Numerical Analysis of the Effect of Flexibility on the Propulsive Performance of a Heaving Hydrofoil Undergoing Sinusoidal and Non-Sinusoidal Motions

Numerical simulations of fluid-structure interaction (FSI) on an elastic foil heaving with constant amplitude in freestream flow are carried out at a low Reynolds number of 20,000. The commercial software STAR-CCM+ is employed to solve the flow field and the large-scale passive deformation of the structure. The results show that introducing a certain degree of flexibility significantly improves the thrust and efficiency of the foil. For each Strouhal number St considered, an optimal flexibility exists for thrust; however, the propulsive efficiency keeps increasing with the increase in flexibility. The visualisation of the vorticity fields elucidates the improvement of the propulsive characteristics by flexibility. Furthermore, the mechanism of thrust generation is discussed by comparing the time-varying thrust coefficient and vortex structure in the wake for both rigid and elastic foils. Finally, in addition to sinusoidal motions, we also consider the effect of non-sinusoidal trajectories defined by flattening parameter S on the propulsive characteristics for both rigid and elastic foils. The non-sinusoidal trajectories defined by S=2 are associated with the maximum thrust, and the highest values of propulsive efficiency are obtained with S=0.5 among the cases considered in this work.

Contrasting thrust generation mechanics and energetics of flapping foil locomotory states characterized by a unified - scaling

Self-propelled flapping foils with distinct locomotion-enabling kinematic restraints exhibit a remarkably similar Strouhal number ( $St$ )-Reynolds number ( $Re$ ) dependence. This similarity has been hypothesized to pervade diverse forms of oscillatory self-propulsion and undulatory biolocomotion; however, its genesis and implications on the energetic cost of locomotion remain elusive. Here, using high-resolution simulations of translationally free and restrained foils that self-propel as they are pitched, we demonstrate that a generality in the $St$ - $Re$ relationship can emerge despite significant disparities in thrust generation mechanics and locomotory performance. Specifically, owing to a recoil reaction induced passive heave, the fluid's inertial response to the prescribed rotational pitch, the principal source of thrust in unidirectionally free and towed configurations, ceases to produce thrust in a bidirectionally free configuration. Rather, the thrust generated from the leading edge suction mechanics self-propels a bidirectionally free pitching foil. Owing to the foregoing distinction in the thrust generation mechanics, the $St$ - $Re$ relationships for the bidirectionally and unidirectionally free/towed foils are dissimilar and pitching amplitude dependent, but specifically for large reduced frequencies, converge to a previously reported unified power law. Importantly, to propel at a given mean forward speed, the bidirectionally free foil must counteract the out-of-phase passive heave through a more intense rotational pitch, resulting in an appreciably higher power consumption over the range $10 \leq Re \leq 10^3$ . We highlight the critical role of thrust in introducing an offset in the $St$ - $Re$ relation, and through its amplification, being ultimately responsible for the considerable disparity in the locomotory performance of differentially constrained foils.

Evolution of wake structures behind oscillating hydrofoils with combined heaving and pitching motion

The wake of an oscillating teardrop hydrofoil with combined heaving and pitching motion was studied numerically at Reynolds number of 8000 and Strouhal numbers of $St=0.21{-}0.94$ . The lower Strouhal number exhibited high efficiency propulsion with small thrust generation. However, larger thrust generation at high $St$ required more power, which lowered the propulsive efficiency. Quantitative assessment of vortex evolution, along with qualitative investigation of the formation and interaction of primary structures, revealed the association with elliptic instability characteristics for both co-rotating and counter-rotating vortex structures in both wakes. With respect to advection of the leading-edge vortex, the pressure distribution further depicted evidence of spanwise instability with distinct temporal evolution along the suction and pressure surfaces of the oscillating foil. Three-dimensional assessment of wake structures located downstream of the trailing edge depicted the existence of dislocations associated with primary vortex ‘rollers’. At low $St$ , these were limited to fine spanwise corrugations (valleys and bulges) on weaker leading edge rollers, which enlarged as the rollers advected downstream. In contrast, at high $St$ , the wake exhibited conjoint hairpin-horseshoe vortex structures that led to stronger deformations on the coupled vortex rollers. The statistical characteristics of secondary structures resembled the long wavelength mode and mode A identified previously for purely pitching and heaving foils, respectively. They also mimicked mode B for stationary cylinders. Novel wake models are introduced based on a complete vivid three-dimensional depiction of coherent wake structures.

Kinematics and hydrodynamics analyses of swimming penguins: wing bending improves propulsion performance

Penguins are adapted to underwater life and have excellent swimming abilities. Although previous motion analyses revealed their basic swimming characteristics, the details of the 3-D wing kinematics, wing deformation, and thrust generation mechanism of penguins are still largely unknown. In this study, we recorded the forward and horizontal swimming of gentoo penguins Pygoscelis papua at an aquarium with multiple underwater action cameras and then performed a 3-D motion analysis. We also conducted a series of water tunnel experiments with a 3-D printed rigid wing to obtain the lift and drag coefficients in the gliding configuration. Using these coefficients, the thrust force during flapping was calculated in a quasi-steady manner, where the following two wing models were considered: (1) an “original” wing model reconstructed from 3-D motion analysis including bending deformation and (2) a “flat” wing model obtained by flattening the original wing model. The resultant body trajectory showed that the penguin accelerated forward during both upstroke and downstroke. The motion analysis of the two wing models revealed that considerable bending occurred in the original wing, which reduced its angle of attack during upstroke in particular. Consequently, the calculated stroke-averaged thrust was larger for the original wing than for the flat wing during upstroke. In addition, the original wing required less work for flapping, indicating more efficient propulsion. Our results unveil a detailed mechanism of lift-based propulsion in penguins and underscore the importance of wing bending.

Development of a Multi-Segment Parallel Compressor Model for a Boundary Layer Ingesting Fuselage Fan Stage

The present methodological study aims to assess boundary layer ingestion (BLI) as a promising method to improve propulsion efficiency. BLI utilizes the low momentum inflow of the wing or fuselage boundary layer for thrust generation in order to minimize the required propulsive power for a given amount of thrust for wing or fuselage-embedded engines. A multi-segment parallel compressor model (PCM) is developed to calculate the power saving from full annular BLI as occurring at a fuselage tail center-mounted aircraft engine, employing radially subdivided fan characteristics. Applying this methodology, adverse effects on the fan performance due to varying inlet distortions depending on flight operating point as well as upstream boundary layer suction can be taken into account. This marks one step onto a further segmented PCM model for general cases of BLI-induced inlet distortion and allows the evaluation of synergies between combined BLI and active laminar flow control as a drag reduction measure. This study, therefore, presents one further step towards lower fuel consumption and, hence, a lower environmental impact of future transport aircraft.

Beneficial wake-capture effect for forward propulsion with a restrained wing-pitch motion of a butterfly

Unlike other insects, a butterfly uses a small amplitude of the wing-pitch motion for flight. From an analysis of the dynamics of real flying butterflies, we show that the restrained amplitude of the wing-pitch motion enhances the wake-capture effect so as to enhance forward propulsion. A numerical simulation refined with experimental data shows that, for a small amplitude of the wing-pitch motion, the shed vortex generated in the downstroke induces air in the wake region to flow towards the wings. This condition enables a butterfly to capture an induced flow and to acquire an additional forward propulsion, which accounts for more than 47% of the thrust generation. When the amplitude of the wing-pitch motion exceeds 45°, the flow induced by the shed vortex drifts away from the wings; it attenuates the wake-capture effect and causes the butterfly to lose a part of its forward propulsion. Our results provide one essential aerodynamic feature for a butterfly to adopt a small amplitude of the wing-pitch motion to enhance the wake-capture effect and forward propulsion. This work clarifies the variation of the flow field correlated with the wing-pitch motion, which is useful in the design of wing kinematics of a micro-aerial vehicle.