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

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来合理有效地预测反应气体混合物的动力学。在燃烧过程中，气体通过许多同时发生的过程混合、反应并产生热量，但其中有些过程很快，有些则慢得多。与时间尺度一样，这些过程的空间尺度也会有许多数量级的变化。现代燃烧器的设计和操作可以通过将完整的、复杂的反应集减少到最小的、必要的少数反应来推进，这些反应的缓慢动力学支配着系统的动力学。这个项目的重点是物理上现实的系统，由热量不完美的理想气体组成，由详细的化学动力学与阿累尼乌斯温度依赖，质量作用定律和多组分扩散描述。本研究将推进先前的工作，开发一种技术，以自动识别固有的反应动力学慢不变流形。对于空间齐次系统，该方法需要通过一种新颖的方法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出慢不变流形，这将成为简化化学动力学的合理方法的关键。这些结果将随后应用于具有平流和扩散的更具挑战性的空间非均匀流动。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。注意力将集中在氢-空气燃烧动力学的详细模型上。随着这项工作的进展，更清洁、更高效的燃烧器可以被开发出来，既可以燃烧氢，也可以燃烧各种各样的燃料。

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.