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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 06 Aug 2024 18:00:39 -0700Algorithms for Reaction Mechanism Reduction and Numerical Simulation of Detonations Initiated by Projectiles
https://resolver.caltech.edu/CaltechCACR:2003.208
The evolution of a homogeneous, chemically reactive system with ns species forms a dy-namical
system in chemical state-space. Under suitable constraints, unique and stable equi-librium
exists and can be interpreted as zeroth-dimensional (point like) attractors in this
ns-dimensional space. At these equilibrium compositions, the rates of all reversible reac-tions
vanish and can, in fact, be determined from thermodynamics independent of chemical
kinetics.
Generalizing this concept, an m-dimensional Intrinsic Low Dimensional Manifold (ILDM)
represents an m-dimensional subspace in chemical state-space where all but the m-slowest
aggregate reactions are in equilibrium, and these aggregate reactions are determined by
eigenvalue considerations of the chemical kinetics. In this context, a certain composition is
said to be m-dimensional if it is on an m-, but not an (m – 1)-, dimensional ILDM.
Two new algorithms are proposed that allow the dimensionality of chemical composi-tions
be determined simply. The first method is based on recasting the Maas and Pope
algorithm. The second, and more efficient, method is inspired by the mathematical struc-ture
of the Maas and Pope algorithm and makes use of the technique known as arc-length
reparameterization. In addition, a new algorithm for the construction of ILDM, and the
application of these ideas to detonation simulations, is discussed.
In the second part of the thesis, numerical simulations of detonation waves initiated by
hypervelocity projectiles are presented. Using detailed kinetics, only the shock-induced com-bustion
regime is realized as simulating the conditions required for a stabilized detonation
is beyond the reach of our current computational resources. Resorting to a one-step irre-versible
reaction model, the transition from shock-induced combustion to stabilized oblique
detonation is observed, and an analysis of this transition based on the critical decay-rate
model of Kaneshige (1999) is presented.https://resolver.caltech.edu/CaltechCACR:2003.208