## University of New Orleans Theses and Dissertations

Spring 5-2021

#### Degree Type

Dissertation-Restricted

Ph.D.

#### Degree Program

Engineering and Applied Science

Mathematics

Linxiong Li

Xiaochuan Yu

#### Abstract

Nondimensionalization is powerful technique and is widely applied in the study of fluid mechanics and engineering because it helps to reduce the number of free parameters, identify the relative size of effects of parameters, and gain a deeper insight of the essential nature of phenomena. The nondimensionalization of 2D theory has been completed by the author (Zhen et.al.,2020) and new dimensionless equations of motion were obtained. In this study, new dimensionless dynamic equations are extended by incorporating new parameters to cope with various environmental conditions. The new dimensionless analysis of dropped cylindrical objects is consisted of four parts.

Part 1, the new dimensionless equations of motion for a dropped cylindrical object are presented and validated. Firstly, the importance of force and moment has been analyzed. Secondly, the effects of factors such as trailing edge, drag coefficient, and drop angle on trajectories of dropped objects are systematically investigated.

Part 2, turbulent boundary flow is considered to extend the new 2D dimensionless equations of motion for dropped cylinders. The cylinders are assumed to be dropped into the turbulent boundary flow. The effects of trailing edge, drag coefficient, and drop angle on trajectories of dropped object with turbulent boundary flow are investigated. It is found that results with turbulent boundary flow seem to agree with experimental results published in Aanesland (1987). Factors such as trailing edge, drag coefficient, and drop angle persistently show significant effects on features of trajectories.

Part 3, various forms of currents are considered to extend the the new 2D dimensionless equations of motion for dropped cylinders. The decreasing exponential current is used to simulate weakening surface current and sinusoidal current is applied to mimic effect of oscillating current. It is found that features of trajectories with uniform current are significant distinguished from those with exponential or sinusoidal currents.

Part 4, Gaussian process is implemented in the new 2D dimensionless equations of motion. The effect of randomness on trajectories is investigated by varying the variance of Gaussian process. It is found that variance demonstrates a significant effect on trajectories.

#### Rights

The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.

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