Local volumetric dilatation rate and scalar geometries in a premixed methane-air turbulent jet flame

The local volumetric dilatation rate, namely, the rate of change of an infinitesimal fluid volume per unit volume, ∇·u, is an important variable particularly in flows with heat release. Its tangential and normal strain rate components, aT and aN, respectively, account for stretching and partially for separation of iso-scalar surfaces. A three-dimensional direct numerical simulation (DNS) of a turbulent premixed methane-air flame in a piloted Bunsen burner configuration has been performed by solving the full conservation equations for mass, momentum, energy and chemical species using tabulated chemistry. Results for the volumetric dilatation rate as a function of the iso-scalar surface geometry, characterized by the mean and Gauss curvatures, km and kg, are obtained in several zones (reactants, preheat, reacting and products) of the computational domain. Flat iso-scalar surfaces are the most likely geometries in agreement with previous DNS. The relationship between density and a reaction progress variable, under a low Mach number flamelet assumption, leads to an expression for ∇·u with contributions from progress variable source and molecular diffusion budget, with a significant contribution from the latter; this approximate expression for the volumetric dilatation rate is studied with DNS results. The joint pdf of aN and aT confirms that the line aT+aN=0 separates mostly expansive flow regions from compressive zones.