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Department of Mechanical Engineering
Stanford University
Abstract-
Premixed turbulent combustion in the corrugated flamelets regime has been addressed by
modeling ofa 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.
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