A fluid─structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness

The effect of non-uniform chordwise stiffness distribution on the self-propulsive performance of three-dimensional flexible plates is studied numerically. Some typical stiffness distributions, including uniform, declining, and growing distribution, are considered. First, the normalized bending stiffness K is derived, which can well represent the overall bending stiffness of the non-uniform plates. For different non-uniformly distributed plates with the same K, the maximum displacement difference between the trailing and leading edges of the plate during the flapping is almost identical. There exists a common optimal K at which all the plates achieve their optimal performance, i.e., the highest cruising speed and efficiency. Second, we reveal what kind of non-uniform distribution could be the best at a specific K in terms of the propulsive performance. The force analysis indicates that a larger bending deformation in the anterior part for the growing distribution leads to a larger thrust. Hence, the large local slope along the anterior flexible plate is preferred to enhance the propulsive performance. The results obtained in this study may shed some light on a better understanding of the hydrodynamic effect on the self-propulsion of the non-uniform stiffness wings or fins of animals.

Optimal chordwise stiffness distribution for self-propelled heaving flexible plates

Flow over a traveling wavy foil attached with a flexible plate has been numerically investigated using the lattice Boltzmann method combined with the immersed boundary method. The influence of the flexibility and length of the caudal fin on the locomotion of swimming fish through this simplified model, whereas the fish body is modeled by the undulating foil and the caudal fin by the plate passively flapping as a consequence of fluid-structure interaction. It is found that the plate flexibility denoted by the bending stiffness, as well as the length ratio of tail and body, plays an important role in improving thrust generation and propulsive efficiency. It is also revealed that there exists a parameter region of the plate length and stiffness, in which positive propeller efficiency can be achieved. The effect of the passively flapping flexible plate on the pressure field and the vortex production on the wake is further discussed. It is found that when the length ratio of caudal fin and body is greater than 0.2, a reverse von Karman vortex street occurs when the bending stiffness is about greater than 1.0, and a great thrust is generated as a result of a large pressure difference occurring across the flexible plate. This work provides physical insight into the role of the caudal fin in fish swimming and may inspire the design of robotic fish.

Length and stiffness effects of the attached flexible plate on the flow over a traveling wavy foil

This paper addresses hydrodynamic performance of fins regarding their trailing edge convexity–concavity and flexibility distribution. The effects of trailing edge convexity–concavity on propulsive performance and vortex dynamics were investigated experimentally utilizing time-resolved particle image velocimetry and force sensors. It was found that the convex trailing edge shape always outperforms the concave shape. Wake contracting by the bent shape of the trailing edge vortex of a convex trapezoidal form resulted in higher thrust and efficiency. The results also showed that the rounded edges of fish fins did not provide additional hydrodynamic advantages. Furthermore, we found that a gradually flexible fin delivered better propulsive performance over a uniformly flexible fin. The hydrodynamic performance of the flexible fins depended on the strength and relative positions of the trailing edge vortexes shed by each fin, which were affected by the flexible deformations of the fins. In the lower Reynolds number operation (approaching, but below the first resonant mode), the fins with larger camber produced a stronger momentum footprint especially considering the far wake elements, while in the higher Reynolds number range due to resonant deformation the extent of trailing edge excursion became dominant in affecting the propulsive performance. The results showed that gradually flexible fins can improve the performance of future watercraft.

Effects of gradual flexibility and trailing edge shape on propulsive performance of pitching fins

Drag-based swimming is usually accompanied with the shape change of rowing appendages to generate asymmetric force during the power stroke and recovery stroke. To implement this in an aquatic robot, one may actively control the surface area of its legs during the swimming. However, a small sized robot with a limited number of actuators should adjust the surface area of legs in passive manner. For this reason, we proposed a novel articulated leg with flexible appendages inspired by a water beetle. These leg structures were designed to implement an efficient recovery stroke with less resistive force during the recovery stroke, while its surface area was increased again if suitable relaxation time was applied to perform improved power stroke. To identify an optimal leg design, 36 different types were fabricated by changing the passive joint thickness, appendage materials, length, and morphology. Several correlations and dominant parameters were identified, and it was shown that the swimming leg with fixed joint and appendage stiffness cannot always generate the largest torque in all the swimming frequency. Also, a two-dimensional dynamic model was proposed based on an underactuated manipulator, and the model validation was proceeded by comparing with two selected leg designs. In addition, a 5.5 cm long robot with one pair of legs was built to further investigate their locomotory performance. By varying the beating frequency and relaxation time, thorough analysis was addressed in terms of the position, velocity, non-dimensional traveled distance, Strouhal number, and quasi-propulsive efficiency. Here, some important relationships between dimensionless numbers were established. Furthermore, it was found that introducing a relaxation phase between the power stroke and recovery stroke can increase the traveled distance per stroke with slight expense of propulsive efficiency.

https://iopscience.iop.org/article/10.1088/1748-3190/ab36c0/pdf

Srinivasa Reddy N

Papers

Effect of flexural stiffness distribution of a fin on propulsion performance