Developing premixed turbulent flames: Part II. Pressure-driven transport and turbulent diffusion

The effects of premixed turbulent flame development on the transition from gradient to counter-gradient transport are modeled phenomenologically. By a nalyzing the balance equation for the second order velocity-progress variab le correlation, the terms controlling the transition are singled out These terms are evaluated for a self-similar regime of premixed turbulent flame d evelopment discussed, in detail, in the first part of the paper (Lipatnikov and Chomiak, 2000c). The regime is characterized by the fact that the prog ress variable profiles, measured by various teams under a wide range of con ditions along the normal to the mean flame brush, collapse to a universal c urve when presenting the profiles in the dimensionless form by using the me an flame brush thickness which depends on the flame development time. Based on these observation, analytical estimates of the mean pressure gradient i n free, one-dimensional, statistically planar and spherical, turbulent flam es are obtained. The results indicate a strong time-dependence of the press ure gradient and, hence, of the transition studied. The transition curves a re computed for different flames and are drawn in the plane of the Damkohle r number and flame development time. The predictions agree reasonably well with the available experimental and DNS data. An analysis of the behavior of various terms in the progress variable balan ce equation, performed for self-similar premixed turbulent flames, has show n that the normalized spatial profile. of the progress variable across the flame brush is mainly controlled by the mean rate of product creation. Thus , detailed modeling of the transport term pu(k)"c " appears to be of minor importance for many applications, especially as the development of the mean flame brush thickness is mainly controlled by classical turbulent diffusio n.