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: left angle bracketwright-pointing angle bracket = Cpleft angle bracketcright-pointing angle bracket(1 - left angle bracketcright-pointing angle bracket) to fourth order in (left angle bracketcright-pointing angle bracket - 1/2), with Cp 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, BT, is introduced, and a relationship between BT and Cp is developed: BT = CpIB where IB is a measure of the flame thickness. It follows that measurements of BT can be used to find Cp, and that measurements of this type for a broad range of conditions can provide an empirical closure for left angle bracketwright-pointing angle bracket good to fourth order in (left angle bracketcright-pointing angle bracket - 1/2). A method for measuring BT based on a control volume analysis and the use of conditional mean velocities is proposed and demonstrated with data from Miles [7]. The model expression for left angle bracketwright-pointing angle bracket 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 Cp, valid for the flamelet regime, is offered.