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 ( G k ) 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 ( G k ) effects study (all employing the in-phase stiffness profile) shows that all the three tested cases ( G k = 0 . 25 G 0 , 0 . 5 G 0 , 0 . 75 G 0 ) acquired thrust and efficiency enhancement while the G k = 0 . 5 G 0 case acquired the largest efficiency benefit and the G k = 0 . 75 G 0 case had the largest thrust. Wake profiles show entire vortex loops may not be formed when G k is small while larger G k 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 ° , G k = 0 . 5 G 0 ) 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.

中文翻译：

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可调刚度对被动俯仰板流体动力学和流动特性的影响

摘要 通过三维数值模拟研究仿生水下推进器的水动力性能和流动特性。推进器由被动俯仰面板构成。由于在前缘采用了刚度集中的扭转弹簧，面板的前缘在周期性的起伏运动下进行规定，而面板则被动地俯仰。扭转弹簧刚度的影响已得到重视。在研究中提出并采用了一种实时可调刚度策略。我们首先使用一系列恒定刚度研究被动俯仰对面板流体动力学和流动特性的影响，然后我们使用基于余弦曲线的波形研究可调刚度效应，其中分别研究了刚度分布和振荡运动之间的相位差 ( φ ) 的影响以及刚度波动幅度 ( G k ) 的影响。有利于推进效率的刚度曲线进一步应用于具有不同振幅的情况。采用基于直接数值模拟 (DNS) 求解器的高保真浸入边界法来获取流体动力学并模拟流动。通过耦合 DNS 流求解器和欧拉刚体动力学方程来求解面板被动俯仰运动。结果表明，在恒定刚度情况下，面板产生类似正弦曲线的俯仰运动，并且在一定刚度范围内，灵活性可以提高效率，同时保持一定程度的刚度可以增强推力。对于可调刚度的情况，发现当刚度变化与垂荡运动同相（φ = 0°）时，平均推力和推进效率都提高了。最大平均推力出现在 φ = 120 ° 处。尾流剖面显示，在恒定刚度情况下和 φ = 120° 情况下，每个循环中的面板都会产生一对细长和扭曲的涡流管，每对涡流管相互连接并导致无利可图的相互作用。而在 φ = 0 ° 的情况下，面板在每个循环中都会产生一对圆形的闭合涡流环，涡流环在从面板上分离后直接分离，从而避免了无益的涡流相互作用。刚度波动幅度 ( G k ) 影响研究（均采用同相刚度曲线）表明，所有三个测试情况（ G k = 0 . 25 G 0 , 0 . 5 G 0 , 0 . 75 G 0 ）都获得了当 G k = 0 时，推力和效率增强。5 G 0 情况获得了最大的效率收益并且G k = 0 。75 G 0 机箱推力最大。尾流剖面显示当 G k 较小时可能不会形成整个涡流环，而较大的 G k 可能会影响涡流环的排列，从而可能产生无益的涡流相互作用。具有可变振荡幅度 ( A * ) 的运动情况的结果表明，采用实时改变刚度曲线 ( φ = 0 ° , G k = 0 . 5 G 0 ) 提高了 A * ( 0 . 4 ≤ A ∗ ≤ 0 . 8 )。