A Novel Large Slosh-or-Spin Low-Speed Underwater Propulsor Bridges the Unsteady and Steady Propulsion Mechanisms of Nature and Engineering

Abstract

We have bridged the unsteady and steady mechanisms of underwater propulsion in nature and engineering by colocating their flapping and steady lifting surfaces in an outwardly conventional propulsor. The feasibility is indicated by the observation of overlap in the mechanisms in propulsion density versus displacement volume from 0.1 to 1 m $^{3}$ . Such an overlap also exists between natural and engineered flyers. A novel, 0.7-m diameter, propulsor has been built where the fins, twistable along their span (0 $^{\circ}$ to 30 $^{\circ}$ ), can either slosh (where roll, pitch, and twist of the fins vary independently) or spin (where the rotational rate, fin pitch, and twist vary independently). Here, we discuss the origin of the novelty of the propulsor, the production of small thrust by slosh and propeller (prop) modes, the control of thrust amplitude by spanwise twisting of the fin, and the abrupt reversing of thrust. The tow speeds are low and close to the minimum induced velocity required for thrust onset by the flapping mechanism in the present propulsor—0 to 0.09 m/s, the fin chord Reynolds number and shaft input power being $\leq$ 8, 250, and $ 1 W. Time-averaged measurements show that thrust is more sensitive to pitch amplitude than to twisting during hovering, an effect that is reversed during slow towing due to the reduction in the spanwise variation of angle of attack. During towing, twist is more effective in the slosh mode than in the prop mode. Steady and quasi-steady thrust modeling is done to compare with prop- and slosh-mode measurements, respectively. The departures of the models are interpreted to mean that the beneficial effects of twist on the leading edge vortex (LEV) augment slosh forces and the rotational effects are detrimental to prop forces. We present simultaneous videography of fins during twisting and thrust reversal, and of thrust time trace as direct evidence of the relationship of cause and effect. Spanwise fin twisting is used to show that near-zero levels of thrust (0 to 1 N in steps of approximately 0.1 N) can be produced in both the slosh and prop modes and can be controlled merely by twisting the fins while keeping all other fin parameters unchanged. Transient-free reversal of the thrust direction has been achieved in the slosh mode while maintaining the same absolute value of thrust. However, thrust reversal in the prop mode is not transient free. This prop-mode transient is weaker due to the change in sign of the pitch angle but a change in the direction of the hub rotation produces a large spike and the reasons are discussed. Fine thrust control with individual fin hydrodynamics at the source that involves the lowest change in inertia is smoother. Smooth thrust reversibility is clearly identified as a unique property of flapping fin hydrodynamics. The mechanism overlap occurs because both fin modes have similar low transitional Reynolds numbers. Dynamical system models of unsteady hydrodynamics and control are shown to be similar suggesting that animal swimmers control vortex shedding ion-by-ion and animal-like motion control is theoretically possible with the proposed propulsor in the slosh mode but not in the prop mode.