Determination of Markstein numbers in counterflow premixed flames

This paper attempts to settle a long-standing issue concerning the differences in Markstein numbers measured by different experimental protocols. Numerical simulations of a counterflow flame with full transport coefficients, but using a fictitious reactive mixture having properties close to those assumed in asymptotic laminar flame analysis, are used to show how to correctly identify the burning velocity and stretch of a stretched flame with a finite width chemical zone. We show how to measure the Markstein number of the flame with respect to both the unburned and burned gases. The numerical values of these numbers differ by a quantity that depends on the internal flame structure. The physical origin of this difference is made evident. Our numerical results are in close agreement with the predictions of asymptotic theory. We show that laboratory experiments on counterflow flames give Markstein numbers related to the unburned gas, whereas laboratory experiments on spherical expanding flames give Markstein numbers related to the burned gases. The range of validity of asymptotic theory, for Lewis numbers departing from unity, is also examined. We conjecture that the so-called consumption velocity of a flame (normal integral of the species consumption rate) may allow a measure of the Lewis number dependent part of the Markstein number, even for realistic flames with complex chemistry and an effective Lewis number not close to unity.