of the sources is made small compared to the interparticle diffusion time, the geometric scaling between cylinders and slabs exhibits values greater than 2:1. The ability of the flame in the discrete regime to propagate in thinner slabs than predicted by continuum scaling is attributed to the flame being able to exploit local fluctuations in concentration across the slab to sustain propagation. As the heat release time of the sources is increased, the discrete source model reverts back to results consistent with the continuum model. Implications of these results for experiments are discussed.

Percolating Reaction–Diffusion Waves (PERWAVES)—Sounding rocket combustion experiments

“…1) that are described by the same power law exponent of 𝛽 = 1∕3 found in the KPZ universality class [14]. • For discrete flames in channels or cylinders with heat losses to the surroundings, the flames exhibit anomalous dimensional scaling in comparison to the classical value found for continuum flames [15].…”

Numerical simulation of the heterogeneous combustion of dust clouds containing polydisperse porous iron particles

“…For example, Lee and Stewart [14] developed a numerical model to investigate the combustion of metallic particles with a focus on the non-equilibrium behavior of reactions and phase change. Lam et al [15] developed a discrete numerical model to explore the combustion of heterogeneous mixtures. Their models, however, did not account for the effects of heat transfer via radiation and polydispersity through particle size distribution.…”