## Electronic Theses and Dissertations

2011

Dissertation

Ph.D.

#### Department

Mechanical, Automotive, and Materials Engineering

#### First Advisor

Rankin, Gary (Mechanical, Automotive, and Materials Engineering)

#### Keywords

Mechanical Engineering.

CC BY-NC-ND 4.0

#### Abstract

The added mass for cylinders and spheres is examined for unidirectional constant acceleration. In the case of cylinders, a numerical model is developed to determine the forces acting on the cylinder. The results of the model are compared to published experimental results and demonstrated to be a reasonable representation of the forces of an accelerating fluid acting on a stationary cylinder. This model is then used to investigate the effect of a constant non-zero velocity before the constant acceleration portion of the flow. Two different non-zero initial velocities are used as well as three different constant unidirectional accelerations and three different diameters. All sets of numerical experiments are shown to produce results that correlated very well when presented in terms of dimensionless forces and dimensionless distance. Two methods are presented for splitting the total force into unsteady drag and added mass components. The first method is based on the linear form of the equation that relates the dimensionless force, added mass, unsteady viscous drag and the dimensionless displacement. The slope includes the unsteady drag coefficient and the y-intercept includes the added mass coefficient. The second method, the Optimized Cubic Spline Method (OCSM), uses cubic splines to approximate the added mass coefficient and the unsteady drag coefficient variation with dimensionless distance. The parameters are optimized using the method of least squares. Both methods are compared with the experimental results. The OCSM produces better results therefore it is applied to the numerical experiment results. The added mass coefficient for the initial portion of the acceleration of a sphere is studied experimentally using a high speed camera to determine the displacement of the sphere and subsequently the acceleration of the sphere. From the acceleration data and a mathematical model of the process, the dimensionless force on the sphere is calculated. The added mass is then determined using two approaches. For the first case the viscous drag is neglected and in the second case viscous drag is included by applying the OCSM. For small values of dimensionless distance, both methods produce added mass values close to those predicted by potential flow theory.

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