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J。这项研究的目的是开发强大的数学和计算工具，以合理和有效地预测反应气体混合物的动力学。在燃烧中，气体混合、反应并通过许多同时过程产生热量，但这些过程中有些很快，有些则慢得多。像时间尺度一样，这些过程的空间尺度可能会有许多数量级的变化。现代燃烧器的设计和运行可以通过将整个复杂的反应集减少到最小，基本的少数反应的慢动态主导系统的动力学来推进。这个项目的重点是物理现实系统，由热量不完美的理想气体组成，由阿累尼乌斯温度依赖关系、质量作用定律和多组分扩散的详细化学动力学描述。这项研究将推进之前的工作，开发一种技术，自动识别反应动力学固有的慢不变流形。对于空间均匀系统，这种方法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这一困难的代数问题。从不稳定不动点到稳定物理不动点的数值积分将确定慢不变流形，而慢不变流形将成为简化化学动力学的合理方法的关键。然后，这些结果将应用于更具挑战性的具有平流和扩散的空间非均匀流动。所研究的系统将采用在实际工程系统的现代科学设计中使用的现实模型。人们的注意力将集中在氢-空气燃烧动力学的详细模型上。随着这项工作有望取得进展，可以开发出更清洁、更高效的燃烧器来燃烧氢气和各种燃料。

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.