An autonomous flexible propulsor in a quiescent flow

Flapping motions of wings and fins are common in nature. Living organisms use such motions to float in a fluid or to propel themselves forward. Some entities, such as tadpoles, use distinct flexible components to generate propulsion. Here we introduce a propulsor consisting of a rigid circular head containing an energy source and a flexible fin for propulsion. The head imparts a sinusoidal torque to the leading edge of the fin and the flexible fin flaps along the leading edge. The flexible propulsor thus moves via an oscillating relative angle between the head and the leading edge of the fin. Unlike a self-propelled heaving and pitching fin, our ‘autonomous’ flexible propulsor has no prescribed motion or constraint referenced from outside coordinates. The immersed boundary method was used to model the interaction between the flexible propulsor and the surrounding fluid. A penalty method, in which the head and fin imparted a periodic torque to each other, was used to connect the head and the fin. The cruising speed and propulsive efficiency of the propulsor were explored as a function of the ratio of the head size to the fin length (D/L), the pitching amplitude (θ_p) and the pitching frequency (f). The cruising speed and the equilibrium position (g_eq) of the flexible propulsor near the ground were also examined. The optimal propulsive efficiency was achieved at the head ratio of D/L = 0.2 at θ_p = 30° and f = 0.2. The cruising speed of the flexible propulsor increased when operating near the ground. The gap distance between the propulsor and the ground was dynamically determined by the pitching motion.