J. M. Powers, S. Paolucci, A. J. Sommese, and C. W. Wampler
The 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.
