An apparatus-independent extinction strain rate in counterflow flames

Resistance to extinction by stretch is a key property of any flame, and recent work has shown that this property controls the overall structure of several important types of turbulent flames. Multiple definitions of the critical strain rate at extinction (ESR) have been presented in the literature. However, even if the same definition is used, different experiments report different extinction strain rates for flames burning the same fuel-air mixture at very similar temperatures using similarly constructed opposed-flow instruments. Here we show that at extinction, all these flames are essentially identical, so one would expect that each would be assigned the same value of a parameter representing its intrinsic resistance-to-stretch-induced-extinction, regardless of the specifics of the experimental apparatus. A similar situation arises in laminar flame speed measurements since different apparatuses could result in different strain rate distributions. In that instance, the community has agreed to report the unstretched laminar flame speed, and methods have been developed to translate the experimental (stretched) flame speed into a universal unstretched laminar flame speed. We propose an analogous method for translating experimental measurements for stretch-induced extinction into an unambiguous and apparatus-independent quantity (ESR_∞) by extrapolating to infinite opposing burner separation distance. The uniqueness of the flame at extinction is shown numerically and supported experimentally for twin premixed, single premixed, and diffusion flames at Lewis numbers greater than and less than one. A method for deriving ESR_∞ from finite-boundary experimental studies is proposed and demonstrated for methane and propane experimental diffusion and premixed single flame data. The two values agree within the range of ESR differences typically observed between experimental measurements and simulation results for the traditional ESR definition.