Chemical closure and burning rates in premixed turbulent flames

Abstract

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 this result if the aforementioned assumptions are satisfied. The burning rate integral, B T , is introduced, and a relationship between B T and C p is developed: B T = C p I B where I B is a measure of the flame 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 demonstrated with data from Miles [7]. 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 p , valid for the flamelet regime, is offered.