Award Date


Degree Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Committee Member

William G. Culbreth

Second Committee Member

Charlotta E. Sanders

Third Committee Member

Alexander Barzilov

Fourth Committee Member

Hualiang Teng

Number of Pages



The purpose of this study is to analyze the theoretical criticality of a spherical uranium-hexafluoride reactor with a transient, pulsed shockwave emanating from the center of the sphere in an outward-radial direction. This novel nuclear reactor design, based upon pulsed fission in a spherical enclosure is proposed for possible use in direct energy conversion, where the energy from fission products is captured through the use of electrostatic fields or through induction. An analysis of the dynamic behavior of the shockwave in this reactor is the subject of this thesis. As a shockwave travels through a fluid medium, the characteristics of the medium will change across the shockwave boundary. Pressure, temperature, and density are all affected by the shockwave. Changes in these parameters will affect the neutronic characteristics of a fissile medium. If the system is initially in a subcritical state, the increases in pressure, temperature, and density, all brought about by the introduction of the shockwave, will increase the reactivity of the nuclear system, creating a brief super critical state that will return to a subcritical state after the shockwave dissipates.

Two major problems are required to be solved for this system. One is the effects of the shockwave on the gas, and the second is the resulting effects on system criticality. These problems are coupled due to the unique nature of the speed of the expanding shockwave in the uranium-hexafluoride medium and the energy imparted to the system by the shockwave with respect to the fissile uranium-hexafluoride. Using compressible flow and shockwave theories, this study determines the properties of the gaseous medium for reference points before, during, and behind the shockwave as it passes through the fissile medium. These properties include pressure changes, temperature changes, and density changes that occur to the system. Using the parameters calculated from the shockwave, the neutron transport equation is solved with the appropriate boundary conditions to identify system criticality, neutron flux, and the appropriate changes to system variables such as buckling, and migration length. The analytical solution is then verified using MCNPX, a Monte Carlo method for computational analysis of the neutron transport equation. Through manipulation of the initial pressure of the system, which is intrinsically linked to the density of the system by the ideal gas Equation of State, neutron and flux multiplication trends are corroborated.

The results show that both compressible flow theory and shockwave theory are in relatively close agreement for parameter changes across, after, and along the shockwave expansion. The solution to the analytical transport equation is in good agreement with the results from MCNPX. The change in the effective multiplication factor is similar between both the analytical solution and the computational solution. Furthermore, a new method for determining the transient effective multiplication factor is devised. These results show the maximum criticality of the reactor is at the initiation of the shockwave. The shockwave creates a local supercriticality until the wave dissipates below Mach 1.

Several tools and methods are employed in this study, including the use of Monte Carlo numerical methods, Euler method solutions, and computer programs, such as MCNP, MATLAB, and Mathcad, which provide necessary the necessary computational abilities to understand the mathematical model of the system.


Criticality; Gaseous; Shockwave; Transient


Nuclear | Nuclear Engineering | Oil, Gas, and Energy