Composition-space premixed flamelet solution with differential diffusion for in situ flamelet-generated manifolds
Résumé
Canonical flame problems have been widely used in the combustion literature to tabulate detailed chemistry. Prior to three-dimensional flame simulations, reference laminar premixed flames are usually solved in physical-space, and, diffusion flames in either physical, or, mixture fraction space. Composition-space solutions would be convenient for premixed flame also, because all the points are relevant for chemistry, as a result of the zoom inside the flame zone; however, differential diffusion is not always easy to introduce with accuracy in these moving-frame coordinate systems, parameterized by their physical-space gradients (or scalar dissipation rates). A projection is discussed in this paper that ensures that differential diffusion is properly accounted for, in any composition-space coordinates, thus allowing for perfect matching between physical- and composition-space solutions, even for premixed flames. Both a diffusion velocity correction, which is necessary to properly conserve mass with Fick’s law, and a differential diffusion effect between the composition-space moving with the flow and fast diffusing species, are introduced. A procedure for rapidly building converged composition-space solutions for premixed flamelets is then proposed and tested. It provides the framework for an efficient in situ calculation of complex chemistry with differential diffusion, to be applied to three-dimensional unsteady flame simulations. The objective is to avoid building a priori look-up tables, whose range of validity is strongly limited by their boundary conditions, which are fixed once for all, therefore lacking of generic character, specifically when pressure, composition and enthalpy of fresh gases are varying in space and time.