Physics – Condensed Matter – Statistical Mechanics
Scientific paper
Feb 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phdt........61h&link_type=abstract
Thesis (PH.D.)--STANFORD UNIVERSITY, 1991.Source: Dissertation Abstracts International, Volume: 52-01, Section: B, page: 0363.
Physics
Condensed Matter
Statistical Mechanics
Reactive Flow, Vibrational Relaxation
Scientific paper
The finite rates of reactions and thermal excitation processes in a gas result in thermochemical non-equilibrium in the hypersonic rarefied flowfield associated with vehicles during atmospheric entry. The low-density nature of this flow is such that the familiar Navier-Stokes equations are not applicable. Alternatively, particle simulation methods circumvent the difficulties of rarefaction by modeling the gas as a collection of moving and colliding particles in accordance with the principles of kinetic theory and statistical mechanics. The Direct Simulation Monte Carlo (DSMC) method of Bird has been applied extensively but is limited by excessive computational expense. An alternative particle simulation, tailored specifically to the vector-processing architecture of modern supercomputers, has been developed by Baganoff and McDonald to optimize computational performance in modeling the three-dimensional non-reactive flow of general gas mixtures including simple models for rotational and vibrational relaxation. The objective of this thesis is to extend the vectorized simulation to treat chemically reactive flows and to enhance the models for vibrational relaxation. A collision selection rule has been developed to yield vibrational relaxation rates which match the experimental fits of Millikan and White. Selection rules for dissociation, atomic exchange, and recombination reactions were developed to yield reaction rates which match those dictated by the Arrhenius experimental fits over the temperature range of interest. The vibrational relaxation mechanics model of McDonald was modified for application to both the simple harmonic and anharmonic oscillator descriptions of the quantized vibrational mode. Reaction mechanics are modeled by proportional addition or removal of reaction energy from each contributing mode in a collision. All of these models retain computational simplicity while satisfying detailed balance and promoting equilibrium. An improved reaction model is introduced which accounts for the coupling of vibrational excitation and reaction processes, and leads to the characteristic dissociation incubation behavior as observed experimentally. These models are verified through simulation of constant-volume gas reservoirs during thermal and chemical relaxation. Steady-state behavior compares well with known equilibrium results. Transient behavior compares well with solutions of time-dependent differential reaction rate equations governing species concentrations in air during chemical relaxation. The non-equilibrium flow about a circular cylinder is simulated to demonstrate application of this extended vectorized particle method to multi-dimensional reactive flows. In all, these phenomenological thermochemistry models enhance the existing vectorized particle simulation while retaining computational efficiency.
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