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

The problem of a definition of speed and burning velocity of a developing turbulent premixed flame of a finite thickness is studied analytically and numerically for planar and spherical cases. Analytical studies are based on the well-documented self-similarity of the normalized profiles of the mean density across the turbulent flame brush. Numerical simulations have been performed with the Flame Speed Closure model of turbulent combustion. The goals of the study are to develop methods for determining two reference surfaces: (1) a "flame speed surface", i.e., 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 (2) a "burning velocity surface", i.e., a 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 proven to be an iso-scalar one. For spherical flames, expressions for determining both surfaces are derived, but these surfaces are different and they are not iso-scalar ones. Simulations have shown that, (1) these features are not well-pronounced under typical conditions, and (2) when investigating spherical flames, one may associate flame speed and burning velocity with the same iso-scalar surface. Various experimental techniques (e.g., pressure records and high-speed tomography) used to measure the speeds of spherical turbulent flames are demonstrated to give results which are close to one another and also to the results computed from the aforementioned expressions.