Elucidating Fluid-Structure Interactions: Studying the Propulsion of Flexible Foils

Natural flyers and swimmers can provide essential new knowledge for the design of more efficient propulsion systems for both aerial and aquatic vehicles. A key feature of many natural flyers, such as birds and insects, and swimmers, such as fish, is the use of flexible wings or fins to navigate their environment and the deformation of these flexible structures in response to fluid dynamics plays a critical role in enhancing propulsive efficiency and maneuverability. However, trying to understand this complex interplay between the flexible structures and the surrounding fluid environment can be challenging because the interaction involves complex dynamics where the properties of the fluid and the structural characteristics of the wing or fin are deeply intertwined. Moreover, this dynamic coupling can significantly affect propulsion performance, and several factors such as thrust generation, energy efficiency, and overall agility play a major role. Furthermore, the non-steady nature of the fluid environment and the non-linear responses of flexible structures under fluid forces add another layer of challenge. To address these challenges, theoretical modeling of such systems is often complicated and requires accurate simulation of the fluid-structure interactions and simplified models which can be beneficial because it is less complex, often need to approximate the behavior of these systems without losing the essence of the underlying physics.

To this end, new study published in Journal of Fluid Mechanics and led by Assistant Professor Feng Du and Professor Jianghao Wu from the Beihang University proposed a simplified analytical model based on elastokinetics and linear potential flow theory. Their study clarified the kinematics and propulsion performance of a flexible thin foil which serves as an idealized representation of a wing or fin and pitches in flow. The new model considers the dynamic forces involved, including the inertial forces of the foil and the non-steady fluid pressures, to determine the average deformation angle of the foil. Professors Feng Du and Jianghao Wu tested the predictions of their analytical model concerning the propulsion performance of a flexible thin foil, an idealized proxy for natural flexible fins and wings, when exposed to fluid dynamics. They investigated several prototypes of thin foils with differing levels of flexibility, which allowed them to simulate varying degrees of natural fin and wing flexibility. These foils were excited by pitching motion at the leading edge and then subjected to controlled flow conditions. With the adjustment in the speed of the flow and the frequency of the foil’s pitching motion, their modelling replicated the non-steady fluid environments these natural systems would encounter. The authors observed that foils with optimized flexibility and properly tuned pitching frequencies demonstrated enhanced propulsive efficiency and thrust generation compared to their rigid counterparts. Specifically, the analytical formulations showed that the resonance conditions where the natural frequency of the foil’s vibration matched the frequency of the pitching motion significantly amplified the propulsion performance. This result highlights the importance of the flow-structure interaction, where the right combination of material properties and motion frequency could exploit natural fluid dynamics to maximize propulsion efficiency. Moreover, the researchers showed that the phase angle between the deformation of the foil and its pitching motion critically influenced the propulsion efficiency. Optimal phase alignment, where the deformation of the foil was synchronized with the fluid forces acting upon it, led to reduced energy expenditure for a given amount of thrust. This optimal synchronization resulted in a reduction of the drag forces acting against the motion of the foil, thereby improving the overall efficiency.

In conclusion, the study findings of Professors Feng Du and Jianghao Wu has far-reaching significance and practical implications specially in bio-inspired engineering, robotics, and fluid dynamics. The development of a simplified analytical model that accurately predicts the propulsion performance of flexible thin foils in fluid environments, bridges a crucial gap in our understanding of fluid-structure interactions and can provide valuable knowledge for optimal design parameters for flexible propelling systems. This knowledge can be directly applied to the development of more efficient and adaptable underwater and aerial vehicles. These vehicles can mimic the natural efficiency of fish fins and bird wings, leading to improvements in energy efficiency, maneuverability, and speed. Moreover, the study can inform the design of bio-inspired robots used in various applications, including environmental monitoring, search and rescue operations, and autonomous exploration. Robots equipped with flexible propulsion systems can navigate complex fluid environments more effectively, performing tasks with greater efficiency and less energy consumption. The new model can be applied to improve the performance of marine and aeronautical vehicles and ships and submarines could benefit from flexible hull designs that reduce drag and enhance propulsion efficiency and also aircraft could incorporate flexible wing elements to improve aerodynamic performance. Indeed, the simplified analytical model can be considered a new useful tool for understanding the complex interactions between flexible structures and fluid flows.