Front Roughening of Flames in Discrete Media

Abstract

The morphology of flame fronts propagating in reactive systems comprised of randomly positioned, point-like sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition of the Green's function for the diffusion equation, eliminating the need to use finite difference approximations. The heat released from triggered sources diffuses outward from each source, activating new sources and enabling a mechanism of flame propagation. Systems of $40000$ sources in a $200$ by $200$ two-dimensional domain were tracked using computer simulations, and statistical ensembles of $120$ realizations of each system were averaged to determine the statistical properties of the flame fronts. The reactive system of sources is parameterized by two non-dimensional values: The heat release time (normalized by interparticle diffusion time) and the ignition temperature (normalized by adiabatic flame temperature). These two parameters were systematically varied for different simulations to investigate their influence on front propagation. For sufficiently fast heat release and low ignition temperature, the front roughness (defined as the RMS deviation of the ignition temperature contour from the average flame position) grew following a power law dependence that was in excellent agreement with the KPZ universality class ($\beta =1/3$). As the reaction time was increased, lower values of the roughening exponent were observed, and at a sufficiently great value of reaction time, reversion to a steady, constant-width thermal flame was observed that matched the solution from classical combustion theory. Deviation away from KPZ scaling was also observed as the ignition temperature was increased. The features of this system that permit it to exhibit both KPZ and non-KPZ scaling are discussed.

References in corpus (4)

• Growing interfaces uncover universal fluctuations behind scale invariance
• Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium
• Effect of spatial discretization of energy on detonation wave propagation
• Influence of Discrete Sources on Detonation Propagation in a Burgers Equation Analog System

Cited by in corpus (6)

• A Quantitative Analysis of the Ignition Characteristics of Fine Iron Particles
• Carrier-phase DNS of ignition and combustion of iron particles in a turbulent mixing layer
• Dimensional scaling of flame propagation in discrete particulate clouds
• Theory of combustion in disordered media
• Thermal inertia effect of reactive sources on one-dimensional discrete combustion wave propagation
• Infection fronts in randomly varying transmission-rate media