טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentElfasi Roei
SubjectInteraction between Two Closely-Spaced Waving Slender
Elastic Cylinders Immersed in a Viscous Fluid
DepartmentDepartment of Autonomous Systems and Robotics
Supervisors Professor Amir Gat
Dr. Yossef Elimelech
Full Thesis textFull thesis text - English Version


Abstract

We study the hydrodynamic interaction between two closely-spaced waving elastic cylinders immersed within a viscous liquid, at the creeping flow regime. The cylinders are actuated by a forced oscillation of the slope at their clamped end and are free at the opposite end. We obtain an expression for the interac- tion force and apply an asymptotic expansion based on a small parameter rep- resenting the ratio between the elastic deflections and the distance between the cylinders. The leading-order solution is an asymmetric oscillation pattern at the two frequencies (ω1, ω2) in which the cylinders are actuated. Higher orders oscillate at frequencies which are combinations of the actuation frequencies, where the first-order includes the 2ω1, 2ω2, ω1 ω2, and ω1 − ω2 harmonics. For in-phase actuation with ω1 = ω2, the deflection dynamics are identical to an isolated cylinder with a modified Sperm number. For configurations with ω1 ≈ ω2, the ω1 − ω2 mode represents the dominant first-order interaction effect due to significantly smaller effective Sperm number. Experiments are conducted to verify and illustrate the theoretical predictions. Force calcula- tion were made to examine the predicted benefits of two cylinder interaction. It was found that anti-phase beating is more efficient than the in-phase sce- nario, in contrast with the commonly used assumptions of maximal efficiency of the synchronised states. Finally, it was found that when two cylinders are connected to the same body, it is possible to create turning manoeuvres simply by changing the phase difference between the cylinders.