Modeling Turbulent Transient Combustion

Abstract

An analytical study investigated the use of a one-dimensional combustion model for transient, premixed flames under conditions similar to those occurring in a spark ignition internal combustion engine. The model numerically integrated basic conservation equations for mass, momentum, energy, and species with effects of turbulence modeled using turbulent diffusivity. To evaluate effects of certain assumptions and to identify significant model parameters, a simplified system consisting of constant-volume adiabatic combustion was considered. With simple chemical kinetics and constant turbulent diffusivity, there were three parameters in the problem: nondimensional speed of sound; nondimensional temperature rise due to combustion; and a Damkohler parameter relating diffusion and chemical reaction rate effects. Two flame types were modeled, a flat flame in linear coordinates and a cylindrical flame. Effects of boundary conditions and numerical parameters were explored. Calculated results for the cylindrical flame were compared to literature data for similar conditions. It was concluded that model results are in qualitative agreement with laminar flame theory and that turbulent, transient, premixed flames can be modeled using the MacCormack predictor-corrector technique to numerically integrate conservation equations for mass, momentum, energy, and species, using suitable parameters for reaction rates and turbulent diffusivity. Equations for the basic model and for boundary and initial conditions are appended.