Determination of Laminar Flame Speed and Markstein Numbers Deduced From Turbulent Flames Using the Bomb Method

Abstract

The flame speed is a central element not only in theoretical combustion and basic research but also a key parameter for several combustion models. Various methods to define and measure laminar flame speed have been applied. One method that is being relevant to determine flame speed and flame stretch (quantified by Markstein numbers) under high pressure and high temperature conditions is the bomb method, where an unsteady spherical expanding flame is investigated in a closed vessel. Especially for higher pressures, instabilities occur in the flame front of spherically expanding flames, due to the decreased flame thickness and diffusion processes. These so called cellular structures increase the flame surface and therefore the laminar flame speed cannot be determined in the usual manner. As high pressures are common under engine conditions, there is a need to be still able to determine the flame speed within these pressure ranges. By exposing the flame to a turbulent flow field, the vortex interactions are mainly responsible for the deformation of the flame surface. This fact can be used to deduce the laminar flame speed from a turbulent flame. In the present work, a turbulent flame speed model to determine unstretched laminar flame speed and Markstein numbers is introduced and validated. For this purpose the flame is exposed to a well-known turbulent flow field that is nearly homogenous and isotropic. By estimating the flame surface, the laminar flame speed can be calculated, using a turbulent stretch model as well as the flamelet assumption in an implicit approach. A high speed 2D laser imaging technique is used to capture the flame propagation. The most significant issue of this method is to correctly identify the surface and the volume of the flame, because solely a cross section of the flame surface can be visualized in the laser sheet. In case of spherical flames, the radius of the cross section corresponds to the flame surface and volume whereas a single radius is not sufficient to quantify a turbulent flame. The idea is to use the circumference of the cross section in a power law approach to quantify the cellular structures as a mean. The implicit model has been validated for methane and hydrogen flame speed at various equivalence ratios at atmospheric and elevated pressure. The results are in a good agreement with laminar determined flame speed and also the Markstein number is obtained qualitatively correct. Although the flame surface and volume cannot be determined directly by 2D measurement techniques, a model has been developed to determine laminar unstretched flame speed and Markstein numbers by investigating unsteady propagating flames in a turbulent flow field.