Chemical closure and burning rates in premixed turbulent flames

Chemical closure for premixed turbulent flames is considered, and with a small number of assumptions regarding its form, a model expression for the mean rate of product formation is obtained: w = C[sub p]c(1 [minus] c) to fourth order in (c [minus] 1/2), with C[sub p] a proportionality factor. Any model regardless of its physical and chemical basis should give this result if the aforementioned assumptions are satisfied. The burning rate integral, B[sub T], is introduced, and a relationship between B[sub T] and C[sub p] is developed: B[sub T] = C[sub p]l[sub B] where l[sub B] is a measure of the flame thickness. It follows that measurements of B[sub T] can be used to find C[sub p], and that measurements of this type for a broad range of conditions can provide an empirical closure for w good to fourth order in (c [minus] 1/2). A method for measuring B[sub T] based on a control volume analysis and the use of conditional mean velocities is proposed and demonstrated with data from Miles. The model expression for w is specialized to the flamelet regime of turbulent combustion, and the result obtained is similar to the Bray, Moss, Champion and Libby crossing density model expression. A clear physical interpretation for C[sub p] valid for the flamelet regime, is offered.