Theory of combustion in disordered media

Schiulaz, Mauro; Laumann, Chris R.; Balatsky, Alexander V.; Spivak, B.

doi:10.1103/physreve.97.062133

Cited by 6 publications

(2 citation statements)

References 15 publications

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“…For a diffusion-controlled scalar field, such as fuel particulates in gas, the accumulated heat at the front from previously ignited sources may make flames in these systems not amenable to classical percolation theory. The transition to percolation behavior by limitation of the long-range accumulation of heat sources via introduction of a loss term was recently explored [27,28].…”

Section: Experimental Observation Of Discrete Percolating Flames and ...mentioning

confidence: 99%

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

et al. 2020

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Section: Experimental Observation Of Discrete Percolating Flames and ...mentioning

confidence: 99%

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

et al. 2020

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“…[16] As recently shown by Schiulaz et al, site-bond percolation theory is applicable to a system wherein strong volumetric heat loss is present so that the heat contribution to ignite a source is limited within its closest neighbors. [17,18] It is rather clear that a simple site-bond percolation theory is inadequate to describe the current results of flame propagation in a highly discrete regime. As shown by Grinchuk and Rabinovich, a modified percolation model that considers heating from previously ignited, non-adjacent sources better agrees with their simulation results of flame propagation in a heterogeneous medium.…”

Section: 2mentioning

confidence: 99%

Dimensional scaling of flame propagation in discrete particulate clouds

Lam

Higgins

2019

Combustion Theory and Modelling

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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.

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