Theory of Combustion in Laminar Flows

Flame balls with thermally sensitive intermediate kinetics

“…It is worth noting that, for large values of β, either equation (8) or the relation β 2 k(T ) = 1 can be used to show that the dimensionless value of the crossover temperature is given by T ∼ 1 − 2β −1 ln β.…”

“…A paradigm in combustion theory, that has dominated the modelling and study of flames from a theoretical and analytical perspective, is the use of a one-step model to describe the chemistry [1][2][3][4][5][6][7][8][9][10][11][12][13], such as with an Arrhenius 'rate constant' k = Ae −T A /T . In these model reaction schemes, the fuel F is considered to produce the product P (with the intervention of an oxidant O 2 in the second example) through a single elementary chemical step.…”

“…References for all the achievements of the one-step model are far too numerous to cite here; the reader can find many suitable citations in texts and review articles on combustion theory and in recent articles on the subject, e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

“…Numerous asymptotic as well as numerical studies based on one-step models of the type (1) have demonstrated this very clearly [1][2][3][4][5][6][7][8][9][10][11][12][13]. For example, the reason why stable flame balls must be non-adiabatic with a lean fuel having a low Lewis number was demonstrated in this way [29,30].…”

The hydrogen–air burning rate near the lean flammability limit

“…first published by Fendell [12]; see Williams [13]. The resulting solution is plotted for completeness in Figure 4.…”