Enhancement and Quenching of Combustion by Fluid Flow

数学科学：流体流动对燃烧的增强和猝灭。众所周知，在许多燃烧现象中，底层流体的湍流平流起着重要作用。根据不同的设置，它可以导致燃烧的显著加速或火焰的熄灭。该项目的主要目标是提高对这一重要现象的基本理解。特别是，这项工作分析地探讨了几何形状、尺度和速度场的强度如何决定平流对燃烧的影响。一个主要的目标是确定最佳的几何形状，以最快的速度熄灭火焰，或最有效的加速。要研究的模型包括具有物理激发反应项的被动反应扩散方程、反应扩散方程系统和具有温度和浓度对流体速度反馈的主动标量模型。分析方法包括基于最大原理的技术、偏微分方程解的估计和泛函不等式，以及一些谐波和谱分析方法。强流体平流对燃烧的影响在许多重要的燃烧过程中起着至关重要的作用。强烈的流体平流可以大大提高燃烧速度，从而提高效率，或者在某些情况下熄灭火焰。这个问题已经被工程师、物理学家和数学家广泛研究过。然而，直到最近几个研究小组的工作，在这个话题上几乎没有严谨的结果。在早期工作中开发的技术的基础上，该项目寻求加深对这一现象的理解，特别是将流体流动的几何特征与燃烧的影响联系起来。该项目的潜在影响是提高对内燃机和恒星等多种环境中燃烧过程的认识。这一研究可能会导致对最有效的火焰抑制或增强方法的直接建议。此外，为解决这个问题而开发的技术在分析其他偏微分方程时可能是有用的。

NSF Award Abstract - DMS-0102554Mathematical Sciences: Enhancement and Quenching of Combustion by Fluid FlowAbstract0102554 KiselevIt 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.