Transient and curvature effects when defining burning velocity and speed of premixed turbulent flames

Abstract

This chapter focuses on the problem of definition of speed and burning velocity of a developing turbulent premixed flame of a finite thickness. It analyzes the problem analytically and numerically for planar and spherical cases in particular. Analytical studies are generally based on the well-documented self-similarity of the normalized profiles of the density across the turbulent flame brush. The numerical simulations are however performed with the Flame Speed Closure model of turbulent combustion. The goal of the study is essentially to develop methods for determining two reference surfaces, namely, a flame speed surface that refers to a surface — the speed of which is controlled by the burning rate integrated across the brush but is not directly affected by the rate of flame thickness growth, and another is a burning velocity surface that refers to surface — the area of which multiplied by the flame speed defined above characterizes the aforementioned burning rate. For planar flames, the former surface is defined and has proven to be an iso-scalar one. However, for spherical flames, expressions for determining both surfaces are derived and these surfaces are different and not the iso-scalar ones. Simulations exhibit that while investigating the spherical flames, it is noted that they are associated with flame speed and burning velocity with the same iso-scalar surface. Various experimental techniques used to measure the speeds of spherical turbulent flames often demonstrate results close to one another.