Date of Award

5-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Bogdan Nita

Committee Member

Ashwin Vaidya

Committee Member

Arup Mukherjee

Abstract

We discuss the equilibrium configurations of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s. Experimental results are presented with both two-dimensional and three-dimensional numerical simulations used to model this problem. We present the effects of flow speed and initial configuration angle between the fiber and the direction of the flow. Investigations reveal that both the orientation of the fiber and the fiber length have a significant impact on the deformation of the fiber as well as on the forces it experiences. Specifically, we measure the drag and lift experienced by the system and measure them against known values in literature. We note, additionally, that longer fibers (i) bend significantly more than shorter fibers and (ii) display oscillatory or flapping motion at much lower flow speeds than their shorter counterparts. In the two-dimensional simulations we reveal that the drag on the fiber is noticeably affected by the size of the sphere. The analysis of the drag is done in terms of Vogel exponents, computed in both 2-D and 3-D, and is compared with the literature. The validity of the reduction of dimensionality is tested against the three-dimensional simulations and qualitatively compared. Both mesh density and convergence studies are performed in 2-D and 3-D to balance the accuracy and convergence rates. We also discuss the robustness of the three-dimensional model and the practicalities of using a lower-dimensional model.

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