Flame surface densities during spherical turbulent flame explosions

A novel way is presented of deriving the proportionality constant, k (mm1), for flame surface density. This comprises simultaneous measurements, by Mie scattering, of mean reaction progress variable and the turbulent burning velocity, during explosions in a fan-stirred bomb. Mean effective laminar burning velocities at the wrinkled flame surface are derived theoretically from the distribution of flame stretch rates, the Markstein numbers, and the possible generation of localised flame instabilities and flame quenching. The changing radial profiles of flame surface density have been obtained, as flames accelerate in different propane-air explosions. The effective value of the rms turbulent velocity acting on the flame is derived from a newly developed power spectral density function. The values of k are similar to those found by researchers employing stationary turbulent flames, but the present work suggests dependencies of k upon Markstein number. Insights are obtained on the inter-relationship of k and turbulent burning phenomena. More research is required on the factors controlling the value of k, including its relationship to flame curvature.