Curvature and confinement effects for flame speed measurements in laminar spherical and cylindrical flames

This paper discusses methods used to obtain laminar flame speeds in spherical laminar premixed flames. Most recent studies express the laminar flame consumption speed as ρb/ρu dR/dt, where R is the flame radius and ρb/ρu is the ratio of the burnt to the fresh gas density (ρb is evaluated at chemical equilibrium and supposed to be constant). This paper investigates the validity of this assumption by reconsidering it in a more general framework. Other formulae are derived and tested on a DNS of cylindrical flames (methane/air and octane/air). Results show that curvature and confinement effects lead to variations of ρb and ρu and to significant errors on the flame speed. Another expression (first proposed by Bradley and Mitcheson in 1976) is derived where no density evaluation is required and only pressure and flame radius evolution are used. It is shown to provide more precise results for the consumption speed than ρb/ρu dR/dt because it takes into account curvature and confinement of the flame in the closed bomb.