Turbulent burning velocity and speed of developing, curved, and strained flames

Abstract

The problem of a physically meaningful definition of speed and burning velocity of a developing turbulentpremixed flame of a finite thickness is studied analytically and numerically in 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, that is, 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, that is, 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 isoscalar one. For spherical flames,expressions for determining both surfaces are derived, but these surfaces are different and they are not isoscalar 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 isoscalar surface. A method for evaluating the unburned mixture velocity, which is needed to convert the observed speed of expanding spherical flames to the speed with respect to unburned mixture, is developed. The method is shown to be applicable to measurements of turbulent flame speeds in stagnation flows also. In all the cases studied, a reference value of the progress variable is found to be a roughly invariant (with respect to flame geometry and development) characteristic determining flame speed and burning velocity surfaces.