Nonadiabatic propagation of a planar premixed flame Constant-volume enclosure

Abstract

The unsteady one-dimensional laminar nonisobaric propagation of a flame through a gaseous fuel-lean combustible premixture, characterized by large Arrhenius activation temperature, is examined under ShvabZeldovich-type formulation, via numerical integration by the method of lines with spline interpolation. The premixture is confined between plane parallel impervious noncatalytic isothermal walls, although adiabatic walls are also considered. The straightforward extension of the Shvab-Zeldovich approximation adopted is suppression of acoustic phenomena, nonessential for present purposes, by taking the pressure to be temporally variant, but spatially uniform. The relative importance of three phenomena not present in isobaric flame propagation (the variation of the diffusion coefficient with pressure, the change of the reaction rate with pressure, and the ex- plicit temporal-pressure-derivative contribution in the energy equation) is studied. Initiation of combustion is effected by two models of ignition: 1) simulation of spark ignition (what minimum enthalpy-augmentation of a given duration at one wall leads to self-sustained propagation of flame across the charge), and 2) simulation of hot-kernel ignition (what minimum enthalpy-augmentation of a given volume at one specific internal site leads to self-sustained flame propagation).time since start of enthalpy addition t*/(D* u /u?) temperature temperature prescribed at wall near ignition [see Eq. (11)] temperature prescribed at wall away from ignition [see Eq. (10)]