Developing Premixed Turbulent Flames: Part II. Pressure-Driven Transport and Turbulent Diffusion

Abstract

The effects of premixed turbulent flame development on the transition from gradient to counter-gradient transport are modeled phenomenologically. By analyzing the balance equation for the second order velocity-progress variable correlation, the terms controlling the transition are singled out. These terms are evaluated for a self-similar regime of premixed turbulent flame development discussed, in detail, in the first part of the paper (Lipatnikov and Chomiak, 2000c). The regime is characterized by the fact that the progress variable profiles, measured by various teams under a wide range of conditions along the normal to the mean flame brush, collapse to a universal curve when presenting the profiles in the dimensionless form by using the mean flame brush thickness which depends on the flame development time. Based on these observation, analytical estimates of the mean pressure gradient in free, one-dimensional, statistically planar and spherical, turbulent flames are obtained. The results indicate a strong time-dependence of the pressure gradient and, hence, of the transition studied. The transition curves are computed for different flames and are drawn in the plane of the Dam-kohler 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 balance equation, performed for self-similar premixed turbulent flames, has shown 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'Jc" 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 diffusion.

Keywords:

• counter-gradient diffusion
• turbulent flames
• modeling

Additional information

Notes on contributors

A.N. LIPATNIKOV

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