Enhancement and Quenching of Combustion by Fluid Flow

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

NSF Award Abstract - DMS-0102554 Mathematical Sciences: Enhancement and Quenching of Combustion by Fluid Flow Abstract 0102554 Kiselev It is known that in many combustion phenomena the turbulent advection of the underlying fluid plays an important role. Depending on the setting, it can lead to a significant speed up of combustion or to the quenching of the flame. The main goal of this project is to improve fundamental understanding of this important phenomenon. In particular, this work explores analytically how the geometry, scaling, and intensity of the velocity field determine the effect advection has on combustion. A primary goal is to determine the optimal geometry for the fastest extinction of the flame, or for the most effective speed up. The models to be studied include passive reaction-diffusion equations with physically-motivated reaction terms, systems of reaction-diffusion equations, and active scalar models with feedback of temperature and concentration on fluid velocity. The methods of analysis include maximum-principle-based techniques, estimates on solutions of partial differential equations, and functional inequalities, as well as some methods of harmonic and spectral analysis. The influence of strong fluid advection on combustion plays a crucial role in many important combustion processes in technology and in nature. Strong fluid advection may drastically enhance the rate of burning, leading to higher efficiency, or, in some situations, extinguish the flame. This question has been extensively studied by engineers, physicists, and mathematicians alike. However, until very recent work of several research groups, there were few rigorous results on the topic. Building on the technique developed in earlier works, the project seeks to deepen the understanding of this phenomenon, in particular relating the geometric characteristics of the fluid flow with the effect it has on combustion. The potential impact of the project is an improved knowledge of combustion processes in settings as diverse as internal combustion engines and stars. The research may lead to direct suggestions on the most efficient ways of flame suppression or enhancement. In addition, the techniques developed for tackling this problem may prove useful in analyzing other partial differential equations.