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Laminar premixed flame extinction limits. II Combined effects of stretch and radiative loss in the single flame unburnt-to-burnt and the twin-flame unburnt-to-unburnt opposed flow configurations

Numerical methods have been used to examine the effects of (a) stretch alone, and (b) a combination of stretch and radiative loss, on the properties and extinction limits of methane–air flames near the lean flammability limit. Two axisymmetric opposed flow configurations were examined: (i) a single flame, unburnt-to-burnt (UTB) system in which fresh reactant is opposed by a stream of its own combustion products at the unburnt temperature, and (ii) a symmetric unburnt-to-unburnt (UTU) configuration where twin flames are supported back to back, one on each side of the stagnation plane. The maximum temperatures achieved in the UTB system are always away from the stagnation plane. For a fixed sufficiently sub-adiabatic product stream temperature, increasing flame stretch or gaseous radiative emissivity, or a combination of both, will augment downstream conductive heat loss, leading to a reduction in Tmax and eventually to an abrupt extinction if the loss rate is sufficiently large. The UTU system is more complex, and offers the additional possibility of purely stretch-induced extinctions where the flames are forced together back-to-back so that radiative loss is restricted to upstream of the maximum temperature. Extinction in these cases occurs by straightforward truncation of the hot sides of the reaction zones. At sufficiently low stretch, near and at the standard flammability limit, radiative loss makes a major contribution to the overall extinction mechanism in both configurations. The detailed effects of flame stretch on extinction behaviour depend on the diffusion characteristics within the near-limit mixtures, in particular the Lewis number, Le, of the deficient component. The effect of high stretch is always to attenuate the composition range of flammability. However, for Le<1 this range is extended at low to moderate stretch, particularly in the UTU situations where downstream radiative loss is not present at extinction. Lewis number effects for a global methane–air chemistry, and with assumed Le≥1, are discussed in the light of numerical results previously presented by Ju et al. (Ju et al. 1998 Combust. Flame 113, 603–614).