The influence of isotropic turbulence on the critical ignition energy

Abstract

Theoretical considerations are presented which indicate that the increase of spark-ignition energy under turbulent-flow conditions is mainly due to an increase in transport phenomena resulting from turbulent heat diffusivity. In order to account for the relatively small diffusion times involved in ignition phenomena, turbulent diffusivity should be considered as time dependent. For diffusion times (t) much smaller than the characteristic lifetimes of the turbulent eddies (defined as time scale/turbulence intensity), the turbulent mass diffusivity Dt becomes equal to u12t/2. This turbulent diffusivity acts on the ignition energy in two ways:o1.By increasing the flame-front thickness according to the proportionality et/e= (u12t/2Dm+1) it causes a relatively important increase in the minimum critical volume of flammable mixture that must be heated up by the ignition energy;2.It increases the fraction ξ of the spark energy that is available for ignition, the complementary fraction (1-ξ) of the spark energy being wasted beyond the critical volume. By increasing the flame-front thickness according to the proportionality et/e= (u12t/2Dm+1) it causes a relatively important increase in the minimum critical volume of flammable mixture that must be heated up by the ignition energy; It increases the fraction ξ of the spark energy that is available for ignition, the complementary fraction (1-ξ) of the spark energy being wasted beyond the critical volume. This secondary effect of turbulent diffusivity is rather small, but depends on the spark duration θ and on the energy release function. Calculations of the fraction ξ as a function of θ are presented under both laminar and turbulent conditions. Experimental evidence of the effect of the spark-duration time and the turbulent diffusivity on ignition energy is obtained from work carried out with flammable methane/air and propane/air mixtures for different turbulent-flow conditions.