Laminar flame propagation/quench for a parallel-wall duct

Abstract

Steady laminar isobaric two-dimensional propagation of a fuel-lean large-activation-temperature premixed flame between plane parallel (isothermal noncatalytic) walls is examined theoretically. A Shvab-Zeldovich engineering-type formulation, with a treatment of convective transport of species and heat in the manner of Oseen, is integrated numerically by quasilinearization/alternating-direction-implicit techniques. Of particular interest in this transcendentally nonlinear elliptical (convective-diffusive-reactive) boundary-value problem is how the flame speed (an eigenvalue) decreases as the wall separation decreases, for different wall temperatures. At a finite wall separation the quenching distance is achieved, such that the flame speed goes abruptly to zero; this critical quenching distance is found to be smaller for hotter walls. This investigation seeks to lend credibility of principle to one possible strategy for reducing the level of unburned-hydrocarbon species exhausted from Otto-cycle-type cylinders. The primary source for hydrocarbon emissions is now generally acknowledged to be the failure of flame to propagate into the narrow piston crevice owing to heat loss to cold walls. Higher wall temperature at the piston crown and rings would seem to abet flame propagation and assist burn-up during the combustion event; also, persistent fuel vapor would be discharged at higher temperature into the hot, oxygen-rich bulk cylinder contents during the powerstroke expansion.