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-p[c](1 - [ c]) to fourth order in ([c] - 1/2), with C-p a proportionality factor. Any model regardless of its physical and chemical basis should give t his result if the aforementioned assumptions are satisfied. The burnin g rate integral, B-T, is introduced, and a relationship between B-T an d C-p is developed: B-T = C(p)l(B) where l(B) is a measure of the flam e thickness. It follows that measurements of B-T can be used to find C -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] - 1/2). A method for measuring B-T based on a control volume analysis and the use of conditional mean velocities is proposed and demonstrat ed with data from Miles [7]. The model expression for [w] is specializ ed to the flamelet regime of turbulent combustion, and the result obta ined is similar to the Bray, Moss, Champion, and Libby crossing densit y model expression. A clear physical interpretation for C-p, valid for the flamelet regime, is offered.