Effect of nonunity lewis number on premixed flame propagation through isotropic turbulence

Abstract

Direct numerical simulations of a passive premixed flame surface propagating through stationary isotropic turbulence have been performed in three dimensions on a 96 3 mesh with a particular emphasis on characterizing the effect of Lewis number on the rate of propagation of the flame surface and flame surface topology. The simulations were based on the flame sheet assumption that implies that the time scale for chemical reaction is short as compared with the time scales for the turbulent fluctuations (so-called flamelet regime). In this limit, the flame surface can be represented by a field equation (Sivashinsky equation) which accounts for local advection of the reaction front due to instantaneous velocity fluctuations and propagation due to reaction. The Navier Stokes equations and scalar field equation for the flame surface were updated using a pseudo-spectral method with fourth order accuracy in time. Lewis number effects were incorporated into the simulations by using a modified Sivashinsky equation for the flame surface. At zero turbulence level, the simulation yielded the familiar steady and nonsteady cellular structures seen previously by several investigators. At finite turbulence levels the flame speed was augmented above the cellular flame speed due to additional wrinkling from the hydrodynamic field. Comparisons with experimental measurements in the literature agree with the simulations to within 30% over a wide range of turbulence intensities and Lewis numbers. In addition spectral analysis of the Sivashinsky equation provides insight into the effect of varying the Lewis number and how that effect may be incorporated into a relatively simple spectral model for the flame surface.