A mathematical model of the cool-flame oxidation of acetaldehyde

Abstract

A detailed mathematical model of the non-isothermal oxidation of acetaldehyde has been found to give a realistic simulation of (i) single and multiple cool flames, their limits, amplitudes and induction periods; (ii) two-stage ignition; and (iii) the negative temperature coefficient for the maximum rate of slow combustion. A simplified form of the model, valid over a limited range of conditions, has been subjected to mathematical analysis to provide interpretations of the effects simulated by the detailed model. It is concluded that cool flames are thermokinetic effects often, but not exclusively, of an oscillatory nature, and that a satisfactory account of cool-flame phenomena must necessarily take reactant consumption into account.

An experimental and kinetic modeling study of the pyrolysis and oxidation of n-C3C5 aldehydes in shock tubes

“…Dating back to the early 1970s Halstead et al [36] discussed cool flames phenomena and low-temperature oxidation. Oscillatory ignitions in the low-temperature regime were studied in the early 80s by Gray and co-workers [37], and in the 90s by Cavanagh [38] and by Di Maio et al [39].…”

Thermokinetic Oscillations in Gaseous Systems

“…Their treatment offered important insights, but was not an explicit development. That came in 1969 from Yang and Gray [ll] and in 1971 from Halstead, Prothero, and Quinn [17].…”

“…Skeleton schemes are all very well, but they always generate the desire for more particular identificationsof intermediates and of velocity constants, etc. In 1971, Halstead, Prothero, and Quinn [17] put forward a detailed mechanism involving 14 elementary steps for cool-flame oxidation of acetaldehyde. They based their scheme on Blanchard's work, identifying peracetic acid (PA) as the key chain-branching agent.…”

“…Their results are striking. With very little massaging of uncertain kinetic parameters they model the major features of low temperature oxidation and cool flames up to the hot ignition boundary, and in a subsequent (1973) paper [17], they accommodated this. Perhaps their model overestimates the richness of behaviour observable in a closed vessel, but if it is regarded more as the first realistic model for the whole hydrocarbon family than as the last word on acetaldehyde, its achievement is most encouraging.…”

A comparison of Galerkin, collocation and the method of lines for partial differential equations

“…Since the system of ordinary differential equations that results from the method of lines can be written immediately in the form iu = f (a) (4) this approach is often used in situations where methods for this standard form are readily available. The first difficulty with the finite element methods is that none of the integrators are designed to deal with systems of the form…”