Front roughening of flames in discrete media

Abstract

The morphology of flame fronts propagating in reactive systems composed of randomly positioned, pointlike 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 200×200 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 nondimensional 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 root mean square deviation of the ignition temperature contour from the average flame position] grew following a power-law dependence that was in excellent agreement with the Kardar-Parisi-Zhang (KPZ) universality class (β=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.

Theory of combustion in disordered media

“…Note added in proof -Additionally, a model similar to ours was used to study the dynamics of front propagation in inhomogeneous systems (see, e.g., Refs. [17,18]). These studies are carried in the region of the first-order transition, and do not investigate the nature of the transition itself.…”

Dimensional scaling of flame propagation in discrete particulate clouds

“…Further details of how the dimensionless equations are derived from the dimensional governing equations for the discrete source model can be found in Appendix A.2 and Ref. [10].…”

“…The temperature field over the entire cloud at specific times was then calculated by evaluating the analytic solution for θ(x, t) by using the solution of source ignition times over a uniform Cartesian grid (see more details in Ref. [10]). The flame speed resulting from the discrete source model was then obtained by fitting the position-ignition-time data of the sources, disregarding 50% of the particles closest to the initiation zone.…”

“…[5,6] The resulting flame propagation is thus dominated by the local heat diffusion among randomly distributed particles rather than a laminar-like reaction front, as in classical flame theory. [5][6][7][8][9][10] The flame propagation behavior identified in such systems has now been recognized as a unique branch of combustion, discrete combustion. [11] In these earlier studies, the discrete regime of flame propagation has been examined in adiabatic systems (or quasi-adiabatic systems with insignificant heat loss).…”

Modelled fracture and calving on the Totten Ice Shelf

“…The KPZ equation has been extensively used to describe, for example, slow combustion fronts or the growth bacterial colonies (e.g. Bonachela et al, 2011;Lam et al, 2017). The 1 dimensional KPZ equation reads: 5…”