Mathematical Fluid Dynamics and Education Turbulent Transport, Combustion, and Compressible Convection

数学流体动力学和教育湍流传输、燃烧和可压缩对流

• 批准号: 9701942
• 负责人: Richard McLaughlin
• 金额: $ 20万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-09-01 至 1999-03-03
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9701942&HistoricalAwards=false
• 关键词: Mathematical; Fluid; Dynamics; Education; Turbulent

9701942 McLaughlin This work is supported by a National Science Foundation Faculty Early Career Development Award. The research component will focus on the theoretical understanding of fluid phenomena. Specifically, these research efforts outline the study of turbulent transport and scalar intermittency, the numerical calculation of enhanced burning speeds in premixed combustion, and theoretical and computational studies of weakly compressible transport phenomena. An underlying theme in this effort is the isolation of how fluid flow properties affect transport phenomena, which may include enhanced mixing rates, enhanced rare event probability, enhanced burning speeds, and enhanced anelastic heat transport. These studies involve a sophisticated integration of modern asymptotic, numerical, and probabilistic techniques. Additionally, this award will support the continued curriculum development of an advanced undergraduate/ graduate level Mathematical Fluid Dynamics course. Such a course is designed to present the student with the essential mathematical tools necessary to understand fluid mechanics and to quickly equip the student with essential techniques for attacking research problems in Applied Mathematics. Additionally, a small demonstration fluids laboratory will be developed to offer visualization of many fluid phenomena. This Faculty Early Career Development Award will provide the principal investigator the opportunity to pursue his research efforts in the understanding of many fluid transport phenomena while additionally developing new educational curricula. Developing sound theories for fluid transport is fundamental in many ways. The experimental understanding of fluid turbulence typically involves the tracking of passive dye, and, consequently, the quantification of how fluid flow properties affect the mixing of such dye is critical. Further, the development of sound transport theories naturally will yield insight into a va riety of mixing applications such as the tracking of atmospheric pollutants. Perhaps most importantly is the potential information such theories may offer to large-scale computational fluids, combustion and climate models in which a common difficulty regards how to treat unresolvable length and time scales. It is an accepted fact in computational fluid dynamics that important, non- negligible, complex fluid phenomena exist which are simply not resolvable on even the largest supercomputers. These sub-grid effects play a dramatic role in many fluids applications such as weather prediction. They cannot be ignored, and a standard approach is to replace them by something simpler-- an effective mixing coefficient. In many applications, the transport theories developed here offer sound justification and quantification of these coefficients, and potentially may offer improvements to existing computational models. Finally, the curriculum effort will involve the development of a small fluids laboratory including a demonstration water tunnel. Through this lab, a student studying the theory of fluids will find exciting visual contact with real fluids phenomena typically unavailable in mathematics coursework, and this visualization will lead to greater excitement and appreciation for the usefulness of mathematical theory in the understanding of observable phenomena. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation- wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers which include both research and education.

9701942 McLaughlin这项工作得到了国家科学基金会早期职业发展奖的支持。 研究组成部分将集中于对流体现象的理论理解。具体而言，这些研究工作概述了湍流运输和标量间歇性的研究，预混合燃烧中增强的燃烧速度的数值计算以及弱压缩运输现象的理论和计算研究。这项工作中的一个基本主题是隔离流体流动特性如何影响运输现象，这可能包括提高的混合速率，增强的稀有事件概率，增强的燃烧速度以及增强的厌氧热传输。这些研究涉及现代渐近，数值和概率技术的复杂整合。 此外，该奖项将支持高级本科/研究生水平数学动力学课程的持续课程开发。 这样的课程旨在向学生提供理解流体力学的必要数学工具，并快速为学生提供基本技术，以攻击应用数学中的研究问题。 此外，将开发出一个小型示范液实验室，以提供许多流体现象的可视化。 该教师早期职业发展奖将为主要研究者提供机会，以在理解许多流体运输现象的同时，在开发新的教育课程的同时，从事研究工作。在许多方面，开发流体运输的声音理论至关重要。 对流体湍流的实验理解通常涉及被动染料的跟踪，因此，对流体流动性能如何影响这种染料的混合的定量至关重要。 此外，声音传输理论的发展自然会洞悉混合应用的范围，例如跟踪大气污染物。 也许最重要的是，这些理论可能为大规模计算流体，燃烧和气候模型提供的潜在信息，其中一个共同的困难对待如何治疗不可避免的长度和时间尺度。 在计算流体动力学中，这是一个公认的事实，它存在重要，不可忽略的，复杂的流体现象，即使是最大的超级计算机，也根本无法解析。 这些亚网格效应在许多流体应用中起着戏剧性的作用，例如天气预测。它们不能忽略，一种标准方法是用更简单的东西代替它们 - 有效的混合系数。 在许多应用中，此处开发的运输理论提供了这些系数的合理理由和量化，并可能对现有计算模型进行改进。 最后，课程工作将涉及一个小型流体实验室的发展，包括示范水隧道。 通过这个实验室，研究流体理论的学生将在数学课程中发现与真实流体现象的令人兴奋的视觉接触，这种可视化将导致对数学理论在理解可观察到的现象的有用性的更加兴奋和欣赏。 国家科学基金会强烈鼓励学术教师作为教育者和研究人员的早期发展。 教师早期职业发展（职业）计划是一个基础范围的计划，在整体职业发展的背景下为初级教师提供了支持。 它在一个计划中结合了最广泛的质量研究和教育的支持，以及传统上代表性不足的科学和工程专业人士的全部参与。 该计划增强并强调了基础对包括研究和教育在内的全面，平衡学术职业发展的重要性。