Modification of the turbulent burning velocity by gas expansion

Abstract

Premixed turbulent combustion in the corrugated flamelets regime has been addressed by modeling of a G-equation containing a gas-expansion term, the form of which was derived by generalizing results of Sivashinsky along lines initiated by Frankel. Previous analyses by the first author of the mean, variance, and two-point correlation spectrum of G, as well as their relation to the turbulent burning velocity, were extended to include the influences of gas expansion. It is shown that this effect has the same form as kinematic restoration but acts in the opposite direction. Because of this similarity in form, no new modeling approximations are required. On average, kinematic restoration dominates gas expansion. In physical terms, this means that the energy-containing eddies at the integral scale are strong enough to suppress gasdynamic instabilities at smaller scales. Gas expansion lessens the smoothing effect of kinematic restoration, thereby increasing the variance of G and the turbulent flame brush thickness. It also increases the turbulent burning velocity by a factor that increases with increasing ratio of unburned to burned gas density and with decreasing ratio of turbulence intensity to laminar burning velocity. The effect on the burning velocity, however, is not large, remaining less than 40% even as the turbulence intensity begins to decrease below the laminar burning velocity.