Slow Invariant Manifolds for Spatially Homogeneous and Inhomogeneous Combustion Systems with Detailed Kinetics

具有详细动力学的空间均匀和非均匀燃烧系统的慢不变流形

• 批准号: 0650843
• 负责人: Joseph Powers
• 金额: $ 30万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-05-01 至 2011-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0650843&HistoricalAwards=false
• 关键词: Slow; Invariant; Manifolds; Spatially; Homogeneous

Slow Invariant Manifolds for Spatially Homogeneous and Inhomogeneous Combustion Systems with Detailed KineticsJ. M. Powers, S. Paolucci, A. J. Sommese, and C. W. WamplerThe objective of this study is to develop robust mathematical and computational tools to predict the dynamics of mixtures of reacting gases rationally and efficiently. In combustion, gases mix and react and generate heat by many simultaneous processes, but some of these processes are fast and some are much slower. Like the time scales, spatial scales of these processes can vary by many orders of magnitude. Design and operation of modern combustors can be advanced by reducing the full, complex set of reactions to the minimum, essential few whose slow dynamics dominates the dynamics of the system. The focus of this project is on physically realistic systems composed of calorically imperfect ideal gases described by detailed chemical kinetics with Arrhenius temperature dependence, the law of mass action, and multi-component diffusion. The present study will advance previous work in developing a technique to automatically identify slow invariant manifolds intrinsic to the reaction dynamics. For spatially homogeneous systems, this method will require solution of the difficult algebraic problem of identification of a large number of physical and non-physical equilibria of the system via a novel method. Numerical integration from unstable fixed points to the stable physical fixed point will identify the slow invariant manifold, which is coming to be realized as the linchpin in a rational method of reduced chemical kinetics. These results will then be applied to more challenging spatially inhomogeneous flows with advection and diffusion. The systems studied will employ realistic models used in modern scientific design of practical engineering systems. Attention will be focused on detailed models of hydrogen-air combustion kinetics. With the advances expected to result from this work, cleaner, more efficient combustors can developed to burn both hydrogen and a wide range of fuels.

具有详细动力学的空间均匀和非均匀燃烧系统的慢不变流形J. M. Powers，S. Paolucci，A. J. Sommese和C. W. Wampler本研究的目的是开发强大的数学和计算工具，合理有效地预测反应气体混合物的动力学。 在燃烧过程中，气体通过许多同时进行的过程混合、反应并产生热量，但这些过程中有些很快，有些则慢得多。 与时间尺度一样，这些过程的空间尺度也可以变化许多数量级。 现代燃烧室的设计和操作可以通过将全部复杂的反应减少到最少来推进，这些反应的缓慢动力学主导了系统的动力学。 该项目的重点是物理现实的系统组成的热量不完美的理想气体描述的详细化学动力学与阿克里乌斯温度依赖性，质量作用定律，和多组分扩散。 本研究将推进以前的工作，在开发一种技术，自动识别慢不变流形固有的反应动力学。 对于空间均匀系统，这种方法将需要通过一种新的方法来解决识别系统的大量物理和非物理平衡的困难代数问题。 从不稳定的不动点到稳定的物理不动点的数值积分将识别慢不变流形，这将被实现为简化化学动力学的合理方法中的关键。 然后，这些结果将被应用到更具挑战性的空间非均匀流与平流和扩散。所研究的系统将采用现实的模型，用于现代科学设计的实际工程系统。 注意力将集中在氢-空气燃烧动力学的详细模型。随着这项工作的进展，可以开发出更清洁，更高效的燃烧室来燃烧氢气和各种燃料。