Effects of tunable stiffness on the hydrodynamics and flow features of a passive pitching panel

Abstract

Three-dimensional numerical simulations are carried out to study the hydrodynamic performance and flow features of a bio-inspired underwater propulsor. The propulsor is constituted by a passive pitching panel. The leading edge of the panel is prescribed under a periodic heaving motion while the panel pitches passively due to the employing of a stiffness-lumped torsional spring at the leading edge. Effects of the torsional spring stiffness have been put emphases on. A real-time tunable stiffness strategy is presented and employed in the study. We first study the passive pitching effects on the hydrodynamics and flow features of the panel using a series of constant stiffness and then we study the tunable stiffness effects using cosinusoidal curve based waveforms, in which the effects of phase difference (φ) between the stiffness profile and the oscillation motion and as well as the effects of stiffness fluctuation amplitude (Gk) are investigated, respectively. The stiffness profile beneficial for propulsion efficiency is further applied to cases with different oscillation amplitudes. A high-fidelity immersed boundary method based direct numerical simulation (DNS) solver is employed to acquire the fluid dynamics and to simulate the flow. The panel passive pitching motion is solved by coupling the DNS flow solver and the Euler rigid body dynamic equation. Results show that for the constant stiffness cases, the panel generates sinusoidal-like pitching motion, and in certain stiffness range, flexibility could benefit efficiency while holding some extent of stiffness could enhance the thrust. For the tunable stiffness cases, it is found that both the mean thrust and propulsive efficiency improved when the stiffness change is in-phase with the heaving motion (φ=0°). The largest mean thrust is found at φ=120°. The wake profile shows that in the constant stiffness cases and φ=120° case, the panel in each cycle generates a pair of elongated and twisted vortex tubes, the vortex tubes in each pair interconnected with each other and induces unprofitable interactions. While in the φ=0° case the panel generates a pair of round and closed vortex loops in each cycle and the vortex loops separated directly after they have been detached from the panel and thus avoided the unprofitable vortex interactions. The stiffness fluctuation amplitude (Gk) effects study (all employing the in-phase stiffness profile) shows that all the three tested cases (Gk=0.25G0,0.5G0,0.75G0) acquired thrust and efficiency enhancement while the Gk=0.5G0 case acquired the largest efficiency benefit and the Gk=0.75G0 case had the largest thrust. Wake profiles show entire vortex loops may not be formed when Gk is small while larger Gk may affect the arrangement of the vortex loops thus may generate unprofitable vortex interactions. The results of cases with motions with variable oscillating amplitudes (A∗) show employing the real-time altering stiffness profile (φ=0°,Gk=0.5G0) improves the propulsion performance in a certain range of A∗ (0.4≤A∗≤0.8). Results from this paper demonstrated the potential of using real-time tunable stiffness in the design of passive pitching propulsors of underwater vehicles that pursue higher performance.