A Critical Study of Models in Turbulent Combustion

Doctoral thesis, 1994

Paper I-III focuse on the problem to validate models for premixed turbulent flames. The main result of paper I is the formulation of an analytical method for prediction of turbulent flame velocities from turbulent flame models. The method is motivated by a mathematical theory by Kolmogorov, Petrovskii and Piskunov (1937). A lower bound for the burning velocity is derived at the leading edge based upon a Taylor expansion of the solution and the solution and the assumption that a stationary flame exists. Numerical solutions of the non-stationary equations are then performed in order to verify that the derived lower bound is the true burning velocity. Applications include the model by Magnussen and Hjertager (1976) and the Bray-Moss-Libby (BML) model (Bray, 1980). The method has been applied by Libby (1989), by Bray (1990) to evaluate the BML-model, by Duclos et al (1993) to evaluate five recent flamelet models and by Fichot et al (1993) to study a transport equation for the flame surface density. Papper II and III are devoted to a critical study of the Bray-Moss-Libby model for premixed turbulent flames. Conditions for well-posedness have been formulated. The turbulent flame velocity and the turbulent scalar diffusivity at the leading edge have been determined analytically in the special case with small rate of heat release. Data from direct numerical simulation of a premixed turbulent flame at the Center for Turbulence Research, Stanford, have been used to validate the BML-model for the mean reaction rate. A new integral length scale Ly, for the flame wrinkles is introduced, which is related to the Taylor scale for the turbulence at the leading edge. Paper IV is independent of paper I-III and is motivated by the problem to predict autoignition in a diesel spray. The goal of the paper is to study a formalism based upon probability density functions (pdf), which formally solves the problem of closure for the non-linear reaction terms. Current models for scalar mixing do not satisfy the requirement that all initial distributions should tend to a Gaussian distribution. A new class of pdf-models is introduced and the convergence towards an asymptotic Gaussian distribution is verified numerically. The pdf-model is applied to study scalar mixing and autoignition of two reactants undergoing a one step, second order, irreversible exothermic reaction of Arrhenius type.