Investigation of Two-Dimensional Counterflow Laminar Flame Using Generalized Coordinates Based Reaction-Diffusion Manifold Approach

Abstract

In this work, the implementation of a reduced model formulation for studying combustion processes is discussed. The reaction-diffusion manifolds (REDIM) approach is used for the reduced model formulation. In REDIM like other manifolds based reduced methods, instead of solving transport equations for every component of the detailed thermo-kinetic state vector, transport equations are solved only for some reduced coordinates. The remaining components of the detailed thermo-kinetic state vector are then expressed as functions of these reduced coordinates, with their values retrieved from precomputed tables. Unlike other methods, in REDIM, these reduced coordinates are of the form of generalized coordinates, which are the indices of grid points of the manifold stored in the tables. This generalized coordinate based formulation is independent of the choice of parameters used to represent the manifold. The current work investigates two-dimensional (2D) counterflow \({\text{C}}{{{\text{H}}}_{{\text{4}}}}\)/air laminar flames using a generalized coordinate based implementation of reduced calculations performed with 2D REDIM. Comparison of species mass fractions and temperature profiles predicted from reduced calculations show good agreement with detailed calculations.