Formalism for spatially averaged consumption speed considering spherically expanding flame configuration

The determination of laminar burning velocity is a complex task. Even though its definition is well established, achieving a good and reliable value of this quantity seems to be too dependent on the experimental procedures. In this study, we report a rigorous derivation of the relation between the spatially averaged consumption speed and the absolute flame speed for spherically expanding flame configurations. The general expression of the consumption speed in confined geometries makes it possible to retrieve classical definitions developed in the literature over the years. It has been highlighted that the analytical development for the consumption speed is free from restrictive assumptions or approximations (stretch or thermodynamical gas states) that are generally made in classical approaches. The development brings up to identify two equivalent radii, one from a surface and one from a volume integration, respectively. The analytical developments are tested using a 3D DNS including full transport and complex chemistry. CH4/air flame at three equivalence ratios (lean, stoichiometric and rich) and a stoichiometric iso-octane/air flame are tested. Results show that any species, reactants or products, can be used to evaluate the analytical expression of the consumption speed.