CAREER: Reactive Processes and Turbulent Flows

职业：反应过程和湍流

• 批准号: 1056327
• 负责人: Andrej Zlatos
• 金额: $ 49.85万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-01 至 2016-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1056327&HistoricalAwards=false
• 关键词: CAREER; Reactive; Processes; Turbulent; Flows

The focus of the research component of this project is analytical study of models of reactive processes, such as combustion, taking place in fluid flow. In recent years, there has been significant progress in the mathematical understanding of the effects of flow on combustion. Nevertheless, the inherent complexity and richness of the phenomena continues to present a challenge to our study of this problem. These models are given by nonlinear partial differential equations, in particular, by reaction-diffusion equations which may also be coupled to equations of fluid dynamics. One of the goals of the proposed research is a continuation of previous work on passive combustion in periodic, random, as well as general inhomogeneous media. The main questions of interest include the effects of flows on mixing and on speed-up of propagation of reaction. In addition, simplified models will be considered and experience gained from their study will be applied to the original problems. Another goal of the project is the study of propagation of reaction in a model of active combustion, with direct feedback of reaction on the fluid motion via the buoyancy force and gravity-induced mixing. In many situations this effect cannot be ignored, particularly in highly turbulent combustion regimes. Although this is a very difficult problem, limited progress has been achieved recently and it is proposed here to build upon these results. The developed techniques will also be applied to the study of other related models, including systems of reaction-diffusion equations and a model of liquid suspensions.Reactive processes, such as burning in internal combustion engines, nuclear reactions in stars, and forest fires, are ubiquitous in nature. Their study is relevant to several branches of science and engineering such as astrophysics, biology, environmental science, and chemical engineering. The research proposed here focuses on the influence of the motion of the underlying medium, such as fluid flow, on the speed of spreading of reactive processes. It aims at improving our understanding of fundamental mathematical models describing such processes, which may provide useful qualitative insights into real life phenomena. An important part of this proposal is its educational component. The principal investigator (PI) plans to develop an undergraduate partial differential equations (PDE) course at the University of Wisconsin, mentor undergraduate mathematics majors in the study of advanced topics, and organize a Research Experience for Undergraduates program in analysis and PDEs. The PI will also teach specialized graduate courses and involve graduate students in working under his supervision.

该项目研究部分的重点是对流体流动中发生的反应过程（如燃烧）模型进行分析研究。 近年来，在流动对燃烧影响的数学理解方面取得了重大进展。 然而，这些现象固有的复杂性和丰富性继续对我们研究这一问题提出挑战。 这些模型是由非线性偏微分方程，特别是反应扩散方程，也可以耦合到流体动力学方程。 所提出的研究的目标之一是继续以前的工作被动燃烧在周期性的，随机的，以及一般的非均匀介质。 感兴趣的主要问题包括流动对混合和反应传播速度的影响。 此外，将考虑简化模型，并将从研究中获得的经验应用于原始问题。 该项目的另一个目标是研究活性燃烧模型中反应的传播，通过浮力和重力引起的混合直接反馈反应对流体运动的影响。 在许多情况下，这种影响不容忽视，特别是在高度湍流的燃烧状态下。 虽然这是一个非常困难的问题，但最近取得的进展有限，因此建议在这些成果的基础上再接再厉。 所开发的技术也将应用于其他相关模型的研究，包括反应扩散方程组和液体悬浮物模型。反应过程，如内燃机中的燃烧，恒星中的核反应和森林火灾，在自然界中无处不在。 他们的研究与科学和工程的几个分支有关，如天体物理学，生物学，环境科学和化学工程。 这里提出的研究重点是底层介质的运动，如流体流动，对反应过程的传播速度的影响。 它旨在提高我们对描述这些过程的基本数学模型的理解，这可能为真实的生活现象提供有用的定性见解。 这项建议的一个重要部分是其教育部分。 主要研究者（PI）计划在威斯康星州大学开设本科偏微分方程（PDE）课程，指导本科数学专业的高级主题研究，并组织本科生分析和偏微分方程项目的研究经验。 PI还将教授专门的研究生课程，并让研究生在他的监督下工作。