Title: Enhancement and Quenching of Combustion by Fluid Flow
Speaker: Professor Alexander Kiselev
Speaker Info: University of Chicago
Influence of the fluid flow can lead to drastic speed up, or, in some situations, quenching of burning. Many important engineering applications of combustion operate in the presence of turbulent advection, and therefore the influence of advection on burning has been studied extensively by physicists, engineers and mathematicians. Nevertheless, rigorous results on this phenomena were scarce until recently.Date: Friday, January 25, 2002
We study a well-established model of premixed fluid combustion: the reaction-diffusion equation with passive advection. We introduce in a rigorous way the quantity measuring the rate of combustion, the bulk burning rate, which is well-defined in any burning regime. For various types of reaction non-linearities we show that there is a class of the flows that are very effective in speeding up the reaction. These flows are characterized by the presence of the long tubes of streamlines connecting the burned and unburned material, and in particular include shear flows in a direction perpendicular to the front. On the other hand, the flows with closed streamlines, such as cellular, are shown to produce weaker burning enhancement.
We also study in detail the opposite effect of quenching the combustion in a shear flow, discovering connections between the structure of the flow and its efficiency in helping extinguish the compactly supported flame.
The methods involve a new functional inequality, a new procedure for estimation of higher order derivatives, maximum principle based techniques, and a study of hypoellipticity of certain degenerate parabolic PDE.