MS17.1: Fluid-Structure Interaction

Adding flexibility to flapping tails enhances swimming performance in terms of thrust generation and efficiency. To date, the majority of studies aiming at assessing this enhancement are concerned with the case of uniform flexural rigidity. Yet, it has been determined that varying this rigidity could further enhance the swimming performance. This study is concerned with assessing the impact of varying the flexural rigidity on different aspects of thrust generation including the beam deflection and flow dynamics along the flexible tail, and the level of generated circulation in the tail's wake.

Purcell’s swimmer is a well-known planar model of a swimming microorganism, comprised of three rigid links connected by actuated rotary joints. This model has been analyzed as a robotic locomotion system governed by first-order nonlinear dynamics with two periodic inputs. In this work we present a macro-scale realization of a three-link robotic swimmer moving in a highly viscous fluid. We propose a simple variant of Purcell’s model with unequal links and a central rigid sphere which represents the added drag of the robot’s central flotation block, and calibrate the model’s parameters to fit experimental measurements. Next, we apply optimal control formulation based on Pontryagin’s Maximum Principle (PMP) in order to find optimal periodic gaits for maximizing the displacement per cycle under bounds on the of joint angles. Employing differential geometric method that transforms the problem to area integral enclosed by the gait trajectory enables visual interpretation which explains topological changes in optimal gaits upon varying the joint angle bounds. Finally, we apply PMP formulation to the problem of maximizing Lighthill’s energy efficiency in order to obtain a boundary value problem whose solution gives energy-optimal gaits for Purcell’s swimmer as well as its variant with a central sphere.

The post-critical aeroelastic behavior of horizontal, suspended, shallow cables is analyzed via a continuous model. Perturbation methods are directly applied to the Partial Differential Equations (PDE) of motion. They are obtained after the formulation of the aerodynamic model, which takes into account the change of the equilibrium configuration of the cable related to the mean wind forces. Bifurcation equations, ruling the galloping and post-galloping behavior, are evaluated and the relevant outcomes are compared with those obtained by numerical simulations.