Generalized description and extrapolation of extinction stretch rates from spherically expanding flames

Abstract

The extinction stretch/strain rate is an important global parameter for validating kinetics and modeling laminar and turbulent flame extinctions. Here, we propose a generalized approach to extrapolate the extinction stretch rate from spherically expanding flames, based on the nonlinear relation between the flame speed and the stretch rate applicable to general Lewis numbers (Le’s). Results show that the extinction events for Le<1, lean hydrogen/air flames can only be obtained by considering finite flame thickness, indicating the importance of finite, incomplete reaction in the extinction of such flames. On the other hand, both the previous nonlinear formulation with complete reaction and the present finite flame thickness descriptions can predict extinction for the Le>1, rich hydrogen/air flames, for which the extinction mechanism is that of preferential diffusion. The effects of equivalence ratio and pressure have also been examined and explained, which highlight the essential role of proper definitions in explaining the extinction stretch rate responses. The present generalized description is particularly useful for the investigations of flame extinction and chemistry at elevated pressures within internal combustion engines.