Author ORCID Identifier

Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation




Mechanical Engineering

First Advisor

Dr. Kozo Saito

Second Advisor

Dr. Nelson Akafuah


A component of the mission in the Institute of Research for Technology Development at the University of Kentucky is advancing research and development and bringing it to the factory floor for continuous improvement. This dissertation delves into the art and science of rotational fluid mechanics in the context of rotary bell atomizers. One outcome proves that an approximation for calculating fluid film thicknesses on high-speed spinning surfaces inferred while working in cylindrical and spherical coordinate systems can be applied to an arbitrary bell profile. However, the analytical limits of this approximation were not investigated. In all cases, a restriction exists that the bell profile curvature is much greater than the fluid film thickness. The validity of this approximation was supported by findings in publications employing curvilinear coordinates created by axisymmetric revolution of a planar curve. This validation enabled rigorous analyses of bell profiles beyond the common cylindrical or spherical profiles. A curvilinear system containing a coordinate of arc length along the bell profile is the arbitrary case, and the most reduced high-speed case collapses to an approximation from an observed pattern in simpler coordinate systems. The jump to varying curvature curvilinear coordinates requires additional mathematics to calculate metric tensor coefficients and spatial derivatives of directional unit vectors, and to develop lengthy vector invariants. Another outcome was to explain the underlying symmetry in the reduced order solution for a coupled rotary system that included centrifugal and Coriolis effects on a conical rotary bell.

Digital Object Identifier (DOI)

Funding Information

I received support and funding, 2017 through 2020, as a TA and RA from the University of Kentucky Mechanical Engineering Department.