On the Dynamics of Nearly-Extinguished Non-Adiabatic Cellular Flames

Abstract

We study the dynamics of a nearly-extinguished and weakly unstable non-adiabatic flame. I For simplicity ,sake, the analysis is conducted in the framework of a thermal-diffusional flame model. ' Using high activation energy techniques and bifurcillion methods, we derive a non-linear partial differential evolution equation for the changes of front shape and velocity.By solving it approximately in a particular case, we show that the spontaneously growing front corrugations, due to diffusive instability. are sufficient to prevent flame quenching: a diffusively unstable flame front can still propagate with heat-loss intensities that would quench a planar one.

The effects of radiation on the dynamic behavior of cellular premixed flames generated by intrinsic instability

“…Under the quenching condition, both Le = 0.5 and 1.0 planar flames had the same burning velocities, S r = 0.59. The calculated burning velocity of nonadiabatic flames was in agreement with the previous theoretical results [20,21].…”

“…For practical combustion devices, e.g. gas turbines, the heat loss to the surroundings of premixed flames plays a significant role in such combustion phenomena as flame instability [20,21], burning velocity, flame quenching, and so on. The heat loss due to radiation affects intrinsic instability essentially, and it is indispensable to develop the research of intrinsic instability of premixed flames in practical combustion devices.…”

Hydrodynamic Stability of Solid and Liquid Propellant Combustion

“…Since these instabilities occur on diffusive time and spatial scales, they are effectively suppressed on the hydrodynamic scales of interest here, just as hydrodynamic instabilities are suppressed in the limit of zero thermal expansion. The two types of analyses overlap in the limit of weak thermal expansion and small wavenumber (long-wave) disturbances, in which case it is usually possible to derive a nonlinear evolution equation for the motion of the flame front (cf Sivashinsky, 1983;Joulin and Sivashinsky, 1983;Margolis and Silvashinsky, 1984). There is a considerable literature on this non-hydrodynamic type of instability not only in gaseous combustion, where it is usually referred to as diffusional/thermal flame instability [see, for example, the review by Margolis and Matkowsky (1983) and the monograph by Buckmaster and Ludford (1983)], but also in condensed-phase combustion synthesis of refractory materials (cf Merzhanov et al, 1973;Matkowsky and Sivashinsky, 1978;Margolis, 1983;Margolis et al, 1985;Booty et al, 1986).…”

A Reduced Model for Flame-Flow Interaction

“…Such higherorder models have long been developed for the flames evolving in quiescent mixtures. Here, depending on the asymptotic strategy adopted, one ends up either with a single fourthorder equation for the flame-interface [4], [5] or with a system of second-order equations for the flame interface and its temperature [6], [7]. The objective of the present work is an extension of the existing higher-order models to incorporate effects due to the background flow-fields, which, to our knowledge, has not previously been undertaken.…”