Experiments on the Effects of Reynolds Number and Advance Ratio on the Unfolding of Disorganization in Low-Speed Underwater Propulsors With Vibrating Blades

Abstract

Ships and submarines are acoustic hazards to marine life. The rational control of acoustic radiation would be possible at least at low Reynolds numbers if the underlying organization buried in seeming randomness is revealed. We build a novel low-speed propulsor where all blades undergo small-amplitude pitch oscillation while spinning at large pitch angles at transitional chord Reynolds numbers (3.75 × 103 ≤ Rec ≤ 3.75 × 104) and advance ratios (0.51 ≤ J ≤ 4.89). We measure and model time-averaged and temporal thrust. The relationship between the time-averaged and the temporal thrust is observed when the latter is mapped as limit cycle oscillation (LCO), or departure from it. High-thrust coefficients occurring at large (30 deg and 45 deg) angles of amplitude of blade vibration are modeled assuming poststall lift enhancement due to flapping blades when a leading edge vortex (LEV) forms, while the lower thrust coefficients occurring at 20 deg are modeled by its absence. The disorganization in temporal thrust increases with J and Rec. An external orthogonal oscillator, perhaps a vibration, is modeled to couple with the thrust oscillator for temporal control of disorganization. The unfolding disorganization is seen as a departure from LCO, and it is attenuated by smooth-wall boundary-layer fencing, compared to unfenced smooth and rough surfaces. When the fencing properties of the leading edge tubercles of whale fins are recognized, the ratio of the spacing of the fences and chord is found to be similar (0.5–1.0) in both whale flippers and aircraft wings.

Multistable autonomous motion of fruit on a smooth hotplate

“…( a ) Plume array from kernels; Ri > 1.0 (middle), Ri = 1.0 (sides). ( b ) Unstable plumes in hot-cold side boundaries; numbers 1 and 2 on right show plume multistability; also shows advancing disorganization 33 in the middle plume cluster; however, only multistability is seen in the sides, triggered by a small increase in Ri from 1.0 and Re from 3.0. ( c ) Summary schema demonstrating the different stages of instability advance to chaos in varying physical domains, all co-existing.…”

A Hemispherical Motor Oscillator for Experiments on Swimming and Flying of Small Animals

“…Overall, Fig. 2 may be seen as a heuristic method of flow visualization or synthesis where there is an underlying limit cycle organization [8].…”

“…In other words, the individual thrust oscillations do not "lock-in" because of the excess energy in the system per cycle of oscillation [7]. In a recent study in our laboratory on a conventional propulsor but with vibrating blades at transitional values of 3.75 Â 10 3 Re c 3.75 Â 10 4 , it has also been found that the emergence of patterns of disorganized limit cycles of thrust is episodic and not continuous [8]. This suggested that smaller animals have more initial condition-dependent mechanisms.…”