Author

Fanny Thomas

Date of Award

5-2017

Document Type

Thesis - Open Access

Degree Name

Master of Science in Aerospace Engineering

Department

Graduate Studies

Committee Chair

Dr. Eric Perrell

First Committee Member

Dr. Narayanaswami

Second Committee Member

Dr. Engblom

Abstract

With renewed interest in planetary atmospheric entry, descent, and landing, NASA has noted a need for improved physics modeling in computational fluid dynamics. Uncertainty in experimental data used in radiation heat transfer computations leads to “over-engineering” of entry body heat shields, at large weight and cost penalties. There is interest in developing hypersonic thermophysics models from the known “first principles” of physics.

A method for computing high temperature gas emissivity and absorptivity from quantum mechanics principles is developed. The Schroedinger wave equation is cast as a discretized matrix eigenvalue problem which is solved using the ERAU parallel supercomputer. The numerical solutions for the wave functions are then integrated to determine the Einstein coefficients for emission and absorption, and hence the gas properties are tabulated as functions of temperature and pressure.

All of the published works found thus far assume Dirichlet or von Neumann boundary conditions for the eigenvalue problem. At best this presumes a priori knowledge of the solution. In general, it is incorrect. The novel boundary condition treatment used here admits simultaneous solution for several wave functions, unlike the “shooting methods” in most textbooks. Therefore the novel boundary condition treatment is used in this thesis. The hydrogen atom is studied, as analytical solutions for verification exist. Numerical solutions have been completed and compare very well with analytical solutions, and with experimental data maintained by National Institutes of Standards (NIST).

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