Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, United States of America.
Aerodynamics and Flight Mechanics Group, Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom.
Bioinspir Biomim. 2022 Sep 7;17(6). doi: 10.1088/1748-3190/ac7f70.
We present new measurements of non-uniformly flexible pitching foils fabricated with a rigid leading section joined to a flexible trailing section. This construction enables us to vary the bending pattern and resonance condition of the foils independently. A novel effective flexibility, defined as the ratio of added mass forces to elastic forces, is proposed and shown to provide a scaling for the natural frequencies of the fluid-structural system. Foils with very flexible trailing sections of< 1.81 × 10N mdo not show a detectable resonance and are classified as 'non-resonating' as opposed to 'resonating' foils. Moreover, the non-resonating foils exhibit a novel bending pattern where the foil has a discontinuous hinge-like deflection instead of the smooth beam-like deflection of the resonating foils. Performance measurements reveal that both resonating and non-resonating foils can achieve high propulsive efficiencies of around 50% or more. It is discovered that non-uniformly flexible foils outperform their rigid and uniformly flexible counterparts, and that there is an optimal flexion ratio from 0.4 ⩽⩽ 0.7 that maximizes the efficiency. Furthermore, this optimal range coincides with the flexion ratios observed in nature. Performance is also compared under the same dimensionless flexural rigidity,*, which highlights that at the same flexion ratio more flexible foils achieve higher peak efficiencies. Overall, to achieve high propulsive efficiency non-uniformly flexible hydrofoils should (1) oscillate above their first natural frequency, (2) have a flexion ratio in the range of 0.4 ⩽⩽ 0.7 and (3) have a small dimensionless rigidity at their optimal flexion ratio. Scaling laws for rigid pitching foils are found to be valid for non-uniformly flexible foils as long as the measured amplitude response is used and the deflection angle of the trailing section is < 45°. This work provides guidance for the development of high-performance underwater vehicles using simple purely pitching bio-inspired propulsive drives.
我们提出了新的测量结果，这些结果来自于具有刚性前缘和柔性后缘的非均匀柔性俯仰翼型。这种结构使我们能够独立地改变翼型的弯曲模式和共振条件。提出了一种新的有效柔性，定义为附加质量力与弹性力的比值，并表明它可以为流固系统的固有频率提供一个标度。具有非常柔性后缘（<1.81×10-5N m）的翼型不会显示出可检测的共振，并且被归类为“非共振”翼型，而不是“共振”翼型。此外，非共振翼型表现出一种新的弯曲模式，其中翼型具有不连续的铰链状挠度，而不是共振翼型的光滑梁状挠度。性能测量表明，共振和非共振翼型都可以实现高达 50%或更高的高推进效率。发现非均匀柔性翼型的性能优于其刚性和均匀柔性对应物，并且存在一个最优的弯曲比（0.4 ⩽⩽ 0.7），可以最大化效率。此外，这个最优范围与自然界中观察到的弯曲比相吻合。在相同的无量纲弯曲刚度*下也进行了性能比较，这突出表明在相同的弯曲比下，更灵活的翼型可以达到更高的峰值效率。总的来说，为了实现高推进效率，非均匀柔性水翼应该（1）在其第一固有频率以上振荡，（2）在 0.4 ⩽⩽ 0.7 的弯曲比范围内，（3）在其最优弯曲比处具有小的无量纲刚度。发现刚性俯仰翼型的标度律在只要使用测量的幅度响应并且后缘的挠度角<45°时，对非均匀柔性翼型仍然有效。这项工作为使用简单的纯俯仰仿生推进驱动器开发高性能水下交通工具提供了指导。
